Home

User's Guide of pHCali

1. Reference Data File with Potentials Part II kh1 13e tid Reference Data File with Potentials Part II kh1 13e tid Reference Data File with pH values kh1 13ph tid Configuration File phcali cfg The content of kh1 13e res file co The content of kh1 13e phv file co rresponding to Figures 2 7 2 8 rresponding to Figures 2 7 2 8 The content of kh1 13e phv file if J and Joy are also fitted The rows of kh1 13e2 tid file to be changed inexample2 The changed rows of kh1 13e2 ti The content of aspph e res file Partial content of aspbeta tid file d file in example 2 6 2 yn ee wY Seay 56 59 61 63 64 19 20 22 22 24 35 38 38 43 43 51 52 CHAPTER 1 INTRODUCTION The program PHCali has two objectives 1 Firstly it makes possible the accurate calibration of pH metric instruments which is essential particularly for the quantitative investigation of complicated equilibrium systems in solution The pH range to be calibrated can also be extended to the non Nernstian ranges 2 Secondly pHCali is able to determine protonation constants of weak acids even if the analytical concentration of the weak acid is not exactly known 1 1 Why pHCali is Useful The presently used pH metric calibration methods have several problems despite the fact that they are being used for more than 50 years 1 Each method applies some simplification
2. JOH arameter 6 8 9 94551E 02 0 c in mol dm3 for the base solution arameter 18 9 1 10366E 03 0 cC C032 in mol dm3 for the impuritites arameter 19 10 1 02000E 01 0 log beta_1 for C032 arameter 20 11 1 63000E 01 0 log beta_2 for C032 arameter 2 12 3 number of given formation constants lt 9 13 9 00000E 00 1 log beta_1 for the weak acid arameter 22 14 1 20000E 01 1 log beta_2 for the weak acid arameter 23 15 1 50000E 01 1 log beta_3 for the weak acid arameter 24 16 2 00000E 00 H A ratio in the weighted material or 0 for curve 1 17 2 50000E 01 0 VO in cm3 for curve 1 arameter 3 18 1 46000E 02 QO TCH O in mol dm3 for curve 1 arameter 32 19 1 02000E 02 QO TC A O in mol dm3 for curve 1 arameter 33 20 0 00000E 00 shift in the measured E pH for curve 1 arameter 34 21 0 00 2 111 1 0e 20 22 0 42 2 179 1 0e 00 23 9 60 11 116 1 0e 00 24 9 98 11 284 1 0e 00 25 0 00 2 123 1 0e 20 26 0 21 2 155 1 0e 20 27 9 81 11 260 1 0e 20 28 10 00 11 336 1 0e 20 29 0 00 2 115 1 0e 00 30 0 20 2 147 1 0e 00 31 9 81 11 211 1 0e 00 32 9 98 11 282 1 0e 00 to Listing 3 4 Lines 3 11 of this file correspond to the values determined during the calibration see lines 7 15 in listing 3 3 but they are now fixed Lines 12 15 of Listing 3 4 contain the initial values of the cumulative formation constants of the aspartate ion Line 16 shows that the material was weighted in form of H2A Line 18 shows the concentration of the strong acid
3. color of curve 1 Possible values and colors 5 1 color of curve 2 0 black 6 brown 12 light red 6 5 color of curve 3 1 blue 7 light gray 13 light magenta 7 2 color of curve 4 2 green 8 dark gray 14 yellow 8 3 color of curve 5 3 cyan 9 light blue 15 white 9 12 color of curve 6 4 red 10 light green 10 9 color of curve 7 5 magenta 11 light cyan 11 13 color of curve 8 0 15 may be reversed with the background color 12 10 color of curve 9 an RGB value should be given Q lt r g b lt 255 after 13 11 color of curve 10 a negative integer e g l rgb 14 21 symbol for the fitted data The possible symbols and their values 15 15 symbol for the skipped data are in the documentation 16 12 size of symbols for the lower left LL graph positive number 17 20 size of symbols for the lower right LR graph positive number 18 16 size of symbols for the upper left UL graph positive number 19 30 height of all titles and the labels of the LL graph positive number 20 25 height of labels for the LR and the UL graphs positive number 21 25 height of texts in the legend a positive number 22 1 thickness of initially calculated curves positive number 23 3 thickness of finally calculated curves positive number 24 1 thickness of connecting lines for the LR UL graphs positive number 25 16 length of major ticks positive number 26 8 length of minor ticks positive number 27 14 colo
4. 2 4 3 The Structure of the pH values File TASKNAME phv Getting Started through Examples 0 eee eee eee eee 3 1 3 2 3 3 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 Calibration in the Nernstian Range oasa aaa Calibration in Extended Measurement Range naana aaa Complete Evaluation of Equilibrium Measurements 3 3 1 Calibration vs cers hates Be ee Crna EE es He ee ees 3 3 2 Determination of Formation Constants 0 Choosing Standard Compound for the Calibration Indication of Experimental or Calculation Problems Extending of the pH Range to be Calibrated 00 0 O CONN 3 A Mathematical Description of Titration Curves 00206 67 A 1 The Equilibrium State at any Point of Titration 0 67 A 2 Calculation of Hydrogen Ion Concentration 00040 69 A 3 Calculation of a Point of the Titration Curve 04 70 A 3 1 Various Definitions of pH and Potential 70 A 3 2 Calculation of the Potential 0 0 004 70 A337 Calculation OR pH eg aa idle AVS wen Be are aera ee we Beker Sua a 71 AA Calculation of Parameter Values 0 0 2 0000 ee eee 72 Notations and Definitions 0 0 0 cee ewe eee eee eee ee ee ee 75 RefETEN COS eo canes Sees es es ke BS oa De et E A ee a Se ES 79 List of Tables 1 1 Program names
5. It can easily be proved that J a2 Jy and Jon 22 Jou The calculation of pH can be summarized briefly on the basis of equations A 6 and A 12 an arbitrary point of the calculated titration curve pH Vm can be determined using the function pH f parameters Vm where the parameters can be BA s By s Ky Vo Cay Cs Cp Ce la Mp Jt and ee A 4 Calculation of Parameter Values The accurate calibration of a pH metric instrument can be divided into two parts 1 At first the accurate values of the calibration parameters have to be determined and then 2 the p H Vm data can be calculated using the determined parameter values for those titration curves which belong to the equilibrium system to be investigated and not to the calibration These calculated points can serve as input data for equilibrium data evaluation programs e g 18 On the basis of the above mentioned calibration parameters any titration curve can be calculated The necessary parameters can be calculated by the minimization of the sum of squares functions defined by the p SBAB Kws Voy Cay Ce Cb Coy E me JH JOH We Ene Eek or A 13a k 1 p S ae BS Kw Vo Cas Cs Cb Coy la Mp H Pu gt a Wk age a pHex A 13b k 1 iS Ngee ihe equations In these equations p stands for the total number of titration points in all titration curves used for the calibration w is the weighting factor of the k measured point Em or pH a
6. than the experimental uncertainty The next step is the calibration of the instrument using pHCali and the first six titration curves This task requires an input file it is named aspph a tid in the present case created from the data of these curves The second section of this file see Subsection 2 2 1 contains the six curves in the order of their serial numbers and titration curves 7 9 are put into the third section of the aspph a tid file for the pH gt p H calculations By running the appropriate pHCali variant with the aspph a tid file the work window visible in Figure 3 6 appears on the screen The upper left and lower right graphs show that there are some bad points on the curves the 10 data before the last one in curve 4 the 7 data before the last one in curve 5 and the 6 data before the last one in curve 6 These points must be excluded but it cannot be done with the help of the operating panel since the erroneous data are not at the beginning or at the end of the curves The user must quit pHCali by pressing the save amp quit button and edit the file with an ASCII editor A relative weighting factor of 0 must be given to the points to be excluded The necessary changes detailed above has been already done in the aspph b tid file By running the program with this file the work window visible in Figure 3 7 appears The comparison of the three weak acid strong base curves suggests that the whole curve 6 should be ex
7. 02 2 48719E 02 10 2 7340E 00 2 3202 2 43600E 02 2 43780E 02 11 2 9280E 00 3 5023 1 74000E 02 1 74011E 02 12 2 9380E 00 4 1272 1 37200E 02 1 37204E 02 3 2 9480E 00 7 8959 8 47000E 01 8 47000E 01 14 2 9580E 00 9 1459 1 58300E 02 1 58300E 02 15 3 3130E 00 11 6713 3 07000E 02 3 07147E 02 16 3 40300E 00 11 7698 3 12800E 02 3 12986E 02 17 3 5160E 00 11 8649 3 18400E 02 3 18632E 02 18 3 6650E 00 11 9634 3 24200E 02 3 24491E 02 19 3 8520E 00 12 0585 3 29800E 02 3 30162E 02 20 4 09900E 00 12 1536 3 35400E 02 3 35854E 02 21 1 0428E 01 12 7430 3 70100E 02 3 71964E 02 22 1 0828E 01 12 7566 3 70900E 02 3 72827E 02 23 1 1228E 01 12 7667 3 71500E 02 3 73476E 02 24 1 1628E 01 12 7769 3 72100E 02 3 74128E 02 25 1 2028E 01 12 7871 3 72700E 02 3 74781E 02 of the p H for a titration point where the measured value is 316 9 mV then the expected value from the Nernst equation can be calculated from the 317 4 316 9 321 758 x 317 4 316 3 321 758 320 450 interpolation equation The solution of this equation is x 321 163 mV This is the potential corrected by interpolation that can be found in the fourth column of all phv files The plH values found in the second column of phv files are calculated from these values based on equation A 8 in case of potential measurement or based on equation A 11 if pH is measured The result of such calculations is shown in Listing 2 7 In practice the first approach has been u
8. 22 Windows 98SE or Linux with kernel 2 4 The files installed on the user s computer Executables phcalid exe DOS and Windows phcalic exe phcaliw exe Windows phcalit phcalit shared phcalix phcalix shared Linux Documentation OOreadme english text file change log english text file Documentation downloadable independently from InterNet pHCalieo pdf english online pHCaliep pdf english printable pHCaliho pdf hungarian online pHCalihp pdf hungarian printable Files for graphics setgrx bat video dat DOS phcali png Linux it can be used as icon Confgiuration file with default values phcali cfg Confgiuration file with default values but with RGB colors phcali rgb Example files phcali tid khi 13e tid kh1 13ph tid kh2 12e tid kh2 12ph tid aspph a tid aspph b tid aspph c tid aspph d tid aspph e tid aspbeta tid ox1 13e tid 0x1 13ph tid oyl1 13e tid oy1 13ph tid mal 13e tid mal 13ph tid 1 4 Installation 11 sul 13e tid sul 13ph tid khi13ej1 tid kh113ej2 tid 1 4 1 DOS Operating System The freely downloadable dphcali zip contains the executable program a part of the docu mentation and the example files The installation itself is very simple The user has to create a directory or folder in windows nomenclature and the contents of dphcali zip has to be extracted into that directory In this directory the program dphcali exe is ready to use If the user wants to access
9. 34 contains a logical value which determines whether the image files created by the program contain an information block in the upper right part or not If the value is TRUE then the information block is present in the other case not Default the information block exists Line 35 also contains a logical value which alters how the program runs If the value is TRUE then pressing the save amp quit button does not really terminate the program rather it returns to the parameter modifying window where the values and the fitting state of the parameters can be modified and a new calculation can be started Default there is no return Limitation This value does not affect the text mode variant of the program because there is no parameter modifying window Line 36 contains the name of the preferred text or ASCII editor between apostrophes If the path of the editor is not listed in the PATH environment variable then the full path must be entered between the apostrophes Default notepad exe under Windows and gvim under Linux This option is not functional under DOS Line 37 contains four integers to determine the position and size of the file chooser and pa rameter modifier windows All numbers must be given in pixels The first two numbers determine how far the upper left corner of the window has to be placed from the upper and left edges of the screen The third and fourth numbers determine the width and height of the wi
10. El meecne tune te deacoeuita be diendde page 70 The standard electrode potencial of the hy drogen electrode Be gelesen uae nee eee eee page 70 The calculated analogue of E EN ites Sheehan he eee ae page 71 The calculated analogue of Em emphasiz ing the fact that Nernst like equation was used for the calculation Bs Bes Sap tbe aah Metra E E E Corel eat page 70 The measured value of the potential dis played and or stored by the instrument Me echt 2 eee Asse a ov ete Roce ee aa page 70 The Faraday constant Voile hee Satan he arate atest orate eet etd ots E AA page 70 The mean activity coefficient FAP anaia ath hl eth that cachet Le page 67 The hydrogen ion HATOS Ian R goes page 67 The i times protonated form of the anion of the weak acid H C oh am i page 68 The hydrogen carbonate ion j 1 or the carbonic acid j 2 a Setetpee tt nutono Eeid eter i Rae page 71 Empirical constant Irving factor JA nra wit teens we nei A page 71 In case of potential measurement it is an 76 Notations and Definitions empirical constant for taking into account the deviation from the Nernstian equation in the acidic range pH lt 2 Jou page 71 In case of potential measurement it is an empirical constant for taking into account the deviation from the Nernstian equation in the basic range pH212 ihe esd Sti gid at E MUG ee ee eas enters page 72 In case of pH measurement it is
11. FORTRAN 77 books e g 12 13 For the titration data the program supposes that the volumes are given in cm the potentials are given in mV the pH values are given in dimensionless pH units and the concentrations are given in mol dm If other units are used then the program will still calculate correctly but the labels on the figures in the text files and on the screen will be incorrect An input file consists of 3 sections of which the first is compulsory must not be omitted and the second or the third is optional one of them may be omitted e The first section see Listing 2 1 contains the parameters that affect all titration curves e The second section see Listing 2 2 contains the titration curves and those parameters that affect only the actual titration curve e The third section see Listing 2 3 contains the Vin Em data pairs for which the p H values i e the negative logarithm of H should be calculated Usually this section contains the titration curves of the system to be studied after the calibration If pH rather than potential has been measured then the above statements are completely valid except that potential values should be replaced with pH values as it is shown in Listing 2 4 This listing contains Listings 2 1 2 3 together but with pH values instead of potentials In the first section see Listing 2 1 in case of the reference example and Listing 2 4 if pH was measured the following data should be gi
12. In this file the following changes have to be made 1 The parameters fitted in the previous run must be fixed now on by changing the 1 s in the 14 character of the appropriate lines to 0 s 2 The weighting factors having 1 0E 20 value should be changed to 1 0E 09 3 The previously fixed values of Ju s Jon must be fitted so the 0 s in the 14 character position of lines 6 7 should be changed to 1 s The affected lines are shown in Listing 3 1 before and in Listing 3 2 after the above detailed modifications e After starting the program with either the PROGNAME kh1 13e2 tid command or by clicking on the appropriate icon and choosing the kh1 13e2 tid file it calculates the values of J and Jon along with the other parameters kept fixed The image file of the final work window of the fitting is shown in Figure 3 5 The comparison of Figures 3 4 and 3 5 may lead to the opinion that the second method is worse than the first one The second one does not enhance the fitting in the basic range moreover it increases the deviation in the acidic range in a small extent Figure 2 7 can ensure however that the values of the usual calibration parameters describing the 44 Getting Started through Examples Results calculated by pHCali v1 30a 20061226 at Tue Dec 26 23 49 23 2006 TASKNAME kh1 13e2 Uncertainties V cm 2 0 10 or 3 01004 Vm E 0 10 mV E 381 50 mV me 59 127 JiJoy 50 7 22 2 mV M pKy 13 796 cp 1
13. added independently into the solution to be titrated The three repeated curves are given for the program as a single curve It can be seen from Table 3 3 that the 8 curve is different from the other two the 7 and the 9 ones therefore 1 0x10 relative weighting factor should be given for the titration points of the 8 curve It is shown in lines 71 130 of the aspbeta tid file The last fact to be mentioned is that the first point of curve 7 is treated to be an erroneous one as line 21 shows this fact Running the program with the aspbeta tid file leads to the work window seen in Figure 3 11 The differences in the lower right and upper left parts clearly indicate that the fitting is not acceptable in the basic range The same can be read from the titration curves in the lower left part It is visible that the equivalence point is different in a small extent from the expected value which can be calculated precisely in this specific example If the concentration of the total anion is also given as a fitted parameter as seen in line 19 of the aspbeta tid file which means that the 0 is to be replaced with a 1 in the 14 character position of the line and the fitting is repeated the resulted work window is the one seen in Figure 3 12 In this window systematic deviation significantly exceeding the experimental uncertainty cannot be found which while the initial concentration of the anion has been increased from 0 0102 M to 0 01086 M In the sp
14. adjusted through the command line in terpreted by a file manager e g Norton Commander FAR Manager etc Only the command line of the operating system can be used for this purpose 6More information can be found through the http grx gnu de web page 12 Introduction e The icon can be defined through the Shortcut option of the New menu If the user wants to register the phcalic exe or phcaliw exe program to the tid exten sion i e file type then it can be done as follows e The Windows Explorer should be started In the View or Tools menu the Folder Options has to be opened e On the File Types tab there is a press button called New or New type After clicking on the button the specific tid extension is to be registered the program is to be linked and optionally the icon is to be defined In older Windows versions the Action must also be declared to be open 1 4 3 Linux Operating System It is important to note before all that the Linux variants of the program are in experi mental stage yet They have been used successfully with several window managers KDE GNOME XCFE Window Maker IceWM and fvwm_2 under two distributions Debian Sarge v3 1r5 with 2 4 27 3 i386 kernel XFree86 s X11 system and SuSE v10 0 with 2 6 13 i686 ker nel X Org s X11 system The successful running is not guaranteed under other systems e g the program works only with mouse under Debian Etch with any arc
15. aia ran ee Uncertainties V cm 2 0 10 or 3 0 10 V E 0 10 mV E i j z a i E 381 50 mV me 59 127 JyJop 0 0 0 0 mV M gt 0 00 1 A a 2 pKy 13 796 c 1 999210 M cco 2 1 49510 M SES ig Br 4 649 Ig B 7 316 b q i Le O PEPEE AIEE ye Nee herana omitted data o 3007 gt fitted data initial curve s 2 x fitted curve s Ph es ore manera fetes a pean LEIERS tine Bhs 4 100 H Mag fl feeeee ees es wituney EEEE oceemey ee 6 04 EENEI negra wee anne pte kee me OE PETA E a ery 7 wW HOO EE Cary AA tiie pegee Lighilans aia OTTES a 8 200 E eee eee eee Sues ners E sean aan ase bes 800 ET Balaren pop hina beteeabee yeas bee V cm Figure 2 8 The image file of the final fitting of the reference example if potential is fitted 2 4 Output Files In this section the interpretation of the result files having res crv and phv extensions can be found The structure of the TASKNAME cin file has already been discussed in Subsection 2 2 1 The difference between the TASKNAME tid and cin files is that the first one contains the initial values of the weighting factors and parameters while the second one contains the final values of them The other text and image files have already been discussed in Section 2 1 2 4 1 The Structure of the Result File TASKNAME res The contents of TASKNAME res is shown in Li
16. board i e letters numbers and punctua tion marks Text files are generally used for storing numbers or simple text They can be changed by editors e g edit com under DOS Notepad under Windows and gvim under Linux Word processors like Word should not be used to change them text mode page 8 This variant of pHCali can be used on character based screen so it can be started from pure DOS window mode page 8 This variant of pHCali can be started on a graphical user interface i e Windows or X Window work window page 29 A window for adjusting the state of mea sured data omitted fitted and carrying out the calculations REFERENCES 1 Gran G Determination of the Equivalence Point in Potentiometric Titrations Analyst 77 661 1952 2 Rosotti F J C and Rosotti H S The determination of stability constants McGraw Hill Book Company Inc 1961 3 Biedermann G and Sill n L G Arkiv Kemi 5 425 1953 4 Rosotti F J C and Rosotti H S Equilibrium Studies of Polyanions I Isopolyvanadates in Acid Media Acta Chem Scand 10 957 1956 5 de Levie R Principles of Quantitative chemical Analysis McGraw Hill Companies Inc 1998 6 Ingman F Still E Graphic method for the determination of titration end points Talanta 13 1431 1966 7 Johansson A Automatic titration by stepwise addition of equal volumes of titrant Analyst 95 535 1970 8 Midgley D McCa
17. button and the data file has to be modified with a text editor The changes detailed above have already been made in aspph c tid file Running the program with this file results in the work window visible in Figure 3 8 The numbers in the upper right part of the window indicate that curves 1 and 6 are completely excluded The next step of the evaluation is to exclude points outside the Nernstian range As the lower right part of Figure 3 8 shows there are systematic deviations between the measured and calculated data at both ends of the strong acid strong base curves The same is valid for the basic ends of the weak acid strong base titration curves Using the operating panel the erroneous points can be excluded in multiple steps and refitting The remaining data do not show significant systematic deviation between the experimental and calculated points as it is shown in Figure 3 9 After terminating the program with the save amp quit button the current state is stored in the aspph c cin file Renaming it to aspph d tid and running pHCali with this file the work window shows this state initially The goal in the previous phase of the evaluation was to separate and exclude questionable experimental data Till this point it was practical to handle the curves separately because the points to be omitted were easier to find The fitting of the remaining points gives those parameters which are required for further equilibrium calculations Fo
18. cm 2 0 10 or 3 0 10 V _ E 0 10 mV E 380 22 mV me 58 881 JyJop 37 4 20 9 mV M pky 13 825 cy 2 000210 M Cog 2 1 488 10 M Ig BA 4 647 lg B 7 300 V cm E E mV Figure 3 4 The image file belonging to the final fit in the second example if JH and Jon are also fitted together with the usual parameters using the operating panel and only the usual calibration parameters listed in the previ ous example should be determined by fitting at first The technical details of this fitting are given in Chapter 2 Figure 2 5 shows the initial work window of this example while the final work window achievable by using the operation panel is shown in Figure 2 7 3 2 Calibration in Extended Measurement Range 43 Listing 3 1 The rows of kh1 13e2 tid file to be changed in examle 2 1 1 37955E 01 1 pkw arameter 1 2 3 81500E 02 1 EO arameter 2 3 5 91267E 01 1 m 1n 10 RT zF arameter 3 4 0 00000E 00 JH arameter 4 5 0 00000E 00 JOH arameter 6 6 1 99925E 01 1 cO in mol dm3 for the base solution arameter 18 7 1 49459E 03 1 cC C0O32 in mol dm3 for the impuritites arameter 19 8 4 64884E 00 1 log beta_1 for the weak acid arameter 22 9 7 31592E 00 1 log beta_2 for the weak acid arameter 23 10 9 87670E 02 1 TCH O in mol dm3 for curve 1 arameter 32 11 0 00000E 00 3 17400E 02 1 0E 20 the next 12 lines are also to be changed TZ ia 13 2 62500E 00 2 54700
19. contains the mathematical description of titration curves in a fully detailed form Every chapter of this manual uses the nomenclature defined in the appendix Among others the various definitions of the pH and the potential are of special importance These are discussed in Subsection A 3 1 This section is worth to read even for those who are already completely familiar with the contents of the Appendix Beside the Appendix the short descriptions can also be found in the Notations and definitions part see page 75 This manual contains 3 main chapters e Chapter 2 contains the detailed description of pHCali In fact this chapter can be used as a reference handbook It is suggested only to run through this chapter while getting acquainted with the program The careful reading of this chapter is advised only if the user intends to use the program permanently An exception is Section 2 1 which gives an overview about pHCali so this should be read at the very beginning Chapter 3 is for getting familiar with the program This chapter demonstrates every capability of the program through examples The examples are not focused on the details rather than to help the user to learn the basic operation with the program The examples adequately refer to necessary parts of Chapter 2 where more detailed information is to be found The study of Example 3 can especially be useful because it describes a complete evaluation of an equilibrium investigation wit
20. equivalence point see Figure 3 6 4 5 Question of the Quantitative Determination of the Total Carbonate Concentration To determine the carbonate content of the titrant base is a very difficult task form the experi mental aspect The equations derived in the appendix suspect that the actual total carbonate concentration can always be calculated using the volume ratios see equation A 3c But this is not true if the studied solution is stirred In practice the stirring is carried out in two ways 4 5 Determination of the Total Carbonate Concentration 59 Em mV E 6 035 cm 0 012 M HCI N E 6 035 cm 0 006 M CH COOH Vm cm 0 025 M KOH 0 00125 M KzCOs _ strirring with magnetic bar under Ar atmosphere Ar bubbling through the solution Vin cm Figure 4 2 Titration of hydrochloride and malonic acid solutions with KOH contaminated by 5 carbonate 1 An inert gas is led into the titrated solution In the acidic range the gas purges the carbonate as carbon dioxide from the solution In basic medium it does not happen 2 An inert gas is led above the solution and the stirring is done for example with a magnetic stirrer In this case the loss of CO2 is much less but it cannot be completely stopped since CO has relatively poor solubility in water These stirring methods lead to different titration curves at higher carbonate concentra tions as it is illustrated in Figure 4 2 In case of bu
21. fittable parameter e In case of strong acid strong base titration this line gives the total concentration of the hydrogen ion T4 in the solution e In case of weak acid strong base titration this line gives how much strong acid was additionally added into the solution Since line 18 gives the value of Ta then Ty datum in line 17 datum in line 15 x datum in line 18 This method of calculating T becomes important when the exact value of Ta is not known so it has to be fitted as well The method used in this program makes it possible to fit the weak acid content and the acidic contamination of the weighted material independently Line 18 also determines a parameter that can be fitted so it contains a real and an integer In case of strong acid strong base titration both values are zero In case of weak acid strong base titration the real number is the total concentration of the anion of weak acid Ta in the titrated solution If the calculation is for a calibration then the value of the integer must be zero so the parameter must be fixed Line 19 contains a shift parameter providing a somewhat dangerous correction method if the potential or pH values of the actual titration curve are accidentally shifted compared to the other curves This problem may occur if the pH meter was calibrated by one buffer before each titration and this calibration was not successful The value of the parameter in line 1
22. necessary for calculating the cumulative formation constants since pHCali can determine them The great advantage of using the program is the ability of fitting the initial concentrations too which can be important if the material to be investigated is hard to weight precisely For determining the cumulative formation constants a tid file has to be created which is similar to that of used during the calibration The only difference is that the third section of the file see Subsection 2 2 1 has no meaning and therefore should be omitted The data file to be created contains the values of the parameters determined during the calibration so these parameters must be fixed The only parameters to be fitted are the cumulative forma tion constants of the investigated material The initial values of the cumulative formation constants of the material should be given in the place of that of the calibration material The second section of the tid file contains the titration curves the same way as for calibration The necessary file for the actual example is supplied in the aspbeta tid file and corresponds 52 Getting Started through Examples Listing 3 4 Partial content of aspbeta tid file 1 4 000E 03 uncertainty of Em or pHm 2 1 0E 02 1 0E 03 uncertainty of V 3 1 37854E 01 0 pkw arameter 1 4 1 49813E 01 0 Id arameter 2 5 9 90078E 01 0 m 1 arameter 3 6 0 00000E 00 JH p arameter 4 7 0 00000E 00
23. order therefore even an irrealistic change in the calculated volume and or pH is not able to influence the average deviation In such case the most expedient solution is to increase the value of the weighting factor of the point in question or if the specific point is not necessary it should completely be removed The latter solution technically means that a weighting factor of 0 0 should be ordered to the point 4 2 Importance of the Constant lonic Strength It is a common rule if the equilibrium is studied in solutions that the ionic strength in the titrated solution must be constant This rule cannot be fulfilled with mathematical strictness because the reactions change the ionic strength themselves But using an appropriate salt to set the ionic strength in both the titrant and the titrated solutions the change of the ionic strength can be kept to be constant within 4 5 error It is practically enough to avoid varying values for the cumulative formation constants during the measurement This practice also helps to keep the additivity of volumes to be valid If the density and the viscosity of both the titrant and the titrated solution are determined by the same ionic strength setting salt the problem of dilatation or contraction can safely be neglected The practice of pH metry is often in direct contradiction to these considerations Titration of very dilute solutions with very concentrated bases is a commonly used technique In such
24. points then all of them will be included again The string E1 or alternatively E 1 in text mode excludes one point from the end of the curve after pressing the Enter key The characters S and E stand for the words Start and End If the user wants to increase or decrease the number of points only by one then the number can be omitted from the string e The functions of the other buttons can be accessed by pressing the uppercase letter indicated 3These points and the vertical line are not drawn in the DOS version since the mouse cannot be used 2 3 Executing pHCali 33 CSE Ee icon a A DRS Wine pkw 13 796 Eps Tiff m 59 12668 Paf PNg Fea ppm E eve Eme edeuate vava Ler fitted data gt initial curve s fitted curve s MMMM curve 1 200 3 e on ae ranan bore es ane a i 100 E NG E ETE aasa AENEA ee Pecceie E mV 100 l ere ey eee ESETE KEARN ORA ied Wa ae et Hela ass ae 200 H PEE E EE RN Deyssi ro ee fondekdean s300 bie cs ctcce eer ee SEPTA Enya Readme reneneas i ve o 2 4 V cm5 Es E a mV Figure 2 7 The final work window of the reference example if potential is fitted on the appropriate button In text mode variants of the program the Enter should also be pressed The Enter has to be pressed twice to terminate the program after entering the Q letter of the save amp Quit button In
25. stability constant of a species can only be determined quantitatively if the concentration of the species is at least 20 of the total anion concentration in one or more points of the titration From this point of view the KH phtalate is not a suitable calibration compound The H2A form is present in 8 or less which is highly disturbing but this value is too low for precise determination of B This is one reason why the success of the fitting is so sensitive to the initial concentration of the strong base if the k1 13e tid file is used see the appropriate part of Section 4 1 By running the supplied data files the user can try that the sensitiveness is not experienced that much using the other calibration materials The importance of the fifth and sixth aspects is that the smaller the overlap of the protona tion processes the smaller the correlation between the corresponding cumulative stability constants is Experienced users know that the reason of the 8 is that the weighting did not happen in the form of H2A Phtalic acid is poorly soluble in water precluding it as a calibration material 62 Practical Guide It can be stated on the basis of the table and the figure that malonic acid seems to be a more suitable calibration compound if either the sum of the scores is viewed or by ranking the compounds according to the order of their first non maximal score the later a compound gets non maximal score for an aspect the better po
26. the aspph e tid file the work window visible in Fig ure 3 10 appears This figure illustrates the final results of the calibration After pressing the save amp quit button the final results are stored in the result files created by the program Two files can always have importance for the user e The aspph e phv file contains the Vm p H values calculated from the original aspartic acid titration curves These data can be the starting data set for further equilibrium calculations for various programs e g 18 The structure of the file is detailed in Subsection 2 4 3 e The aspph e res file contains the final results of the calibration which is also shown in Listing 3 3 The contents of the res files described in full detail in Subsection 2 4 1 The calibration is completed by the evaluations done so far Comparing the method of the program to other usual calibration methods the following advantages of pHCali can be mentioned e All titration curves can be handled simultaneously e Despite the fact that there are no any neglection during the evaluations the cumulative formation constant s of the calibration material is are not needed to be known The se value s can be determined during the calculations e g lines 16 17 in Listing 3 3 e The carbonate content of the titrant base can be determined and it can be taken into account during further evaluations It is not available with the conventional calibration procedures used so
27. the program from other directories then either 1 the installation directory should be inserted into the PATH environment variable or 2 the program name has to be called together with its path e g C PHCALI PHCALID EXE In the latter case the configuration file see Subsection 2 2 2 must be copied into the specific directory if the user wants to use it there By default the graphical engine of pHCali does not utilize the capabilities of the com puter s video cards thus the graphics is slow and the resolution is low The GRX20DRV environment variable should be set to get fast and high resolution for the figures It can be done for example with the SETGRX BAT by running this batch file from the command line This file contains a command SET GRX20DRV lt driver gt gw lt width gt gh lt height gt nc lt colors gt where the value of the video card driver lt driver gt can be stdvga stdega et4000 c15426 mach64 ati28800 s3 VESA or memory the horizontal resolution lt width gt can be e g 640 800 1024 the vertical resolution lt height gt can be e g 480 600 768 and the number of colors lt colors gt can be 2 16 256 64K or 16M It is important to note that pHCali uses only 16 colors but lower color depths are not always supported by present video cards so at least the 64K value should be set in these cases 1 4 2 Windows 95 98 Millenium 2000 XP and 2003 Operating Systems The installation proce
28. the reference example the main objective is to omit the points from the non Nernstian area and get the calibration data of the used pH metric instrument By using the operation panel with keyboard the final result can be achieved step by step if the S10 Enter C E20 Enter 2 Enter E20 Enter C E5 Enter 1 Enter E5 Enter c Enter S4 Enter C4 2 Enter E Enter C commands are entered Using the mouse the same steps should be carried out in order to achieve the work window displayed in Figure 2 7 74 The savable image file corresponding to this work window is shown in Figure 2 8 Enter keys inside parenthesis can only be given in text mode Under Windows operating systems and in the console or window mode the focus is not automatically set back to the work window if the user switches between the windows of the running applications After returning to the work window the user should left click on the work window and should press the Enter key to give the focus back on the work window of pHCali In many cases the same must be done if the mouse and keyboard are used in combination 4In the reference example the points to be omitted are denoted in the kh1 13e tid file For them the relative weighting factor is given as 1 0e 00 instead of the usual 1 0e 00 34 Reference Guide Results calculated by pHCali v1 30a 20061226 at Tue Dec 26 22 54 54 2006 TASKNAME kh1 13e ma Ema Tae ey
29. under different operating systems 8 2 1 Examples for the interpretation of lines containing input data 18 3 1 Weak acid strong base titration data in example 3 45 3 2 Strong acid strong base titration data in the third example 45 3 3 Titration data in the third example for determining the formation contants of aspartate 10n ans maners anio Bm Ae ee ern a a er ie des Gh ak der ship Hales irah th Med 46 4 1 Comparison of the possible standard compounds for the calibration 60 List of Figures 2 1 2 2 2 3 2 4 2 9 2 6 2 7 2 8 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 Input and output files of the program aaaea ee 16 Available symbols base colors and line widths oaoa aaa 23 The file chooser window in case of the reference example 28 The parameter modifier window in case of the reference example 29 The initial work window of the reference example if potential is fitted 30 The initial work window of the reference example if pH is fitted 30 The final work window of the reference example if potential is fitted 33 The image file of the final fitting of the reference example if potential is fitted 34 The initial work window of the kh2 12e tid file if potential is fitted 40 The final work window of the kh2 12e tid file if potential is fitted 40 The work window of the kh2 12ph tid f
30. which illustrates the issue of an obviously failed calculation If the fitting described above is carried out in two steps then good results can be obtained e Not only the values of the relative weighting factors have to be changed in the k tid file The status of the parameters E and m should also be changed from fitted 0 to fixed 1 by changing the characters in the 14 character position in lines 4 and 5 After this modification the program has to be run with the k tid file e The k cin file created at the end of the running has to be renamed to k1 tid In this file the status of two parameters E and m have to be changed back from fixed to fitted by replacing the 0 s with 1 s Now the execution of the program with the k1 tid file leads to the work window displaying the good results The good results can be obtained in one step also if the user does not change the status of the above mentioned parameters rather s he gives better initial value for the concentration of the strong base In this case beside the weighting factors to be modified the initial values of the base concentration should also be changed to 2 00000E 01 from 0 19 M to 0 2 M in the eighth line of the k tid file The calculation with the modified file instantly supplies the correct result so the two step procedure is not necessary This shows that 5 difference between the initial value and the real one may lead to a poor estimation This example is
31. 0 or precisely a number between 9 91 and 999 0 means that the program termi nates to read the input file regardless of anything that is beyond the actual line 1000 0 or precisely a number between 999 1 and 10000 0 means that the program finishes the reading of titration curves and it supposes that the remaining part of the file contains only such titration points for which the Em pHm gt p H calculation should be carried out based on the result of the calibration Lines 90 171 should be interpreted the same way as the previous ones because they de scribe the weak acid strong base titration The remaining lines of the reference data file contain the third part see Listing 2 3 or the appropriate lines of Listing 2 4 in case of pH measurement In these lines the titration data 14These expressions require the really precise values from the first two lines of the input file 22 Reference Guide Listing 2 3 Reference Data File with Potentials Part III kh1 13e tid 1 0 0000 317 4 2 0 1000 316 3 3 0 2500 314 6 the next 64 lines are omitted from the manual 4 11 6280 372 1 5 12 0280 372 7 Listing 2 4 Reference Data File with pH values kh1 13ph tid 1 0 00169 uncertainty of pHm curve 1 HCl 2 0 002 0 0003 uncertainty of Vm curve 2 KH phthalate 3 1 38000E 01 1 pkw arameter 1 4 0 00000E 00 1 Id arameter 2 5 1 00000E 00 1 mc 1 arameter 3 6 0 00000E 00 JH p arameter 4 7 0
32. 00 1 094 38 0 1000 1 113 39 0 2500 1 142 the next 64 lines are omitted from the manual 40 11 6280 12 749 41 12 0280 12 758 are entered the measured volume and the measured potential or pH in each line It is important to note that the values of Vm are not used during the Em pHm p H calculations They are present for the easier identification of the data only 2 2 2 The Configuration File phcali cfg The properties of pHCali can be adjusted by changing the contents of the phcali cfg file The presence of the configuration file is not required If it is not present the program uses the default settings It is a text file with a simple structure every line in it determines a property and every line except five ones contain one data The data can be integer or real numbers boolean values TRUE or FALSE constants or strings The integers generally refer to the symbols and lines used in the figures Their more important values are shown in Figure 2 2 The data 15For the sake of an example the strong acid strong base titration data are repeated in the third part of the reference data file In practice however the titration curves of the equilibrium system to be investigated after the calibration should be included in the third part 2 2 Input Files 23 Available symbols and their codes fjo Om Ae 8 KM O88 Ve Xm Xea Pde Bao Xan Haz a z Naas Cas Wo a7 A0 O09 Yeo Qe Ce ps Base colors and their
33. 00000E 00 JOH p arameter 6 8 1 90000E 01 1 cO in mol dm3 for the base solution arameter 18 9 1 00000E 03 1 c CO32 in mol dm3 for the impuritites arameter 19 10 1 02000E 01 0 log beta_1 for C032 arameter 20 11 1 63000E 01 0 log beta_2 for C032 arameter 21 12 2 number of given formation constants lt 9 13 4 60000E 00 1 log beta_1 for the weak acid arameter 22 14 7 30000E 00 1 log beta_2 for the weak acid arameter 23 15 0 00000E 00 H A ratio in the weighted material or 9 for curve 1 16 6 03500E 00 VO in cm3 for curve 1 arameter 31 17 1 00000E 01 1 TCH O in mol dm3 for curve 1 arameter 32 18 0 00000E 00 TC ADO in mol dm3 for curve 1 arameter 33 19 0 00000E 00 shift in the measured E pH for curve 1 arameter 34 20 0 0000 1 094 1 0e 00 21 0 1000 1 113 1 0e 00 22 0 2500 1 142 1 0e 00 the next 64 lines are omitted from the manual 23 11 6280 12 749 1 0e 00 24 12 0280 12 758 1 0e 00 25 1 00 26 1 00000E 00 H A ratio in the weighted material or 9 for curve 2 27 6 03500E 00 VO in cm3 for curve 2 parameter 35 28 0 00000E 00 0 TCH 9 in mol dm3 for curve 2 parameter 36 29 1 Q00600E 01 QO TC A O in mol dm3 for curve 2 parameter 37 30 0 00000E 00 shift in the measured E pH for curve 2 parameter 38 31 0 0000 3 672 1 0e 00 32 0 1000 3 755 1 0e 00 the next 71 lines are omitted from the manual 33 11 5790 12 751 1 0e 00 34 11 9790 12 763 1 0e 00 35 12 3790 12 769 1 0e 00 36 1000 0 37 0 00
34. 1 287 2 5 94 11 270 256 7 11 231 254 3 2 00 2 086 286 8 5 92 11 267 256 4 2 20 2 115 285 3 6 50 11 460 268 1 11 290 257 7 2 20 2 120 284 6 6 51 11 480 269 1 2 40 2 151 283 0 6 62 11 492 269 8 11 481 269 3 2 40 2 157 282 7 6 70 11 530 272 0 2 61 2 191 280 6 6 82 11 536 272 5 11 566 274 2 2 61 2 196 280 2 7 00 11 598 276 1 2 80 2 232 278 2 7 00 11 575 274 6 11 606 276 5 2 81 2 237 277 8 7 20 11 637 278 3 3 00 2 279 275 4 7 21 11 616 277 1 11 644 278 8 3 00 2 282 275 2 7 40 11 671 280 3 3 21 2 331 272 4 7 41 11 652 279 2 11 681 281 1 3 20 2 330 272 4 7 60 11 701 282 3 3 42 2 391 268 7 7 60 11 682 281 0 11 711 282 7 3 40 2 386 268 7 7 80 11 728 283 8 3 63 2 460 264 7 7 80 11 712 282 7 11 737 284 2 3 60 2 442 265 2 8 00 11 755 285 4 3 80 2 526 260 8 8 00 11 738 284 4 11 765 286 0 3 80 2 520 260 9 8 41 11 806 288 4 4 01 2 615 255 5 8 41 11 787 287 2 11 809 288 6 4 00 2 604 256 0 8 80 11 843 290 7 4 20 2 728 248 7 8 80 11 829 289 7 11 849 291 0 4 24 2 734 248 3 9 24 11 885 293 1 4 40 2 870 240 5 9 22 11 867 291 9 11 885 293 3 4 40 2 847 241 7 9 63 11 915 295 1 4 60 3 079 228 0 9 60 11 898 293 9 11 921 295 3 4 60 3 035 230 5 9 98 11 941 296 6 4 81 3 536 200 9 10 00 11 932 295 8 11 951 297 1 4 81 3 408 208 4 0 004 pH unit uncertainty The titrations were carried out with a conventional calibrated 10 cm burette in a cell thermostatted to 25 C Th
35. 14 25 omitted data from start end 5 2 50 fitted data p H 3 7 11 6 O 26 omitted data from start end 6 Estimated parameter values 7 Name Final value Std deviation Initial value of the last calculation 8 pKw 1 379553E 01 2 249750E 02 1 414066E 01 9 EQ 3 814998E 02 3 293109E 01 3 756276E 02 10 1n1ORTZF 5 912668E 01 1 308592E 01 5 697842E 01 11 JH 0 000000E 00 fixed Fitting is not recommended 12 JOH 0 000000E 00 fixed Fitting is not recommended 13 C_base 1 999245E 01 5 755079E 05 2 000092E 01 14 C_C03 1 494589E 03 5 548072E 05 1 799731E 03 15 1gB1_CO3 1 020000E 01 fixed 16 lgB2_C03 1 630000E 01 fixed 17 1gB1_A 4 648838E 00 7 687519E 03 4 727018E 00 18 1lgB2_A 7 315919E 00 1 141487E 02 7 358921E 00 19 VO_c1 6 035000E 00 fixed 20 THO_cl 9 876698E 02 2 553896E 05 9 906755E 02 THO_base 0 000000E 00 21 TAO_c1 0 Q000000E 00 fixed 22 Shft_cl 0 000000E 00 fixed 23 VO_c2 6 035000E 00 fixed 24 THO_c2 0 000000E 00 fixed CTHO_base 1 006000E 01 25 TAO_c2 1 006000E 01 fixed 26 Shft_c2 0 900000E 00 fixed 27 Experimental uncertainties 28 2 000E 03 or 3 000E 04 Vm cm3 for the volume whichever is larger 29 1 000E 01 mV for E 30 Goodness of Fit statistics 31 Number of iterations 13 32 Number of function evaluations 66 33 Number of Jacobian evaluations 15 34 Rank deficiency 0 35 Average of weighted deviation of volume 3 386902E 03 36 only for curve 1 3 313719E 03 37 only for curve 2 3 427
36. 14600E 02 3 18440E 02 5 4 7500E 01 1 1788 3 11800E 02 3 15289E 02 6 2 4530E 00 1 9534 2 66000E 02 2 66444E 02 7 2 5510E 00 2 0532 2 60100E 02 2 60375E 02 8 2 6250E 00 2 1445 2 54700E 02 2 54837E 02 9 2 6900E 00 2 2494 2 48500E 02 2 48599E 02 10 2 7340E 00 2 3323 2 43600E 02 2 43640E 02 11 2 9280E 00 3 5094 1 74000E 02 1 73995E 02 12 2 9380E 00 4 1318 1 37200E 02 1 37199E 02 13 2 9480E 00 7 8848 8 47000E 01 8 46994E 01 14 2 9580E 00 9 1295 1 58300E 02 1 58299E 02 15 3 3130E 00 11 6445 3 07000E 02 3 07053E 02 16 3 4030E 00 11 7426 3 12800E 02 3 12914E 02 17 3 5160E 00 11 8373 3 18400E 02 3 18644E 02 18 3 6650E 00 11 9354 3 24200E 02 3 24570E 02 19 3 8520E 00 12 0301 3 29800E 02 3 30315E 02 20 4 09900E 00 12 1248 3 35400E 02 3 36119E 02 21 1 0428E 01 12 7117 3 70100E 02 3 72467E 02 22 1 0828E 01 12 7252 3 70900E 02 3 73195E 02 23 1 1228E 01 12 7354 3 71500E 02 3 73870E 02 24 1 1628E 01 12 7455 3 72100E 02 3 74498E 02 25 1 2028E 01 12 7557 3 72700E 02 3 75085E 02 Listing 2 8 The content of kh1 13e phv file if J and Joy are also fitted 1 Vm p H Em Ec Nernstian from JH amp JOH 2 0 0000E 00 1 0668 3 17400E 02 3 21106E 02 3 1 0000E 01 1 0855 3 16300E 02 3 19824E 02 4 2 5000E 01 1 1144 3 14600E 02 3 17864E 02 5 4 7500E 01 1 1619 3 11800E 02 3 14681E 02 6 2 4530E 00 1 9398 2 66000E 02 2 66436E 02 7 2 5510E 00 2 0400 2 60100E 02 2 60446E 02 8 2 6250E 00 2 1317 2 54700E 02 2 54980E 02 9 2 6900E 00 2 2370 2 48500E
37. 200 H aiei Paced EE ise ierdesta Leben e ene esiisa 5 re PETTEN OO it E ARETE tate ee fu bswhdabiSe 1 ee Seer E EE Gams 300 Heese eed pereadeste es ANENE ARANETA ira L L i 1 i L 12 i 10 2 4 6 8 10 0 2 0 1 0 0 0 1 0 2 V em Eo Em mV Figure 3 1 The initial work window of the kh2 12e tid file if potential is fitted Number of skipped data Ski cS E S Ec fess ct EE pKw 13 820 m 59 0424 0 010 C005 E EREE cone E ces 3 Vo Vm cm 0 000 0 005 O omitted data fitted data initial curve s BOG E EOE ra eee sai aati 2 TT fitted curve s E curve 1 100 E REEE UNA Ba ee eee PESEE be E S Obs es erences TE T E E E S E Ka W 100 H Ries et eat fore T i see tint sad EN Eees ime aii pas 200 Heese reese ee eee pepak baissan a 300 K i PROSTORNA iaz TEITE eer hag i fi i i i f i 0 2 4 6 8 10 02 01 0 0 0 1 0 2 V cm Es Em mV Figure 3 2 The final work window of the kh2 12e tid file if potential is fitted while the usage of the operating panel is described in Subsubsections 2 3 4 1 and 2 3 4 2 Figure 3 1 shows the work window In the lower right figure of the work window the differences between the measured and calculated potentials are displayed These values are rather small considering that the 3 2 Calibration in Extended Measurement Range 41 experimental uncertainty of t
38. 21 4 6 81 11 557 274 3 3 00 5 017 112 7 11 797 288 2 3 05 5 025 112 2 7 43 11 634 279 1 2 79 4 936 117 5 7 20 11 635 279 0 3 22 5 098 107 9 11 820 289 8 3 22 5 085 108 8 7 80 11 671 282 5 3 00 5 012 113 1 7 63 11 707 283 1 3 48 5 198 101 9 11 848 291 6 3 42 5 163 104 1 8 23 11 745 285 7 3 20 5 081 109 0 8 01 11 758 286 2 3 61 5 257 98 4 11 873 293 0 3 60 5 240 99 5 8 80 11 805 289 4 3 40 5 159 104 3 8 42 11 807 289 1 3 83 5 357 92 3 11 898 294 6 3 81 5 338 93 7 9 24 11 845 291 6 3 61 5 245 99 1 8 82 11 848 291 5 4 02 5 467 86 0 11 927 296 4 4 01 5 445 87 4 9 62 11 877 293 6 3 80 5 333 94 0 9 20 11 883 293 6 4 20 5 581 79 3 4 23 5 582 79 1 10 00 11 899 295 4 4 01 5 443 87 5 9 60 11 915 295 5 4 42 5 763 68 5 4 42 5 738 70 0 4 20 5 556 80 8 9 99 11 946 297 3 4 64 6 028 52 7 4 635 979 55 5 Table 3 2 Strong acid strong base titration data in the third example Curve 1 Curve 3 V pHm Em Vo pHm Em V pHm Em V pHm Em cm mV cm mV cm mV cm mV 0 00 1 816 302 7 5 00 9 575 41587 4 90 4 054 170 2 0 00 1 829 302 0 5 00 8441 979 0 40 1 862 300 2 5 22 10 649 220 1 5 03 9 889 475 3 0 40 1 870 299 5 5 20 10 519 212 2 0 81 1 909 297 3 5 40 10 909 235 2 0 80 1 919 296 3 5 42 10 889 234 0 1 24 1 965 294 0 5 60 11 081 245 5 10 945 237 2 1 20 1 970 294 8 5 62 11 084 245 7 1 63 2 022 290 8 5 80 11 203 252 6 11 116 247 5 1 61 2 026 290 4 5 80 11 202 252 7 2 01 2 08
39. 4 3 20 10 103 187 7 3 61 3 095 227 5 9 20 10 842 231 4 4 44 3 538 200 7 8 00 9 930 177 4 3 AO 10 244 196 4 3 80 3 189 221 5 9 40 10 987 239 8 4 60 3 626 195 5 8 20 10 053 184 5 3 10 408 206 1 4 00 3 297 215 0 9 60 11 105 246 8 4 72 3 691 191 7 8 55 10 303 199 5 4 10 609 218 0 4 20 3 401 208 9 9 81 11 211 253 1 4 80 3 736 189 0 8 80 10 499 210 9 4 10 806 229 8 4 41 3 514 202 4 9 98 11 282 257 4 4 90 3 795 185 4 9 21 10 853 232 0 4 j 10 957 238 6 4 60 3 619 195 9 5 00 3 857 182 0 9 60 11 116 247 5 4 11 089 246 7 4 81 3 736 189 1 5 12 3 928 177 6 9 98 11 284 257 5 4 11 166 251 0 5 00 3 849 182 5 5 20 3 980 174 6 5 20 3 969 175 3 5 34 4 074 168 9 10 00 11 336 261 0 5 40 4 113 166 8 shown in Table 3 2 e The device was again adjusted with the same buffer solution e 25cm solution containing 0 015 M HCl and 0 0102 M aspartic acid was titrated with the same 0 1M KOH solution The three parallel measurements are given as curves 7 9 in the present example The measured Vm pHm Em data points are listed in Table 3 3 The aspartic acid content is derived from the exactly known concentration of the aspartic acid stock solution The HCl content came from the HCI stock solution the concentration of which was determined from the previous titrations During the experiments the ionic strength was set to 0 5 M using more concentrated KCl sto
40. 576E 03 38 Average of weighted deviation of E 2 832030E 02 39 only for curve 1 2 648744E 02 40 only for curve 2 2 930560E 02 the specific lines The names of the parameters in the program and their meanings are the following Name Meaning of name pKw PKw EO or Id E or Ig 1n10RTZF orm me or m JH or JH p Ju or JP JOH or JOH p Jon or JGy C_base Ch C_co3 Ce 1gB1_C03 lg BY 1gB2_C03 lg BS lgBi_A lg B i 1 9 VO_ci Vo value for the i experimental curve i 1 10 THO_ci In case of the i experimental curve i 1 10 it is the portion of the total hydrogen ion concentration in the solution to be titrated which is added as strong acid A more detailed description can be found at the explanation of line 17 of the kh1 13e tid file in Subsection 2 2 1 TAO_ci The total concentration of the anion of the weak acid in the solution to be titrated for the i experimental curve i 1 10 Shft_ci The shift parameter of the potential or pH values for the i experimen tal curve i 1 10 A more detailed description can be found at the explanation of line 19 of the kh1 13e tid file in Subsection 2 2 1 36 Reference Guide In the lines 11 12 of Listing 2 6 a remark can be found which notifies the user not to fit the parameters J and Jon The reason of this advice is also mentioned in Subsection 2 4 3 and the detailed explanation can be found in Section 4 8 Lines 20 and 24 also contain remarks They m
41. 6 06 4 910 119 8 1 22 2 328 272 4 5 80 4 492 144 3 0 F 8 5 80 4 558 0 60 2 213 279 2 6 20 5 980 56 3 1 60 2 409 267 7 5 92 4 655 134 6 0 3 8 5 91 4 716 0 81 2 249 277 1 6 34 8 339 83 5 2 00 2 512 261 5 6 00 4 780 127 3 1 5 6 00 4 951 1 03 2 292 274 5 6 58 8 851 113 6 2 20 2 564 258 4 6 40 8 497 92 6 1 5 6 10 5 401 1 20 2 325 272 4 6 80 9 109 128 9 2 40 2 624 255 0 6 53 8 786 109 7 1 4 6 20 7 733 1 40 2 365 270 1 7 00 9 285 139 3 2 60 2 687 251 1 6 60 8 889 115 9 1 6 6 31 8 411 1 61 2 413 267 6 7 21 9 437 148 1 2 80 2 755 247 0 6 70 9 023 123 5 2 i 6 6 43 8 705 105 2 1 82 2 465 264 3 7 40 9 563 155 9 3 00 2 835 242 4 6 84 9 155 131 7 2 3 5 6 61 8 974 121 0 2 02 2 518 261 3 7 62 9 695 163 5 3 20 2 915 237 7 6 90 9 211 134 7 2 8 6 80 9 170 132 7 2 20 2 563 258 6 7 80 9 812 170 5 3 40 3 001 232 6 7 00 9 292 139 7 2 1 7 00 9 335 142 6 2 41 2 626 254 7 8 00 9 928 177 2 3 60 3 098 226 8 7 14 9 401 146 1 2 3 f 9 474 151 0 2 60 2 686 251 3 8 20 10 056 185 0 3 80 3 195 221 0 7 28 9 493 151 6 3 9 605 158 6 2 80 2 755 247 1 8 40 10 183 192 3 3 98 3 289 215 5 7 40 9 573 156 1 3 9 724 165 6 3 00 2 830 242 7 8 60 10 335 201 4 4 10 3 353 211 6 7 50 9 633 159 7 3 9 846 172 7 3 20 2 910 237 6 8 82 10 512 211 6 4 22 3 418 207 8 7 60 9 694 163 3 3 9 974 180 2 3 40 2 996 232 8 9 00 10 675 221 6 4 32 3 470 204 8 7 80 9 810 170
42. 9 may correct this shift Precise measurements however must not be replaced by any mathematical correction thus this line must get a value of 0 0 in most cases A possible application of this parameter is described in Section 4 3 This situation might occur only for the determination of the cumulative formation constants of a weak acid It must not be applied during calibration since it is based on an exactly known Ta value 2 2 Input Files 21 Lines 20 88 contain the complete titration curve Each line describes one titration point Their order is arbitrary it is advisable but not compulsory to sort the data by the increasing volume of the titrant Repeated measurements that is where the contents of lines 15 18 are the same can be given as a single titration curve as it is shown in the example of Subsection 3 3 1 after the omission of the erroneous measured data Every titration point is given by three real numbers the measured volume Vm the potential or pH Em or pH and the relative weighting factor wr The value of the last parameter is 1 0 by default so this value is valid if it is not given by the user explicitly In this case a Slash must be used to terminate a line see second paragraph of Subsection 2 2 1 on page 18 The relative weighting factor determines the contribution importance weight of the specific titration point within the sum of squares function see Section A 4 Wp is not equal to any of the weight
43. 999210 M cco 2 1 495 10 M IgB4 4 649 Ig B 7 316 0 010 g 0 005 S E 0 000 4 ee 0 005 3 i n a E T EAE gi ac ad aac Sib ac am ae RA Stale ack es 300 Ln ONE A A O omitted data E pp aeeai e fitted data initial curve s 2 Piosssssssne nel ol Te ps Seg ie Seta ede fitted curve s mm curve 1 z eerie es TE ETE AT E rrr aeda TEA g ee ese Presser ETEENI 200 i t H MM curve 2 i 100 ees NG pees eee ee ees bv etaners bette eee be Minnow iis E mV 100 L Serres Pees epe nea ed whee l Maeeeeat Rk ashe 8 EPEE Srs GFS nii nrg cies Mee ores wage aaa REREN ORNE ENI EREE TOE eee anonse TEE ee TONIES an 2300 STEETS aes ee teiabmead giebeata Ga Fionna eee eee Say V cm l E E mV Figure 3 5 The image file belonging to the final fit in the second example if JH and Jon are fitted and the other parameters are fixed after a previous fitting Nernstian range are correct To resolve this virtual contradiction some facts should be considered Fitting Jy together with the other parameters results smaller deviation in the pH 1 2 range at the expense of worsening the other calibration parameters This worsening is hidden by the first method if the user is not careful enough A more detailed description of the problem can be found in Section 4 8 The last method offered by pHCali
44. E 02 1 0E 20 14 3 40300E 00 3 12800E 02 1 0E 20 the next 23 lines are also to be changed T5 i 16 1 20280E 01 3 72700E 02 1 0E 20 17 3 43700E 00 3 11900E 02 1 0E 20 the next 24 lines are also to be changed LEO 5 See 19 1 23790E 01 3 73300E 02 1 Q0E 20 Listing 3 2 The changed rows of kh1 13e2 tid file in examle 2 1 1 37955E 01 0 pkw arameter 1 2 3 81500E 02 0 E0 arameter 2 3 5 91267E 01 QO m 1n 10 RT zF arameter 3 4 0 00000E 00 1 JH arameter 4 5 0 00000E 00 1 J arameter 6 6 1 99925E 01 cO in mol dm3 for the base solution arameter 18 7 1 49459E 03 0 c C032 in mol dm3 for the impuritites arameter 19 8 4 64884E 00 0 log beta_1 for the weak acid arameter 22 9 7 31592E 00 0 log beta_2 for the weak acid arameter 23 10 9 87670E 02 0 TCH O in mol dm3 for curve 1 arameter 32 11 0 00000E 00 3 17400E 02 1 0E 00 the next 12 lines have also been changed T2 gt keg 13 2 62500E 00 2 54700E 02 1 0E 00 14 3 40300E 00 3 12800E 02 1 0E 00 the next 23 lines have also been changed jf ii 16 1 20280E 01 3 72700E 02 1 0E 00 17 3 43700E 00 3 11900E 02 1 0E 00 the next 24 lines have also been changed lE rn 19 1 23790E 01 3 73300E 02 1 0E 00 The latter figure shows that the calculations are based only on the points within the Nernstian range After clicking save amp quit button the result files are created and the program stops running e One of the result files kh1 13e cin should be renamed to kh1 12e2 tid
45. UsER s GUIDE pHCau VERSION 1 324 20070323 1 1 2 GABOR PEINTLER BAL ZS KORM NYOS B LA GYURCSIK HOME PAGE HTTP WWW STAFF U SZEGED HU PEINTLER APRIL 1 2007 University of Szeged Department of Physical Chemistry University of Szeged Department of Inorganic and Analytical Chemistry This documentation and the program pHCali described in it may be used and distributed freely complying with the following regulations e The programs and included data files can be distributed only in their original compressed archives without any modification The distribution of the documentation is possible only in PDF form without any change The programs data files and documentations are free only the expense of the media and shipping handling cost can be charged on the user e Anyone can use the program freely even for commercial purposes Charging the use of the program is strongly prohibited in any way e g rental fee service charge fee of distribution together with an instrument etc e If the use of pHCali lead the user to reach any result this fact should clearly be indicated when the result is published Allnames and abbreviations e g DOS Windows ODRPACK DISLIN Linux PostScript Acrobat Reader Zip Unzip etc together with the definitions of image formats eps pdf hpgl svg java wmf tiff png ppm bmp and gif used in this document are either trademarks or copyrighted properties of the appropri
46. a initial curve s GE curve 1 WME curve 2 MEE curve 3 MMMM cirve 4 ME curve 5 6 Resi ite tonte dant bain tea TTET oes i i 0 00 0 02 0 04 0 06 pH PH Figure 3 9 The final work window of the aspph c tid file in example 3 or the initial work window of the aspph d tid file This file contains one more change in line 143 the shift parameter of the contracted weak acid strong base titration curve is also fitted The usage of this parameter corrects the problem indicated by the initial linear fitting on the pH Em points that is the significant 50 Getting Started through Examples O ofnitted data fitted data initial curve s fitted curve s eso ct lt E S went pkw 13 785 Eps Tiff m 0 9901 Paf Ng fis s i f i L 0 00 0 01 0 02 0 03 0 04 0 05 pHe PHm Figure 3 10 The work window of the aspph e tid file in the third example differences in the intercepts of the straight lines see page 20 in Subsection 2 2 1 From the two possible parameters the one belonging to curves 4 6 should be fitted because these curves are shifted compared to the others as shown by the values of the intercepts In this case the titration curves belonging to the aspartic acid solutions are not influenced by this parameter during the further calculations By running the program with
47. age media usually in a hard drive of a computer image file page 8 A file including the data of a picture It can be displayed on the screen and or can be printed on a printer operating panel page 31 The upper right part of the work window It makes possible the inclusion exclusion of data as well as the recalculations with the modifications orthogonal distance regression page 8 Procedures used for parameter estimation usually take into account only the experi mental error of the dependent variable and the values of the indpendent variable are considered as exact ones On the other hand the orthogonal distance regression is able to take into account the errors of both variables if the experimental uncertainty is known for both variables parameter modifier window page 28 A window for modifying the initial values and fitting state of the parameters PROGNAME page 39 The name of the executables to be used relative weighting factor page 21 It determines the contribution of the spe cific titration point RGB color page 23 It is a method for defining colors The method resolves each color to its three com ponents red green and blue ones and the intensities of these pure colors should be given TASKNAME page 15 It is the base name of the actual task chosen by the user text file page 8 This type of file includes almost only displayable characters found on the key
48. ake the calculation of the total hydrogen ion concentration easier in the solutions to be titrated On the basis of line 20 in the reference example the concentration of the strong acid is 0 0988M in case of the first titration curve Since no weak acid is added to the solution this value corresponds to the total hydrogen ion concentration In line 24 it is found that no strong acid is added into the second solution to be titrated but there is hydrogen ion bounded to the weak acid in the solution so the total hydrogen ion concentration is 0 1 M A more detailed explanation is given in the discussion of line 17 of the kh1 13e tid file within Subsection 2 2 1 e e Experimental uncertainties lines 27 29 in Listing 2 6 This section only repeats the experimental uncertainties of the measured potential or pH and the measured volume originally given in the TASKNAME tid file dle dle dle se ke Goodness of Fit statistics lines 30 40 in Listing 2 6 In the last section the most important statistical parameters are listed In the reference example lines 31 33 give the number of iterations the number of function evaluations based on the equations A 14 and the number of Jacobi matrix calculations If any of these numbers is larger than 200 300 then the user can be sure that 1 either wrong initial values have been entered or 2 the task is badly conditioned and the correlation of the parameters is unacceptably high The same should b
49. al The definition of pH has been given by S rensen at the beginning of the 20th century as the negative logarithm of the activity of the hydrogen ion The analytical methods like pH metry however aim to determine concentrations thus more interpretations of pH have been used in practice since the original definition was given These interpretations are more widely used than the original one and unfortunately they are not equivalent to each other Like pH potential also have more interpretations This situation causes several problems nowadays thus the following notations are introduced in order to avoid misunderstanding pHa stands for the negative logarithm of the activity of the hydrogen ion pHa lg an p H stands for the negative logarithm of the concentration of the hydrogen ion p H 1g H pH stands for the measured value of pH i e this value is displayed and or stored by the instrument pH denotes the calculated pH value which can be determined from the volume and other parameters of the titration curve In others words it is the calculated analogue of pHin pH means the general use of the concept e g in words like pH metry pH sensitive etc Em stands for the measured value of potential i e this value is displayed and or stored by the instrument E denotes the calculated value of the potential which can be determined from the volume and other parameters of the titration curve In others words it is the ca
50. an em pirical constant for taking into account the deviation from the Nernstian equation in the acidic range pHS2 page 72 In case of pH measurement it is an em pirical constant for taking into account the deviation from the Nernstian equation in the basic range pH212 page 67 The ion product constant of water defined with concentrations page 71 Empirical constant actual slope of the Nernst like equation page 71 Empirical constant actual relative slope of the Nernst like equation page 67 The number of protonation steps concern ing the anion of the weak acid OTE gxticutaculadidrd aE EEES page 67 The hydroxide ion Ok E eta E T sai eae E S E page 72 The number of titration points of all titra tion curves used for the calibration pH The general use of the pH concept pHa page 70 The negative logarithm of the activity of the hydrogen ion plH page 70 The negative logarithm of the concentration of the hydrogen ion pHe The calculated analogue of pH pH page 71 The calculated analogue of pHm emphasiz ing the fact that Nernst like equation was used for the calculation pHm page 70 The measured pH value displayed and or stored by the instrument PKw page 67 Negative logarithm of the ion product con stant of water defined with concentrations page 67 The charge number of the completely de protonated anion of the weak acid Only compounds having really smal
51. aning of the specific lines are the following Line 1 determines the colors of the background and the foreground used for frames and texts This line can have three different syntaxes 1 The line includes only one logical value which can be TRUE white background and black foreground or FALSE black background and white foreground 2 The line includes one logical value followed by two integer ones The meaning of the logical value corresponds to the previous syntax but now it determines only the default color of the background for transparent PNG and GIF image files see the second line The two integer values give the colors for the background and foreground respectively 3 The line includes one logical value followed by six integer ones The meaning of the l6The precise definition of those characters which can be used for data separation can be found in the first part of Subsection 2 2 1 The file phcali rgb is the same as the original configuration file but the colors are given as RGB values 18 Among the others this method can also be used for defining colors in Windows operating systems 24 Reference Guide Listing 2 5 The configuration file including the default values phcali cfg 1 TRUE background is white TRUE or black FALSE or VGA RGB colors 2 FALSE disables FALSE or enables TRUE transparency for PNG GIF files 3 8 color for axis grids labels and axis titles 4 4
52. are inaccessible and every change needed to be done in the input file should be done prior running It can be seen from the above interpretations that the two possible values of the second parameter exclude each other so they cannot be given together at the same time 21Under Linux it should not be forgotten that phcalit or phcalix must be typed instead of the simple file names if the actual directory is not given in the PATH environment variable 28 Reference Guide E pHCali v1 30a 20061226 i lolx Help File lt Quit Editafile kh1 13e TASKNAME kh1 13e Input files The kh1 13e tid file must include the input data The phcali cfg file can optionally include some configuration data Output files The kh1 13e res file will store the results The kh1 13e crv file will store the experimental and calculated curves The kh1 13e phv file will store the backcalculated p H values The kh1 13e cin file will store the modified input data The phcali msg file stores the messages of the program Figure 2 3 The file chooser window in case of the reference example 2 3 2 Usage of the File Chooser Window If pHCali has been started without any command line parameters which is most likely when it is started from icon the TASKNAME will be phcali This default string can be changed through the file chooser window which is shown in Figure 2 3 in case of the reference example The w
53. ate companies organizations or persons 1 2005 2007 University of Szeged Department of Physical Chemistry CONTENTS 1 1 1 1 2 1 3 1 4 Concisely about PAG allt dhe win Se oe Ad hs Ghee OE Soe ae G How to Read this Manual 3 99 ce as ck Sew a Sg Pe el ho a Re em eh TSta EAE ess oe hth Sse aah ae cis hina Fe So Zoe te Tasha te hace Mike ae 1 4 1 DOS Operating System i s ara howd hehe ai ho tw ae eh aes eee oe 1 4 2 Windows 95 98 Millenium 2000 XP and 2003 Operating Systems 1 4 3 Linux Operating Systems wi awk Set hk bale wip hee Oko Re eR Reference Guide 0 2 te ee ee ew ee ee eee ee ee 2 1 2 2 2 3 2 4 Overview of the Program aaas oc a hae Wa Se BS Iput Files gus eid rae marea a a E Bae A ee ha eae 2 2 1 The Input Data File TASKNAME tid or TASKNAME cin 2 2 2 The Configuration File phcali cfg ooa aaaea Executing pHCali naau au aaa 2 3 1 Optional Command Line Parameters aaau 2 3 2 Usage of the File Chooser Window aaas aaa 2 3 3 Usage of the Parameter Modifier Window 2 3 4 Usage of the Work Window o s sase ate at hee oe KS SS Be ees 2 3 4 1 Use of the Operating Panel with Mouse 2 3 4 2 Use of the Operating Panel with Keyboard OQ tput Files ne a nigte a ana mea O Mig Bae aion a a E e 2 4 1 The Structure of the Result File TASKNAME res 2 4 2 The Structure of the Curves File TASKNAME crv
54. ats using other applications e g Ghostscript and GSview programs mentioned above pdf means Portable Document Format which is mostly displayed in Adobe Acrobat Reader hpg means Hewlett Packard Graphics Language file This can be used for printing on plotters svg means Scalable Vector Graphics file This format is suitable for publishing vector graphics on the Web jav means Java Applet format This form is for displaying the figure on HTML pages wmf stands for the Windows Metafile format which can directly be inserted into Word documents tif means Tagged Image File Format png means the Portable Network Graphics format which is suitable primarily for dis playing graphics on HTML pages ppm means Portable Pixel Map format This format is to be displayed with special programs bmp means the Windows Bitmap format which is mainly for specific purposes in Windows environment gif means the Graphics Interchange Format This format is to be displayed primarily on HTML pages If the name of the image file to be created is already exists the program takes the first six characters of the TASKNAME and appends the string _1 _2 etc together with the appropriate extension The string created in this way will be the filename of the created image file If more than ten image file names exist starting with the first six characters of the TASKNAME then the program continues with the numbering except t
55. bbling through the solution the curvature caused by the carbonate content vanishes from the titration curve It results significant shifting of the formally detectable equivalence point Modeling the extent of the evaporation of carbon dioxide is practically impossible This fact required to carry out systematic study of how much the different conditions influence the CO leaving The experiences coming from the calculations with pHCali are the following e In case of bubbling inert gas through the solution the program was not able to determine the carbonate concentration quantitatively in any of the measurements The fitting of the carbonate concentration gave the 10 50 of the real value e In case of mechanical stirring the program was able to determine the carbonate concen tration quantitatively if the following conditions were valid o co Ton lt 2 and To lt 0 025 M or 0 co Ton lt 1 and Tor lt 0 25M e Independently of the stirring method the badly determined carbonate concentration did not influence the other parameter values so the calibration of the device was possible Itis obvious from the above observations that pHCali cannot be used for the quantitative determination of the carbonate content if the titrant base is strongly contaminated with carbonate But this contamination can be indicated clearly and it cannot be smeared by the function transformations This fact is a surprising but unambiguous ex
56. c end of the curves It is obviously not the case in the figure and the difference between the deviations is much larger than the experimental uncertainty of the potential The same phenomenon can be experienced if the user evaluates the titrations with oxalic acid malonic acid or succinic acid instead of the KH phtalate titration The oxalic acid and malonic acid titrations also show that such differences do not exist in acidic medium The The user can check it by using the installed ox1 13e tid ma1 13e tid and sul 13e tid files 4 8 Extending of the pH Range to be Calibrated 63 o o10 Skip m less at E 5 0 005 H 2 0 000 o gt 0 005 E TEE AAE 5 0 omitted data s H fitted data initial curve s fitted curve s MMM curve 1 x MMM curve 2 100 E ERMi P aoe Sew TES ee ate l PERLET pees beseteeeties E mV 100 t eden be eae ee iste we a8 Jaye sana d niet wa ease 4 RARAN TPR 200 E PITIE aye eee RENNER ETE i ase tide E des 300 E EATR eee Tee SETENE Bearra PREET rere ie y 0 2 V cm Eg Em mV Figure 4 4 The work window of using the kh113ej1 tid file deviations from the Nernstian behaviour are the same for both the strong acid strong base and the weak acid strong base titrations as well The different quality and quantity of the ionic strength determining ions can explain
57. calit and phcalix are compiled with static libraries which means that the executables contain everything that is needed during runtime These programs can be installed and run without the help of the root user but their size is reasonably large The file lphcali tgz contains the executables compiled with shared libraries under the names phcalit shared and phcalix shared These programs are significantly smaller in size but they depend on libraries within the following packages libg2c0 libmotif3 and the DISLIN version 9 0 libraries The user may delete the not used executables The position of the program window might slightly differ from the desired one under some window managers e g under fvwm_2 8At file level the following dynamic libraries are necessary during runtime to run the shared executables 1 4 Installation libdislin_d so 9 libg2c so 9 libm so 6 libgcc_s so 1 libc so 6 libXm so 3 libXt so 6 1ibX11 so 6 lib ld linux so 2 libXmu so 6 1ibSM so 6 libICE so 6 libXext so 6 libXp so 6 and libdl so 2 CHAPTER 2 REFERENCE GUIDE This chapter demonstrates the usage of pHCali on a real experimental system The experi mental data consist of two titration curves e 6 035 cm 0 1 M HCl solution has been titrated with 0 2 M KOH solution for the first curve and e 6 035 cm 0 1006 M KH phtalate solution has been titrated with the same 0 2 M KOH solution for the second one In the titrant and each solution t
58. cases the relative change in volume is rather low V Vo lt 1 0 thus it is suspected that the change in the ionic strength can be neglected due to the tiny dilution This is not true however The variation of the ionic strength depends not only on the ratio of the volumes but on the ratio of the concentrations too and the concentration in the titrant is much higher than that in the titrated solution It is also suspected that the dilatation or contraction can be neglected because their contribution to the volume of the titrated solution is very small But the independent variable of the titration curves is not the Vo Vm but the Vm itself which has very small values due to the high concentration of the titrant base Using pHCali these errors can be caught on the upper left graph of the work window the curves after the equivalence points have systematic deviation which exceed the experimental uncertainty 4 3 Potential or pH should be Measured The answer both if possible otherwise the measurement of the potential is suggested It is bad news for chemists who prefer thinking in pH units rather than in potential But the Do not forget that strictly additive volumes are supposed for the formulae used for the calculations see the Appendix 58 Practical Guide exceptional measurement of pH makes the recognition and the elimination of some classes of experimental errors difficult or even impossible The reason of this advice is rathe
59. ck solutions 3 3 1 Calibration The first step of the evaluation is to check if the technical parameters were constant during the measurement In order to do this linear regression has to be carried out for the pHm Em data pairs of each titration curve the points omitted from the regression are striked out in the tables The fitted straight lines are Curve 4 pH 0 016900 E 6 9214 Curve 1 pH 0 016898 E 6 9330 Curve 5 pH 0 016903 E 6 9213 Curve 2 pH 0 016900 E 6 9319 Curve 6 pH m 0 016889 E 6 9198 Curve 3 pHm 0 016901 E 6 9315 Curve 7 pHm 0 016905 E 6 9318 Curve 8 pH m 0 016887 E 6 9278 and Curve 9 pHm 0 016901 E 6 9319 The comparison of the intercepts suggests that there was an experimental problem during the one buffer calibration of the pH meter The intercept values are smaller by 0 01 pH unit 3 3 Complete Evaluation of Equilibrium Measurements 47 Skip less at o omitted data fitted data S35 initial curve s MME curve 1 WME curve 2 GEE curve 3 sr MMMM curve 4 B curve 5 A Steer Pr ees bce Poe vewweRes NE curve 6 a i i fi i L i L i i 0 2 4 6 8 10 0 02 0 00 0 02 0 04 V cm pH pH Figure 3 6 The work window of the aspph a tid file in the third example after the first one buffer calibration than after the others This value is significantly greater
60. cluded because it differs significantly from the others This fact can clearly be seen either from the figure or in table 3 1 as well The same comparison for the strong acid strong base curves suggests that curve 1 should also entirely be excluded from the further calculations although its deviation is smaller than that of curve 6 as it can be seen either from the figure or in Table 3 2 In order to omit the erroneous curves only from the calculations and to leave them on the graphs all relative weighting factors for curves 1 and 6 must be set to 1 0x107 In this way these points do not contribute to the sum of squares function see equation A 14 practically thus they do not influence the fitting These points however remain detectable for the program and they are displayed on the figures 48 Getting Started through Examples Number of skipped data i feS ES Ec ecg ot E s wen pkw 13 780 Eps Tiff m 0 9885 Pdf prg a f WwW N o omitted data fitted data initial curve s EE curve 2 GEE curve 3 GMM curve 4 3 E curve 5 2 Fo rs ark es Pesce e neers NN curve 6 777 i i i 1 i 1 i i i 1 i 0 2 4 6 8 10 0 01 0 00 0 01 0 02 0 03 0 04 V cm5 pHe pHm Figure 3 7 The work window of the aspph b tid file in the third example In order to change the relative weighting factors pHCali has to be terminated with the save amp quit
61. codes o Eo Be fe Be foe cs 7 Ge Bo Poo Lan cz fas ja4 Wos In case of black background the codes of the white and black colors are exchanged Sample linewidths and their codes Ss Ge E 1 6 11 16 21 26 Figure 2 2 Symbols base colors and line widths available on the graphics screen as well as their codes may be followed with remarks which must be started with a slash Data and the leading slash of remarks must be separated at least one space or tabulator character Lines must not be omitted not even if they are not being used by the specific variant of the program e g the text mode variant does not contain the parameter modifying windows of the other variants The file phcali cfg with the default settings is shown in Listing 2 5 If an integer number defines a color this number can be replaced by four integer values in any line of the phcali cfg file In this way not only the colors listed in Figure 2 2 can be chosen any color can be defined as an RGB color In this case the first value of these four integer ones must be negative and the following three values are the intensities of the red green and blue components respectively The intensity values must be in the 0 255 range For example the 1 9 255 0 numbers defines the pure green color or the black and white colors can be defined as 1 9 9 0 and 1 255 255 255 respectively The me
62. d in Subsection 2 4 3 It is very important to emphasize that this method can only be successfully used if two conditions are true 1 The value of the ionic strength and the salt used for setting it in the strong acid strong 4 8 Extending of the pH Range to be Calibrated 65 base titration curve must practically be the same as those in the system to be investigated 2 The deviation from the Nernst equation in the non Nernstian ranges are reproducible APPENDIX MATHEMATICAL DESCRIPTION OF TITRATION CURVES During the calibration the experimental data of strong acid strong base and weak acid strong base titration curves are being evaluated For this procedure the calculated analogue data must be created by suitably changing the parameters of the mathematical equations Ideally the goal is to get smaller differences between the experimental and calculated data than the experimental uncertainty The required equations are derived within this appendix in detail The equations describing the strong acid strong base and weak acid strong base titrations can be treated similarly as described below on the basis of 15 A 1 Description of the Equilibrium State at any Point of Titration During the titration only those species must be taken into account which can be built from the components of the hydrogen ion the anion of the weak acid and or the carbonate ion The following species and their cumulative formation cons
63. d wineut pandet sage ones Sa reene Maia tadctassweactawacat Co a a a aa la ae a d 5 Oo omitted data fitted data Fikia Sips ss a eaa ftia curves fitted curve s f i oO E curve 1 4 2 r GRE eene EEIT IEPER peu nek EEIE i i fi i i i fe 2 4 6 8 10 0 020 0 015 0 010 0 005 0 000 0 005 V cm pH PH Figure 3 12 The final work window of the aspbeta tid file in the third example if the total concentration of aspartate ion is fitted the literature data according to 19 pK 13 73 13 81 lg B 9 63 lg B2 13 31 and lg B3 15 26 CHAPTER 4 PRACTICAL GUIDE During creation of pHCali the authors carried out more than 40 calibration measurements besides the evaluation of earlier measured data in order to test the program These measure ments included testing of various calibration materials systematic changing of the carbonate content of the strong base solutions measurements at various ionic strengths and using dif ferent pH ranges In the course of the evaluation of the experimental data large amount of empirical knowledge was collected which may help the precise calibration It is not closely related to the usage of the program rather to the chemistry of the calibration systems This knowledge is discussed in this chapter 4 1 Sensitivity of the Orthogonal Regression for the Initial Values and Correlation of the Parameters The success of or
64. dure of the program is the same as installing the program under DOS The compressed archive wphcali zip contains all three variants of the executables It is important to note that the graphics of phcalid exe works intrustably if it is started from the command line of Windows 2000 XP or 2003 operating system due to incompatibility issues Nevertheless phcalic exe and phcaliw exe run flawless under any Windows versions Furthermore the graphical capabilities of the latter programs depend only on the specific operating system and do not require any preconfiguration pHCali does not write any information into the registry of Windows so the programs data files or even the whole directory can be moved freely In case the user wants to start the program by clicking on an icon then the icon should be created in one of the folders belonging to the Start menu or on the Desktop according to the followings e Right click on an empty area of the opened folder or the Desktop A folder can be opened in a window by 1 highlighting the name of the folder through the Start Programs or Start All Programs menu 2 right clicking the name and 3 choosing the Open menu 4Self extracting archive is not distributed for security reasons The zip file can be unpacked using e g Unzip exe which can be downloaded from the http www info zip org pub infozip UnZip html web page It is important to note that the environment variables cannot be
65. e The line connecting the points have no meaning it only provides better visibility for the trend of the curve The volume horizontal axis of this figure is the same that of the lower left figure so it is not drawn again The range of the vertical axis in the upper left figure can be set to arbitrary values in line 32 of the phcali cfg file 4 The operating panel can be found in the upper right corner It makes possible 1 to exclude previously fitted points or to reinsert previously excluded points to both ends of the curves 2 the fitting can be carried out multiple times according to the changes made and 3 the program can be terminated The beginning and the end of a curve is to be understood as the following titration points can be given in arbitrary order by the user These data are sorted by the program along with increasing volume of the titrant prior to any calculation According to this the beginning means the point with the least volume and the end means the point with the greatest volume regardless of their position given in the input file If data of multiple repeated titrations are given within one titration curve then the data of the experimentally different titrations are mixed An example for this is shown in Section 3 3 2 3 4 1 Use of the Operating Panel with Mouse The look of the operation panel is shown in Figure 2 5 The tasks of the buttons are described next e Each of the 10 buttons on the left side which are gro
66. e 1 parameter 32 4 0 00000E 00 TC ADO in mol dm3 for curve 1 parameter 33 5 0 00000E 00 shift in the measured E pH for curve 1 parameter 34 6 0 0000 317 4 1 0e 00 7 0 1000 316 3 1 0e 00 8 0 2500 314 6 1 0e 00 the next 64 lines are omitted from the manual 9 11 6280 372 1 1 0e 00 10 12 0280 372 7 1 0e 00 11 1 00 0 0 0 0 12 1 00000E 00 H A ratio in the weighted material or 0 for curve 2 13 6 03500E 00 VO in cm3 for curve 2 parameter 35 14 0 00000E 00 0 TCH 9 in mol dm3 for curve 2 parameter 36 15 1 Q00600E 01 QO TC A O in mol dm3 for curve 2 parameter 37 16 0 00000E 00 shift in the measured E pH for curve 2 parameter 38 17 0 0000 164 9 1 0e 00 18 0 1000 160 0 1 0e 00 the next 71 lines are omitted from the manual 19 11 5790 372 2 1 0e 00 20 11 9790 372 9 1 0e 00 21 12 3790 373 3 1 0e 00 22 1000 0 0 0 0 0 e it gives the ratio of the stoichiometric numbers the hydrogen ion and the anion in the weighted form of the weak acid For example this number is 1 0 2 0 and 0 0 in cases of KH phtalate see line 90 oxalic acid and sodium oxalate respectively The meaning of this line is clarified and detailed more deeply in the explanations of lines 17 and 18 Line 16 is the initial volume of the solution to be titrated For pHCali itis a fittable parameter so the line contains a real and an integer number see explanations of lines 3 14 Line 17 contains a real and an integer too The real number is a
67. e differences of the measured and calculated potentials are smaller than the experimen tal uncertainty i e 0 1 mV is 2 2 lt p H lt 11 6 It follows that J and Jon do not influence the Nernstian range only if the relationships J H lt 0 1 mV and Jon lt mV are valid If the kh113ej1 tid input file is used then J4 50 7 mV M and Jon 26 0 mV M and the above mentioned relations are valid only within the 2 7 lt p H lt 11 4 range Even if the other parameters are fixed the fitting of J and Joy unnecessarily constricts the availability of the Nernst equation This effect can significantly affect the results of p H calculations at the edges of the Nernstian range causing a shift of several hundredth pH units In case of the kh113ej2 tid file similar calculations lead to the result that the valid range of the Nernst equation decreased to 2 6 lt p H lt 11 5 so the effect is the same The fitting of Ju and Jou decreases the precision of the calibration instead of improving it These considerations are based on the experimental data measured by the authors with their electrodes but it is enough to warn the user to check the validity of equation A 9 for the used instrument before applying Jy and Jon As an alternative extension of the calibration pHCali offers an interpolation method for the calculation of p H values in the non Nernstian ranges to eliminate the above problems with Jy and Jou This method has already been detaile
68. e electrode and by setting up constant ionic strength with a suitable salt On the other hand me which can be calculated from the experimental data shows how ideal is the used hydrogen ion selective electrode The more the relation me 422 is true the more the Nernstian characteristics of the electrode is valid In practice E and m are strictly constant only within a specific pH range and Em and lg H are linearly proportional only in this range The deviation from this behavior is taken into account according to 2 even nowadays This work suggests that equation A 8 is to be extended with additive terms Kw E E me lg HH Ju H Jon HA A 9 where Jy and Jop are empirical constants although their values can be approximated with theoretical calculations 2 Briefly every point of the titration curve E Vm can be calculated on the basis of equations A 6 and A 9 E f parameters Vm where the parameters can be BA s Bs 8 Kw Vo Cay Cs Coy Cc Es ME Ju ans Jou A 3 3 Calculation of pH pH metric instruments usually give a pH value and not the directly measured potential This pH is calculated from the measured potential according to a previous calibration based on one or two buffer solutions and this value is stored or displayed No matter how the calibration happens the instrument calculates pHm according to a pHm a a2 Em A 10 type equation where a and az are constants d
69. e fitting step Besides the determination of the calibration parameters it lets the user e to utilize the maximum precision of measurements e to discover the possible experimental errors more easily e to indicate or even quantitatively determine the carbonate content of the titrant base and e to extend the usable pH range in a trustable way Furthermore the program is able e to handle multiprotic weak acids that can be weighted accurately as calibration material e to determine the protonation constants of any weak acid with composition of HjA t i lt 9 q 1 2 even if the total concentration is not known precisely Moreover e the program is capable to calculate the pH defined with the equilibrium concentration of the hydrogen ion in every measured point of the chemical system to be studied These p H data are the most suitable input data of any equilibrium evaluation program 1 2 Concisely about pHCali To calibrate a pH metric instrument the program requires the same experiments as Gran s method 1 namely two titration curves are necessary 1 a weak acid strong base titration curve where the analytical concentration of the weak acid is exactly known and 2 a strong acid strong base titration curve Both curves are necessary to determine the instrumental parameters the ion product constant of water and the precise concentrations of the strong base and the strong acid stock solutions During the experiments eithe
70. e order of the experiments is given below e The used instrument was preliminarily adjusted using one buffer solution 0 05 M KH phtalate assuming that the slope is Nernstian e 25cm of 0 02000 M KH phtalate solution was titrated with 0 1 M KOH solution and this experiment was repeated two more times These experiments are given as curves 4 6 in this example The measured Vm pHm Em data points are shown in Table 3 1 e The device was again adjusted with the same buffer solution e 25cm 0 02 M HCI solution was titrated three times with the same 0 1 M KOH solution These are curves 1 3 in the current example The measured Vm pHm Em data points are 7In everyday terminology this procedure is called one point calibration but it is not enough for precise pH measurement This procedure is called adjustment in this guide to distinguish it from the precise calibration 46 Getting Started through Examples Table 3 3 Titration data in the third example for determining the formation contants of aspartate ion Curve 7 Curve 8 Curve 9 V pHm Em V pHm Em V pHm Em V pHm V pHm Em V pHm Em cm mV cm mV_ cm mV cm3 cm mV cm3 mV 0 00 2 111 285 2 5 50 4 199 161 7 0 00 2 123 284 4 5 40 4 157 0 10 00 2 115 285 1 5 60 4 275 157 2 0 42 2 179 281 0 5 60 4 283 156 7 0 21 2 155 282 6 5 50 4 237 5 0 20 2 147 282 915 86 4 545 141 5 0 80 2 244 277 5 5 70 4 377 151 0 5 63 4 355 0 40 2 179 281 2
71. e told if the value in line 34 is greater than zero Lines 35 40 give the average deviations of the measured and calculated points for both the potential or pH values and the volumes The average deviation is not only calculated at once for all points but also independently for each titration curve In case the user wants more detailed information concerning the fitting pHCali should be set to generate the phcali odr file also see Section 2 1 and the description of line 33 of the phcali cfg file 2 4 2 The Structure of the Curves File TASKNAME crv The TASKNAME crv text file contains all the titration curves of all titrations The purpose of this file is to allow the user either to evaluate the results by further calculations or to make figures based on the output data The file consists of 11 columns The first row of the file contains the titles of the columns and the titration curves follow in the next rows The first line of every titration curve contains 11 asterisks separated with spaces and the serial number of the titration curve The purpose of this leading line is to separate the individual curves After the title line of the curve the titration data can be found The 11 columns contain the following data Column Column name Content of the column 1 Vm The measured volumes Vm 2 Em or pHm The measured potentials or pH s Em or pHm 3 EcO or pHc0 Calculated potentials or pH s using the initial values of the parame
72. e written into the fourth column For example let s consider the kh1 13e crv file belonging to Figure 2 7 In columns 1 2 and 5 of this file the data of Vm Em and E can be found Since both J and Joy are zero in this fitting the value of E is nothing else than the potential calculated assuming that the Nernst equation is valid for the actual point In other words E is the expected value of the measured data In the second and third lines of this data file see Listing 2 7 it is shown that the measured data are 317 4 and 316 3 mV instead of the expected 321 758 and 320 450 mV due to the deviation from the Nernst equation If the user needs the value Tt is worth to mention that columns 1 and 2 can be used in the input files of the program PSEQUAD 18 or other programs for calculating stability constants without any further modification The same data can be found in columns 1 3 and 4 of a phv file The data in a crv file however regard to the fitted points from the second part of the corresponding tid file while the data in a phv file regard to the data from the third part of the corresponding tid file for which p H values must be calculated 38 Reference Guide Listing 2 7 The content of kh1 13e phv file corresponding to Figures 2 7 2 8 1 Vm p H Em Ec Nernstian from interpolation 2 9 0000E 00 1 0841 3 17400E 02 3 21758E 02 3 1 0000E 01 1 1027 3 16300E 02 3 20450E 02 4 2 5000E 01 1 1315 3
73. ecified experiments the weighted material was C4H704N H20 where an additional gravimetric measurement clarified that the weighted material has lost its crystalline water partially so the obtained results are acceptable lg B 9 67 lg B2 13 29 and lg B3 15 16 For the sake of comparison This file also illustrates that parallel titration curves can be given together with the same header lines since the parameters included in the header are identical for these curves 3 3 Complete Evaluation of Equilibrium Measurements 53 ta Skip c less _at saveaQuit pKw 13 785 m 0 9901 4 L Peres eee ere ee ee AT E EY i O omitted data fitted data Bibi Bi ALEE ETATE E vase a EA Giclee PEPE oo eae a initial curve s fitted curve s 5 Mill curve 1 3 ak 2 EAEE asc EEFETE VE PREIEI in i o 2 4 6 8 10 V cm PHo PH mn Figure 3 11 The final work window of the aspbeta tid file in the third example if the total concentration of aspartate ion is fixed Number of skipped data S E pKw 13 785 m 0 9901 10 o 2 R m h 2 L o N i LY S E EET E AE E T casmuguiees Anpa ae SSDs et z A a ar eo4 aA N AAN EE Sa NEA i g or S G m r Eee J S z Ge EE EOE teats a Cee o Q 1 ERER REE OE EESE AAEE E DI Brae s ae aa a i AAA A Eee EAE ANEN AE E AE ra EEE AE AOE cain a T EE E T a oi aedie
74. efault The function of these ones are the same as that of the save amp quit button except that they also save the last work window into an image file The format of the file see Section 2 1 in detail is given on each button The figures in the image file look alike as in the work window but the operating panel is replaced by an information box which contains the most important parameters of the fitting The information box can be omitted by changing the 34 line of the phcali cfg file If the user wants to save more phases of his her work it can be done in more steps using the cin files see Section 2 1 2 3 4 2 Use of the Operating Panel with Keyboard The only accessible input device is the keyboard in text mode and it is an alternative device in console and window modes which can be combined with mouse The following differences appear by using the operating panel from the keyboard e The acutal curve can be selected by pressing the appropriate number key s and press ing the Enter key afterwards In console and window modes the Enter key is not necessary e The combination of the s S e and E characters and typing the number of the points to be omitted included can be used to change the number of the points to be fitted E g the string S13 or S 13 excusively in text mode and Enter includes 13 previously excluded points into the fitting at the beginning of the curve If there were less previously excluded
75. ere fixed all the points of the strong acid strong base titration curve were included and only Ju and Jon were fitted This stage can be found in the kh113ej1 tid file In case of the second figure all parameters were fitted together in the second step This stage is stored in the kh113ej2 tid file It is obvious from Figure 4 4 that J and Jon cannot describe the deviation from the Nerns tian behaviour There are still significant and systematic deviations on the strong acid strong base titration curve In Figure 4 5 this deviation is closer to the experimental uncertainty 64 Practical Guide Skip less_at pKw 13 816 E mV 200 L 100 100 b 200 H 300 H ipa en ONESIES Q omitted data k fitted data initial curve s fitted curve s Lop iii ouve 1 MB curve 2 m 58 8983 V cm5 Figure 4 5 The work window of using the kh113ej2 tid file but the slope has changed significantly which means that Jy and me are in unacceptable correlation with each other If J and or Jon is fitted the user would certainly expect that the J H and Jon a expressions do not influence the Nernstian range It can be checked very simple The kh1 13e crv file contains the calculated final curves of the reference example see Fig ure 2 7 It can be seen from the 7 and 8 columns of the file that the range in which th
76. etermined and stored by the instrument during the previous calibration In ideal case ag 5 The value of pH can be calculated on the analogy of equation A 10 by substituting equation A 8 pHe a1 a2 Ee ay a2 E a2 me Ig H Ia m 1g H pH A 11 where the value of m is 1 in case of ideal Nernstian behavior and Ig is an empirical constant The first one can be considered as the actual relative slope and the last one is called Irving factor in the literature 17 These parameters can also be calculated if potential was measured Ig a a2 E and m a2 me Where it is necessary the notation pHN of the calculated pH emphasizes that the calculation was carried out on the basis of the Nernst equation only without the extension terms see equation A 12 below 6The values of a and az can easily be determined if both pHm and Em are stored 7It must be mentioned that the derivation of the Irving factor given in 17 supposes that the behavior of the electrode is ideally Nernstian m 1 and the derivation takes only the diffusion potential into account It has to be noted however that the value of Ig is also influenced by the value of y 72 Mathematical Description of Titration Curves In case of pH measurement the pH range to be studied can be extended too on the analogy of equation A 9 Kw pH la m 1g H yy HH Jha HA A 12 where J and Kr are empirical constants
77. ettit L D A Study of Some Problems in Determining Stoichiometric Proton Dissociation Constants of Complexes by Potentiometric Titrations Using A Glass Electrode Anal Chim Acta 38 475 1967 18 Z kany L Nagyp l I Peintler G PSEQUAD for Chemical Equilibria Update 5 01 2001 19 IUPAC Academic Software Stability Constants Database Release 2 Otley 1996
78. f the individual data pairs see Subsection 2 2 1 in detail The extension cin is the abbreviation of computed input pHCali is able to carry out the calculation either in a single step or in subsequent smaller steps allowing full user s controll If the user wants to carry out the calculations in more steps or s he wants to continue the work later then it can be done by the help of this file Changing the name of the file to another TASKNAME with tid extension the calculation can be continued with the renamed file TASKNAME res contains the final results of the calculations and parameters describing the circumstances of the calculation The extension res is the abbreviation of results The fully detailed description of the structure of this file is given in Subsection 2 4 1 TASKNAME crv contains the measured and the calculated curves The extension crv is the abbreviation of curves The user can create arbitrary figures with arbitrary programs using the data in this file The fully detailed description of the structure of this file is given in Subsection 2 4 2 TASKNAME phv contains the results of the Em pHm p H calculations based on the data pairs given in TASKNAME tid The extension phv is the abbreviation of pH values At the end of the TASKNAME tid file the user can supply the titration curves of the equilibrium system to be studied after the calibration curves In this case the file TASKNAME phv will contai
79. far Line 13 in Listing 3 3 indicates that the titrant is contaminated with 1 carbonate anion which is a significant amount when precise measurements are required 3 3 Complete Evaluation of Equilibrium Measurements 51 Listing 3 3 The content of aspph e res file 1 Input file ASPPH e tid 2 Curve s 3 1 66 fitted data p H 2 0 11 6 22 30 omitted data from start end 4 2 79 fitted data p H 3 7 11 3 O 27 omitted data from start end 5 Estimated parameter values 6 Name Final value Std deviation Initial value of the last calculation 7 pKkw 1 378540E 01 3 984947E 02 1 372830E 01 8 Id 1 498100E 01 8 726922E 03 1 369870E 01 9 m 9 900779E 01 4 091968E 03 9 959890E 01 10 JH p 0 000000E 00 fixed Fitting is not recommended 11 JOH p 9 000000E 00 fixed Fitting is not recommended 12 C_base 9 945512E 02 9 304050E 05 9 940650E 02 13 C_C03 1 103565E 03 8 882159E 05 1 007220E 03 14 lgB1_C03 1 020000E 01 fixed 15 lgB2_C03 1 630000E 01 fixed 16 lgB1_A 4 718486E 00 1 232788E 02 4 696890E 00 17 lgB2_A 7 425175E 00 1 776282E 02 7 391980E 00 18 VO_c1 2 500000E 01 fixed 19 THO_cl 2 007876E 02 1 872289E 05 2 016670E 02 CTHO_base 0 000000E 00 20 TAO_c1 0 Q000000E 00 fixed 21 Shft_cl 0 000000E 00 fixed 22 VO_c2 2 500000E 01 fixed 23 THO_c2 0 000000E 00 fixed CTHO_base 2 000000E 02 24 TAO_c2 2 Q000000E 02 fixed 25 Shft_c2 7 997806E 03 3 722839E 03 0 000000E 00 26 Experimental uncertain
80. fitted in practice The titrant base hopefully does not have that much carbonate contamination to get enough experimental information from the titrations to determine the cumulative formation constants correctly The values of these constants at the actual ionic strength can be taken from databases or tables see 19 for example In the second part of the input data files shown in Listing 2 2 for the reference example and in the appropriate lines of Listing 2 4 if pH was measured the titration curves should be entered In the reference example lines 15 89 define the strong acid strong base titration curves while lines 90 171 define the weak acid strong base ones Each titration curve begins with a header five data four of these are fittable parameters before the measured points They are the followings Line 15 contains a real number which e must be 0 0 in case of strong acid strong base titration and The experimental uncertainty of pH is 0 00169 pH unit in each installed data file Theoretically this value corresponds to 0 1 mV so the results of the analogue calculations become comparable In practice any similar value e g 0 002 works perfectly 20 Reference Guide Listing 2 2 Reference Data File with Potentials Part II kh1 13e tid 1 0 00000E 00 H A ratio in the weighted material or 0 for curve 1 2 6 03500E 00 0 VO in cm3 for curve 1 parameter 31 3 1 00000E 0 1 1 TCH O in mol dm3 for curv
81. fitting might miss the minimum even when the best initial values are entered This fact can be illustrated on the reference example of Chapter 2 The inital work window of the kh1 13e tid file is shown in Figure 2 5 while the final work window after omitting the points outside of the Nernstian range is displayed in Figure 2 7 The exclusion of the points however is not needed to be done from the graphical work window By suitably choosing the values of the relative weighting factors the tid file can be written so that pHCali is able to distinguish between the points even before the fitting procedure It can be simply done for the reference example in the following way e The kh1 13e tid file should be copied to k tid 55 56 Practical Guide Skip less at wn pkw 1 906 Eps Tiff m Pdf pNg o omitted date fitted data fitted curve s MMMM curve 1 V cm5 Figure 4 1 The final work window of the reference example in case of a bad fitting e In the k tid file all weighting factors are set to 1 0 but they are written in two forms 1 0e 00 or 1 0e 00 The first form is connected to the points which are excluded from the fitting in Figure 2 7 If the strings 1 0e 00 in the k tid file are changed to 1 0e 20 then the execution of the program would directly lead to the work window seen in the referenced figure But the real result can be seen in Figure 4 1
82. h the help of pHCali Chapter 4 helps the user to master the program effectively and trustworthily pHCali is not simply another method for evaluation of calibration measurements The program has many other features These capabilities however can only be used if the experimental data are accurate enough and carry appropriate amount of experimental information for the calibration Furthermore the orthogonal distance regression has some properties that are different from the conventional regression methods and they may confuse the 10 Introduction inexperienced user a little bit For these reasons this chapter summarizes hints and the practical experience collected so far which can improve the accuracy of the calibration and the determination of stability constants 1 4 Installation Minimum requirements e 386DX 40 MHz processor e 2 Mbyte DOS Windows or 6 Mbyte Linux free disk space e 4Mbyte memory in text mode or 8 Mbyte in other modes VGA compatible graphics card but the calculation itself does not require graphics capa bility and e MS DOS 5 0 Windows 95 or Linux with kernel 2 0 Acceptable configuration e 486DX 100 MHz processor or better e 2 Mbyte DOS Windows or 6 Mbyte Linux free disk space 4 Mbyte for each variant of the manual in PDF format e 8 Mbyte memory in text mode or 32 Mbyte in other modes VESA compatible graphics card with 800x600 resolution and 8bit color depth and e MS DOS 6
83. he actual titration curve The second upper botton end adds previously omitted points to the end of the curve The lower two buttons start and end do the opposite operation i e they remove more points from the actual curves for the next fitting By clicking on the left side of one of the buttons in the third column the number of points is changed by one On the other hand clicking the right side changes the number of points by a maximum of five This fact is emphasized by the displayed one and five dots in the operating panel The different clicking areas are separated with a vertical line drawn through all the buttons within the third column The fourth column of the operating panel contains buttons with miscellaneous functions and labels The Calculate button carries out the fitting regarding the changes made through the operating panel The work window is redrawn at the end of the calculations The WOFKIAGMY button is not a clickable one it only changes its background color from CARS to magenta until the calculations are finished The two text legends contain the two most important results of the fitting namely the pKw and the slope of the Nernst like equation The EMS button creates the result files and either stops running or returns to the parameter modifier window depending on the setting in the 35 line of the phcali cfg file In the last two columns of the operating panel 12 buttons can be found with background by d
84. he latter case the background color is determined by the document in which the image file was inserted Default as defined in the first line Line 3 defines the colors of the axes grids axis titles and labels of the figures The values can be between 0 15 or can be given as RGB color Default dark gray Lines 4 13 define the colors of the ten possible curves respectively The values can be between 0 15 or can be given as RGB colors Default 1 red 2 blue 3 magenta 4 green 5 cyan 6 light red 7 light blue 8 light magenta 9 light green and 10 light cyan Line 14 defines the symbol of the fitted data in the figure The value can be between 0 23 Default solid circle e Line 15 defines the symbol of the experimental points excluded from the fitting The value can be between 0 23 2 2 Input Files 25 Default empty circle o Lines 16 18 define the sizes of the symbols used in the lower left lower right and upper left figures of the graphical window respectively The value can be between 0 32768 but it is meaningful only between 0 109 Default lower left 12 lower right 20 and upper left figure 16 Line 19 defines the sizes of the axis titles and axis labels in the lower left figure of the graphical window The value can be between 0 32768 but it is meaningful only between 0 100 Default 30 Line 20 is the same as line 19 except that it corresponds to the upper left and lower right figures Defau
85. he point that only the first five characters are taken from the TASKNAME The first seven of the above mentioned formats are vector graphics which means that they can be enlarged or shrinked without loss of quality The last five formats are bitmaps which may suffer loss of quality due to resizing The resolution of the svg tif png ppm bmp and gif image files to be saved can be changed arbitrarily through the configuration file The size of ps type image files corresponds to the size of an A4 paper The size of the other image types inherits the ratio of the size of the work window The following sections detail each step of the usage of the program Section 2 2 describes the structure of the input files Section 2 3 details the use of the program while in Section 2 4 the interpretation of the output files is given Homepage http www cs wisc edu ghost Under pure DOS this option is not working probably due to a bug of the DISLIN library 3Homepage http www adobe com During the creation of such files the colors are lost a greyscale image is saved Homepage http www w3 org Graphics SVG Homepage http java sun com applets 7Homepage http www awaresystems be imaging tiff faq html SHomepage http www libpng org pub png Homepage http netpbm sourceforge net doc ppm html 10Information http www dcs ed ac uk home mxr gf x 2d GIF89a txt 18 Reference Guide Table 2 1 Examples for the interpretat
86. he used instrument was 0 1 mV Extremely erroneous points to be excluded cannot be found Perhaps the first and the last points of the strong acid strong base titration curve might be excluded with the help of the operating panel After omitting these two points the state of the work window is shown in Figure 3 2 After clicking the save amp quit button the program creates the result files and terminates Three result files have been created 1 The kh2 12e cin is the same as kh2 12e tid except for two differences 1 The cin file contains the fitted values of the parameters instead of the initial ones and 2 it includes the changed weighting factors according to the modifications done via the operation panel The program uses the relative weighting factors for the exclusion inclusion of the experimental points This topic is discussed in Subsection 2 2 1 where choosing the titration point to be fitted is detailed The purpose of this result file is to save the modifications in the form of input data and let the user carry out further evaluations by using this file Since there are no further calculations in the first example this file has no significance at this moment 2 The kh2 12e res file contains the essential results of the fitting The detailed discussion of this file is given in Subsection 2 4 1 but for users familiar with curve fitting the file itself may seem self explanatory Maybe the names of the parameters inside pHCali sh
87. hitecture The executables some parts of the documentation and the example files are to be found in the freely downloadable lphcali tgz file The installation is suggested to be done the following way e A directory should be created within the home username directory of the user in which pHCaili will be installed e The file lphcali tgz has be copied in the previously created directory and extracted with the tar xzf lphcali tgz command e The file 1lphcali tgz can be deleted after extraction Certainly there are other means of the installation If more than one users want to use the program and they do not want to have multiple copies of it on the fixed drives then the administrator root may copy the executables to the appropriate directories The above described method however does not require the help of the system administrator any user is able to carry out the installation alone After the installation the programs are ready to use In case the directory of the pHCali exists in the PATH environment variable then the program can be started from an X terminal window with the phcalit phcalix phcalit shared or phcalix shared commands Oth erwise phcalit phcalix etc commands should be used The programs can also be started by clicking on an icon The creation procedure of an icon depends very much on the window manager or graphical desktop used The file phcali png can be used as the image file of the icon The executables ph
88. hoosing one parameter the values of the other fields are automatically updated The initial value of the chosen parameter can be changed within the number field The change is interpreted by the program after pressing the Enter key If the syntax of the value is correct then it is also displayed in the list The same stands for the check box In case it is checked the specific parameter is to be fitted If the user requested the program to return to the parameter modifier window in line 35 of the phcali cfg file then the program can only be terminated from this window using the Quit button 2 3 4 Usage of the Work Window Before opening the work window pHCali carries out the fitting with the initial parameter values and draws the results on the screen The initial look of the work window is shown in Figure 2 5 in case of the reference example Figure 2 6 shows the appearance of the work window when the measured pH values are fitted instead of potentials The work window is split into four parts 1 The lower left part the figure shows the titration curves Each curve is plotted with different colors The symbols represent the measured data The solid symbols are the points that were taken into account during the fitting and the empty symbols show data eliminated from the calculations The dashed lines represent the curve calculated using the initial values of the parameters while solid lines give the curves calculated using the 2Main
89. i can be run from a character based window opened in graphical user interface i e DOS window in Windows or terminal in X Window Either mouse or keyboard can be used as input device This variant has two menu windows beside the work window The first one is called file choosing window and the second one is called parameter modifying window All the input parameters can be altered through these two windows without the use of command line arguments The messages of the program appear in the character based window If no such window is opened then the program automatically opens one at start and closes it before exiting This mode is to be started mainly from command line but may also be started via clicking on the icon Window mode This variant of pHCali can be started from a graphical workspace as well as from command line The only difference of this mode from the console one is that window mode creates a file called phcali msg to store the program messages and it does not write them on the screen 1 3 How to Read this Manual The installation of the program and the example files under different operating systems are described in Section 1 4 The program is expected to be used by people already familiar with the calibration pro cedure of pH metric instruments and with the chemical and mathematical background It is not the purpose of this manual to discuss these basics but for the sake of clarity of the notation system the Appendix see page 67
90. ile if pH is fitted 2 42 The image file belonging to the final fit in the second example method 1 42 The image file belonging to the final fit in the second example method 2 44 The work window of the aspph a tid file in the third example 47 The work window of the aspph b tid file in the third example 48 The work window of the aspph c tid file in the third example 49 The final work window of the aspph c tid file in example 3 or the initial work window of the aspph d tid file 2 008 49 The work window of the aspph e tid file in the third example 50 The final work window of the aspbeta tid file in the third example if the total concentration of aspartate ion is fixed 00048 53 The final work window of the aspbeta tid file in the third example if the total concentration of aspartate ion is fitted 0004 53 4 4 1 4 2 4 3 4 4 4 5 The final work window of the reference example in case of a bad fitting Titration of hydrochloric and malonic acid solutions with KOH contaminated by 5 carbonate Titration of different acid solutions with KOH solution The work window of using the kh113ejl tidfile 0 The work window of using the kh113ej2 tidfile 00 Listings 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 3 1 3 2 3 3 3 4 Reference Data File with Potentials Part I kh1 13e tid
91. ile the second number gives the relative error of the measured volume Vm expressed in ratio In the first case every measured volume has a constant uncertainty In contrast the error is linearly proportional to the measured volume in the second case The program calculates the error in both ways for every measured data and it uses the bigger value for the further calculations If only one method can be applied for the burette that is used then the value belonging to the other method must be zero Is is important to know that the success of orthogonal fitting depends largely on the accurately given experimental uncertainties That is why the values of these data should be given with great caution Lines 3 14 contain those parameters that affect all titration curves All lines except line 12 contain one real and one integer number The real one is the initial value of the parameter The integer indicates whether the corresponding parameter should be fitted 1 or fixed 0 Lines 3 11 define the following parameters pKw E or Ia me or Mp JH or ee Jon or Jor Cv Ce lg BY and lg BS respectively Line 12 gives the number of cumulative formation constants of the titrated weak acid In case of KH phtalate this value is two so lines 13 and 14 contain the values of lg 8 and lg B3 It must be noted that the cumulative formation constants of the carbonate ion are in lines 10 11 Theoretically these parameters may be fitted but they must not be
92. indeed an extreme one which may only occur if KH phtalate is used as it is The followings work with every variant of pHCali but the necessary modifications can be carried out most simply through the parameter modifier window 4 2 Importance of the Constant lonic Strength 57 described in Section 4 6 The latter considerations can be summarized so that it is a good idea to modify the initial values to be fitted in case of wrong results The lower left graph of the work window gives a great help Here the curves calculated with the initial parameter values are drawn with dashed lines Using these curves it can be estimated which parameter has to be modified and to which direction But before doing any changes it is advised to press the calculate button several times and check if the result improved or not The number of iterations is maximized in the program so the too slow convergence may alone cause the error for a poorly conditioned task In such cases the use of calculate button skips the maximum number of iterations An example can be seen using the 0x1 13ph tid if the 1 0e 00 strings are changed to 1 0e 20 see Section 4 6 Besides wrong final results it may also occur that the fitting is perfect but the volume data of an excluded point is misfitted resulting in distorted figures on the work window In most cases the reason for this behavior is the too small weighting factor i e it is less then one by many magnitudes of
93. indow contains two menus three buttons an information line and an information box below the others The functions can be accessed with the mouse or with the use of Tab Space and or Enter keys as usual The purpose of the menus and buttons are the following The Help menu displays the version number and the purpose of the program and it also informs how this manual can be accessed The File Change TASKNAME item or the information line makes possible to change the name of the task The button activates the open file dialog box of the operating system and lists the files having tid extension for the choice The name of the chosen file will be the TASKNAME without its extension The same name will be displayed in the information line as well The TASKNAME can also be changed in the information line without using the open file dialog box The OK button goes forward to the parameter modifier window The Quit button terminates the program The Edit a file button lets the user to start the preferred text editor in order to modify an arbitrary text file The preferred editor can be set in line 37 of the phcali cfg file The default is notepad exe under Windows and gvim under Linux The information box displays detailed information about the files to be read and the files to be created Its contents are actualized if TASKNAME is changed through either the File Change TASKNAME menu item or the information line 2 3 3 Usage of the Parame
94. ing factors defined in Section A 4 w w and wY In fact wr is rather used to calculate them using the following equations WR WR 5 and w me o 0 The values of the relative weighting factors are handled by the program in the following way wY e The largest value of them is 1 0 this is means the greatest contribution e If the value of the relative weighting factor is lt 0 0 then the specific point is omitted it will appear neither in the calculations nor on the figures These data are called deleted ones e If the weighting factor is a positive number but its value is lt 0 00001 then the program will remember the presence of the point and display it on the figures but pHCali will not include that point in the calculations These are the skipped data against the deleted ones e If the 0 00001 lt wp lt 1 0 relations are true then the program will use the given weighting factor at the calculations for the specific titration point Line 89 declares the end of the first titration curve A titration curve ends if e the TASKNAME tid file ends or e the given value for the volume is a negative number In this case the potential pH and the weighting factor should also be given or they should be replaced with a slash The value of the negative number may be interpreted in three different ways 1 0 or precisely a number between 0 99 and 9 9 means that a new titration curve follows in the input file 10
95. ing the icon of pHCali starts the program to calculate the required values If the program is started from icon then the appropriate file should be chosen from the file chooser window This method is the most simple one but it may most easily lead to wrong values so the usage of this method is not suggested The reasons are analyzed more deeply in Section 4 8 but as it can also be seen from the result of the fitting here see the lower right graph of Figure 3 4 this method leads to large and systematic deviations at high pH 2 The calculations are carried out in several successive steps e The program should be started as in case of the first method The experimental points in the non Nernstian ranges typically the pHms2 and pH 212 values should be omitted 42 Getting Started through Examples omitted data fitted data Initial curve s fitted curve s Number of skipped data Skip S E S E less at E esr pkw 13 823 Eps Tiff m 0 9976 Pdf pNg E curve 1 ES Sen ee ee A MEM curve 2 o 2 4 6 8 10 0 002 0 002 V cm5 pH pH Figure 3 3 The work window of the kh2 12ph tid file if pH is fitted E mV 200 H 100 E 100 H 200 H 300 E fitteddata initial curve s fitted curve s Results calculated by pHCali v1 30a 20061226 at Tue Dec 26 23 36 15 2006 TASKNAME kh1 13e Uncertainties V
96. ion of lines containing real R and integer I types for input values variable names and default values R 0 00 R2 3 14 I 365 R3 2 78 In 999 line to be read value of the variables after reading 0 00 3 14 365 2 78 999 1 41 1 73 12 2 24 24 1 41 1 73 12 2 24 24 1 41 1 73 12 2 24 24 1 41 1 73 12 2 24 24 1 41 1 41 3 14 365 2 78 999 1 41 12 24 1 41 3 14 12 2 78 24 1 41 12 24 1 41 3 14 12 2 78 24 rey 0 00 3 14 365 2 78 24 2 2 Input Files 2 2 1 The Input Data File TASKNAME tid or TASKNAME cin Each line of the input file contains one or more numbers that can be integers or reals The data are separated by one or more spaces Comma can also be used for separating data however only one comma can be placed betweeen two data This comma can be combined with one or more spaces After the data remarks may appear which must be separated from the data with at least a space or tabulator character and a slash Most data have default values so it is not required to give every data In this case however either 1 the place of the missing datum must be indicated with two neighboring commas and only spaces can be put between the commas or 2 the line has to be closed with a slash Both notations mean that there are missing data in the actual line and their default values must be used Table 2 1 gives some examples for the syntax of input data The detailed and precise rules of data reading can be found in
97. irst example the program can be started in two ways 1 by typing the command PROGNAME kh2 12e tid Enter or 2 by clicking on the icon of the program In the latter case the file chooser window appears see Subsection 2 3 2 and the user can choose the file kh2 12e tid from this window After pressing the OK button the parameter modifier window appears which can also be closed by clicking on the OK button After these steps all variants of the program open the work window The detailed inter pretation of the figures in the work window can be found in the first part of Subsection 2 3 4 39 40 Getting Started through Examples 0 015 7 Number of skipped data i SES Ec wot E S in pkw 13 827 Eps Tiff m 58 9959 Pdf pNg 0 010 0 005 0 000 2 Vo Vm cm 0 005 Lworking Cacuiate O omitted data E oe beeen eee ees Tend Oe Oe E 5 fitted data x Initial curve s 200 iD lt PEE FERVER INESE fitted curve s i E curve 1 rA eee hay Seeker RAA 100 Hes a ee eee eee eee z glera PEE ate a ee aE EE E hdres Pe E E TTE ata t o i gt ON E ERE ts see E EE E be E te ee ne ee ers oie lJ ki i 5 Bibesiciihiesi caas vis heaven ee wg ees Se tae nee eae tt EEE 100 p Baa ba ea ew TED Bh wa eee ee ee rr ret st E Soi I EEEE ARSE ASEE enone Ai E SELALA EEE E ESEE AEA
98. is the interpolation If the value of both Jy and aJon are fixed to zero the program automatically chooses this option i e the command PROGNAME kh1 13e tid automatically uses the interpolation in this example The essence of the interpolation is that the first strong acid strong base titration curve is taken from the input file and accordingly to the deviations of this curve from the Nernstian behavior the program corrects the titration data for the calculation of the p H values More information concerning the interpolation can be found in Subsection 2 4 3 and in Section 4 8 The limitations of the above methods are that 1 at least one strong acid strong base titration curve must be present 2 the ionic strength must be the same and set by the same medium in this titration and in the titrations belonging to the system to be studied after the calibration and 3 the response sign of the used electrode must be reproducible in the non Nernstian ranges too Measurements carefully planned and carried out usually fulfill these conditions 3 of ex 3 Complete Evaluation of Equilibrium Measurements The last example presents a complete investigation of an equilibrium reaction starting with the calibration and ending with the determination of the cumulative protonation constants the conjugated base of an unknown weak acid in the present case the aspartate The perimental data have been measured in a student s laborato
99. l q can be used for calibration purposes page 68 The protonation degree of the weighted form of weak acid page 72 The weighted sum of squares to be mini mized page 19 Experimental uncertainty of the measured volume OY mae ihe ch ke NS a e a ara lath page 19 Experimental uncertainty of the measured potential or pH The absolute temperature Ta page 68 The total concentration of the anion of the weak acid Te page 68 The total concentration of the carbonate ion TH page 68 The total concentration of the hydrogen ion Vo page 68 The initial volume of the solution to be titrated page 68 The total volume of the titrant base added at a given titration point 77 page 21 The abbreviation of relative weighting fac tor page 72 The weighting factor of the volume wy page 72 The weighting factor of the potential or pH page 67 The equilibrium concentration of X species page 70 The charge number of hydrogen ion Definitions console mode page 8 This variant of pHCali can be started from character based windows opened in graph ical user interface i e Windows or X Window Cala tile Aico eines eee tees page 8 See text file file chooser window page 28 A window for the modification of the base name of the given task see TASKNAME file page 8 Whole bulk of data that can be referred to gether by one name and it is placed in a stor
100. lculated analogue of Em A 3 2 Calculation of the Potential The theoretical electrode potential E from the Nernst equation can be given with the E E met Ag ay A 7 equation where E is the standard electrode potential of the hydrogen electrode its value is 0 V by defini tion R is the molar gas constant T is the absolute temperature z is the charge number of hydrogen ion i e its value is 1 F is the Faraday constant its value is 96485 31 C mol and ay is the activity of the hydrogen ion Its defining equation is ay y H where y is the mean activity coefficient In practice the calculated potentials are treated on the analogy of equation A 7 with the Ee E me Ig H E A 8 pH does not equal to p H as A 11 and A 12 equations will show below A 3 Calculation of a Point of the Titration Curve 71 equation where E and m are empirical constants They can be considered as formal standard potential and the actual slope respectively Where it is needed the notation EN emphasizes that the calculation was carried out using the Nernst equation only without the empirical extension terms see equation A 9 below E includes the reference electrode potential the diffusion potential and the mean activity coefficient of the investigated solution so their values should be kept to be constant during the measurement The constant values can generally be achieved by choosing an appropriate referenc
101. llum C Improved linear titration plots for weak acid titrations Talanta 21 723 1974 9 Schwartz L M Advances in acid base Gran plot technology J Chem Educ 64 947 1987 10 GNU Compiler Collection Home page http gcc gnu org 11 Boggs P T Byrd R H Rogers J E Schnabel R B User s Reference Guide for ODRPACK Version 2 01 Software for Weighted Orthogonal Distance Regression National Institute of Standards and Technology NISTIR 4834 1992 Home page http www boulder nist gov mcsd Staff JRogers odrpack html or http www netlib org 12 Page C G Professional Programmer s Guide to Fortran 77 University of Leicester UK 2001 Home page http www star le ac uk cgp fortran html or http www fortran com 13 Chievers I D Sleightholme J Interactive Fortran 77 University of London Computer Centre UK 1984 Home page http www kcl ac uk kis support cit fortran f77book pdf or http www fortran com 14 Michels H DISLIN the scientific data plotting software Home page http www mps mpg de dislin 79 80 References 15 Nagypal I Beck M Chemistry of Complex Equilibria Ellis Horwood Chicester 1990 ch 4 page 136 16 Press W H Flannery B P Teukolsky S A Vetterling W T Numerical Recipes in Pascal The Art of Scientific Computing Cambridge University Press Cambridge 1989 Home page http www nr com 17 Irving H M Miles M G and P
102. lt 25 Line 21 defines the size of the legend text in the lower left figure of the graphical window The value of the number can be between 0 32768 but it has practical meaning only between 0 100 Default 25 Line 22 defines the thickness of the lines in the lower left figure of the graphical window for the curves calculated from the initial parameter values The value of the number can be between 0 32768 but it has practical meaning only between 0 59 Default 1 Line 23 is the same as line 22 except it regards to the curves calculated from the final parameter values of the fitting Default 3 Line 24 defines the thickness of lines connecting the points in the lower right and upper left figures The value of the number can be between 0 32768 but it has practical meaning only between 0 50 Default 1 Lines 25 26 define the lengths of the major and minor ticks respectively in all figures of the graphical window The value of the number can be between 0 32768 but it has practical meaning only between 0 39 Default 16 major ticks and 8 minor ticks Lines 27 30 determine the background colors of 27 the Calculate and the point selector buttons 28 the save amp quit button 29 the working button and 30 the image file export buttons The value of the number can be between 0 15 or can be defined as RGB color Default Calculate BANESE Working and limageltiles Line 31 determines the minimum and ma
103. ly the wrong initial values can be identified by the help of these curves 30 Reference Guide 0 015 Number of skipped data Skip p SE S E c jess at Baam PS wmf Z ooy pkw 14 141 Eps Tiff 2 0 005 m 56 9784 Pdf png E hi gt oo L i Heal pee mes aie a ve oro 300 eee eee ee ee A o omitted data i i fitted data initial curve s fitted curve s 200 E EEEE fhe ETEA Palae i BE curve Vo 100 H N oe pee os AEDE PAE AIT APET TEE See ETETA 5 Ss Ojbiesseeee healers EEFT EPET ETETE TTT E i S i W SAOO Ei cates ties pe eagciga eth eet E E S200 Errrases rim ifj karetane E TEE A 300 H ET Besserssebessererejererireret fi fi i i i 1 i i i 1 i o 2 4 6 8 10 12 04 0 2 00 0 2 0 4 0 6 08 V cm Eo Em mV Figure 2 5 The initial work window of the reference example if potential is fitted o E 7 0 000 1 gt 0 005 0 015 Skip p ooo 0 005 Berar e ice ae erent es Ratan g Cae aie Ree eee Sel bape ct RU ha its 8 Alt hea RE AD AEII AET ET SEINS iE E ee ee er E ee Se certs ere eee ers eee ETO ee eet ee ee ee ers ee ee ee nr oer ere ra Ser ETE Rp wales wonetditnlnnciaceaceeerbeaes mesons gill E E TE omitted data De fitted dato E fhe initial curve s O A LINII CETT EEE erreren fitted curve s Bee cena da E T veel cts s
104. many other analytical methods there is still no generally accepted calibration method in pH metry Many methods are being used some of them are minor modifications of others 5 9 but the choice among the methods is based on local belief or trust rather than professional considerations The previously mentioned problems have already been known for very long time and many practical solutions have been developed to avoid them They work reasonably well as long as the studied chemical system is simple enough and the problems are not coupled But nowadays there is no simple chemical system to study and the fact of coupling is extremely In this document an electrode is called a Nernstian one if the above mentioned linear relationship is true but small deviation from the ideal slope i e 59 16 mV at 25 C may exist 7 8 Introduction Table 1 1 The name of the executable program under different operating systems operating system text mode console mode window mode DOS phcalid exe Windows phcalid exe phcalic exe phcaliw exe Linux statically linked phcalit phcalix Linux dinamically linked phcalit shared phcalix shared hard to discover in practice This may lead to identification of nonexistent species or ignoring existing ones in small concentration due to the lack of precise calibration pHCali intends to fill in these gaps by accomplishing the calibration without model sim plifications in a singl
105. mber in parentheses gives the page number where the most important usage of the notation or definition can be found or there is a more detailed explanation on the referred page Notations Ajy ees tsar an Sere Shee Pascal fo tad te page 71 A constant used by the pH metric instru ment to calculate the displayed pH from the measured potential a2 page 71 A constant used by the pH metric instru ment to calculate the displayed pH from the measured potential AHF aE E T EEA page 70 The activity of the hydrogen ion A a r E T ET E E a Sar page 67 The completely deprotonated anion of the weak acid Be page 67 The cumulative formation constant of the i times protonated anion of the weak acid defined by concentrations oe page 68 The cumulative formation constant de fined by concentrations of the hydrogen carbonate ion j 1 or the carbonic acid j 2 Ca page 68 The analytical concentration of weak acid in the solution to be titrated Ch Sen A tri eA hee the eu oe teenie page 68 The analytical concentration of hydroxid ion in the titrant base Ceo seer tide hia btn ted set aha A E AE ass Re page 68 The analytical concentration of carbonate ion in the titrant base The carbonate ion Ce wi Sli tei Saree oa et el page 68 The analytical concentration of additional strong acid in the solution to be titrated E aaeain eee eke tet page 71 Empirical constant formal standard poten tial
106. most obvious one is the Metapad Homepage http www liquidninja com metapad 2 3 Executing pHCali 27 Line 40 contains two integers to determine the horizontal and vertical size given in pixels of the savable image files These values influence the image files only if their form is svg tif png ppm bmp or gif Default 853 pixels horizontally and 603 pixels vertically 2 3 Executing pHCali pHCali can be run 1 from a command line by typing the name of the executable and the parameters 2 by clicking on the icon of the program or 3 by dragging one of the data files onto the icon of the program After starting the program e interprets the command line parameters in case of dragging the name of the data file is interpreted as the first command line parameter e opens the file chooser window in console and window mode in which the TASKNAME can be modified this window does not exist in text mode e opens the parameter modifier window this window does not exist in text mode as well in which the initial values and the fitting status of the parameters can be modified then e it opens the work window in which the fitting the inclusion exclusion of the experimental points can be done After completing the tasks in this window the program stops running or returns to the parameter modifier window if the user requests this in line 35 of the phcali cfg file 2 3 1 Optional Command Line Parameters The program can be s
107. n the V p H data pairs for the system to be studied This kind of data is the most practical input format for any further evaluation The fully detailed description of the structure of this file is given in subsection 2 4 3 phcali msg contains the messages in case of windowed mode versions of the program Originally the console mode versions send these messages to the screen phcali odr is the output file generated by the ODRPACK library and it contains a much more detailed description of the computation process and the results than the TASKNAME res file By default the file phcali odr is not created until the user requests it through line 33 of the phcali cfg The reason why the example files contain the numbers of the parameters besides their names is the more easily interpretable phcali odr This manual does not detail the structure of phcali odr The required information can be found in 11 Beyond the text files the figures created during the calculation can also be saved into image files under names TASKNAME where the extension can be one of the 12 supported image formats 2 1 Overview of the Program 17 ps means PostScript file which can be printed on PostScript printers directly or can be converted to other image formats using other applications e g Ghostscript and GSview eps means Encapsulated PostScript file which is mainly for inserting graphics into TEX documents but it can also be converted into other form
108. n curves significantly The hydrogen ion concentration is very low around the equivalence point thus small amount of carbonate will be able to form a buffer system according to the Henderson Hasselbach equation and it can be indicated by the orthogonal regression 4 6 How to Choose a Standard Compound for the Calibration In traditional calibration methods such as Gran s method 1 KH phtalate is used almost exclusively as the calibration standard compound In this practice the only point considered is that the calibration compound must be suitable to be weighted precisely the other possible criteria are neglected Subsection 1 1 has already detailed what problems arose with KH phtalate Indeed the necessity of simplified evaluation procedures in the pre computer era led to the fact that no other compound is used By using pHCali there are no necessary restrictions Compounds having more compli cated protonation processes can also be used as calibration material so the authors examined more compounds as applicable calibration materials The aspects of the selection and the comparison of the evaluation are summarized in Table 4 1 The four rows following the header row and the names of the data files show the values needed to apply the aspects The lower part of the table contains six criteria and the points gathered by each compound The interpretation of the points are given in the caption of the table The order of the aspects 4 6 Cho
109. nd the index k generally points to the k titration point The sum of squares function defined by equations A 13 can take into account only the experimental errors of the measured potential or pH not those of the volume In order to take also the uncertainty of the volume into account the definition of the sum of squares function has to be modified according to the following equations Awe S Bi BF Kw Vo CasCs Cbs Co Ver E Me Jn Jon p D We Ema Eek WE Vm Vex or A 14a k 1 S Be Kw Vo Ca Cs Cp Coy Veb la Mp Pi Sa p J We PHine pHo wX Vink Vex A 14b k 1 Sih ase as where V is the calculated volume w is the weighting factor of the volume and w is the weighting factor of the potential or pH Equations A 14 make it possible to carry out the calculation by orthogonal regression A 4 Calculation of Parameter Values 73 In usual calibration procedures the values of BS s Vo Ca and probably those of f s are well known so the aim is to determine the values of Kw Cs C Ce and perhaps those of B A s Besides them the values of E mg Jy and Joy can be determined in case of potential measurement or those of Ig mp J and J p in case of pH measurement If these parameters are accurately known an arbitrary Em or pH value can be transformed into a p H value for which the equations describing chemical equilibria can be applied NOTATIONS AND DEFINITIONS The nu
110. ndows Default The width and height are 636 and 400 pixels respectively The window is centered in both directions on the screen This option is not functional under DOS Line 38 contains four integers to determine the position and size of the work window All numbers must be given in pixels The first two numbers determine how far the upper left corner of the window has to be placed from the upper and left edges of the screen The third and fourth numbers determine the width and height of the windows Default The weight and height of the window are 90 of those of the screen respectively The window is centered in both directions on the screen This option is not functional under DOS Line 39 contains a logical value If it is TRUE the program skips the file chooser and parameter modifier windows and opens directly the work window This option has the same effect as the second command line parameter see Subsection 2 3 1 Default the above mentioned two windows appear when pHCali is executed This option is not functional under DOS This possibility may make the study of the examples in Chapter 3 easier if the user uses the console or window mode variant of the program 20 Although Notepad is the default text editor in Windows it is too simple even for the most basic editing tasks For example this editor does not display the actual character position Notepad can be replaced by numerous free and or commercial editors Perhaps the
111. nt of water pK and or the slope of the Nernst equation me or m By checking these two values the user can easily verify the goodness of the fitting therefore these values are displayed in the work window of the program Any other parameter value or statistical number may suggest some information for the user even in a very detailed form see the phcali odr file in Section 2 1 but these pieces of information did not prove to be always valid according to the experience obtained so far 4 8 Extending of the pH Range to be Calibrated Jy and Joy or interpolation should be used pHCali offers two methods to extend the calibration to the non Nernstian ranges 1 fitting Jn and Jon or Jy and J defined in equation A 9 or A 12 or 2 the interpolation In practice almost exclusively the first method is used presently but the theoretical foundations of this method have not been elaborated for the glass electrode see 2 It has been pointed by the use pHCali that systematic errors can certainly be committed if J and or Jon is fitted These risks are detailed in the following The final result of the reference example is shown in Figure 2 7 if the calibration was carried out within the Nernstian range The lower right part of the figure shows the first sign of the applicability of Jon If equation A 9 were applicable then the deviations in the potentials of both titration curves should be the same in the non Nernstian range at the basi
112. o be titrated the ionic strength has been set to 1 0 M with KCl so the change of the ionic strength during the titrations has always been less than 6 Both potential and pH have been registered during the experiments so both Em Vm and pHin Vin data series are available see the reference files kh1 13e tid and kh1 13ph tid supplied The explanations are based on the Em Vmn titration curves but whenever the pHm Vm Curves need to be handled differently the difference is emphasized 2 1 Overview of the Program The different variants of the program their execution and the data files required by them have already been described in Section 1 2 pHCali reads the input data from and writes the results into text files during runtime Figures representing the final results of the calculation can be saved as image files The filenames of the text and image files cannot be chosen freely The user must choose a name for each task to be evaluated This will be called TASKNAME from now on The TASKNAME must comply with the naming conventions of the used operating system and it must not contain spaces the use of underline sign _ is suggested instead The name of each input and output file is started with the given TASKNAME After the TASKNAME the extension stands separated from the name with a period There are text files that are connected to pHCali rather than the actual task The names of them begin with phcali and their extension determines thei
113. onnected to the weighted weak acid it was added into the initial solution indepentently Tt means that the anion of the weak acid was weighted in H A 4 form e g in case of KH phtalate q 2 but r 1 A 2 Calculation of Hydrogen lon Concentration 69 The equilibrium concentrations from equations A 2 can be substituted into equa tions A 3 and both A t and C Oz t are set off then the n 2 Tu i BA HHH IAT gt j BS TH CO3 H Ky H A 4a i l j 1 sags VAS Be wn A 4b re Te C03 gt BS r A 4c j l equations will be the result They contain three unknown quantities the equilibrium con centrations of the three components if the total concentrations and the cumulative formation constants are known The values of H A97 and COZ can be determined from equa tions A 4 with appropriate numerical methods and the equilibrium concentration of any species can be calculated using equations A 2 A 2 Calculation of Hydrogen lon Concentration at a Point of Titration Curve Rearranging equation A 4b for A97 and equation A 4c for COZ substituting these values into equation A 4a transforming the right side of the resulted equation to zero and multiplying the rearranged equation by H the n 2 i pa Ht eon joes aidi j l ID BolT 1 peH i 1 j l Ht Ty Ht K 0 A 5 equation will be the result If the total concentrations are substitu
114. osing Standard Compound for the Calibration 61 E Hcl Se een E KH phtalate E oxalic acid E malonic acid E succinic acid pHm V cm Figure 4 3 Titration of 6 035 cm 0 1 M acid solutions with 0 2 M KOH solu tion represents their order of importance too e The first two aspects the solubility and the capability to be weighted precisely are oblig atory If a compound got less than five points for any of these criteria then it was not suitable for calibration The authors examined more compounds those listed in the table but those which did not fulfill the above mentioned conditions are not discussed here Four compounds have remained after the first selection Their typical titration curves are shown in Figure 4 3 together with a typical strong acid strong base titration curve With the help of the figure the points given for the further aspects can be understood more easily The importance of the third aspect is that the too low or too high value of a stability constant must be determined together with the Jy or Jon from the same sections of the titration curves It certainly leads to otherwise avoidable correlations If the calibration only covers the Nernstian range the protonation processes in the Jy or Jon influenced range will be disturbing but the appropriate cumulative formation constants cannot be determined quantitatively The fourth aspect applies a general principle i e the
115. ould be identified These names can be found in the second part of Subsection 2 4 1 in detail 3 The kh2 12e crv file contains the measured and calculated curves The interpretation of the individual columns can be found in Subsection 2 4 2 The calibration can be carried out with the pH V titration curves as well In this case the objective is the same but the values of Ig and m defined in equation A 11 are determined instead of E and mg The kh2 12ph tid file provided during the installation contains the input data needed For this case the look of the work window is shown in Figure 3 3 The files created during the calculation can be interpreted the same way as potentials were measured 3 2 Calibration in Extended Measurement Range The second example demonstrates the capabilities of pHCali when the calibration also re quired outside of the Nernstian ranges This example is the same as the reference example throughout the guide so the experimental conditions of this measurement are described in the introductory part of Chapter 2 The program provides three methods for taking the deviation from the Nernstian behav ior into account 1 The user fits the values of J and Jop together with the usual calibration parameters It can be done by changing the 0 s to 1 s in the 14 column of lines 6 and 7 in the kh1 13e tid file see Listing 2 1 After saving these modifications either 1 the command PROGNAME kh1 13e tid or click
116. perience 60 Practical Guide Table 4 1 Comparison of the possible standard compounds for the calibration The data given in percent mean the largest ratio of the concentration of H2A species in the solutions to be titrated The points of the aspects are within a 1 5 range in which 5 is the best value so the largest total point corresponds to the most appropriate compound data and aspects KH phtalate oxalicacid malonic acid succinic acid data files kh1 13e ox1 13e mal 13e sul 13e without the extension tid kh1 13ph ox1 13ph ma1 13ph sul 13ph oyl 13e oy1 13ph lg Ky 4 7 3 6 5 1 Dez lg K2 2 7 1 1 2 6 4 0 max cm a Ta at Tu 0 2 M 8 42 85 97 max CH a Ta at TH 0 02 M 8 10 61 90 1 solubility 5 5 5 5 2 quantitatively weightable 5 5 5 5 3 the protonation processes are 5 2 5 5 inside the Nernstian range 4 lg K2 can accurately be 2 3 5 5 determined 5 the protonation processes are 3 4 4 2 not overlapped 6 there is no overlap with the 4 5 3 3 protonation of HCO Total point 24 24 27 25 Another important experience is that the carbonate content must always be fitted even if the level of the contamination is less than 0 1 Fixed 0 0 M value of carbonate concentration always resulted wrong slope and wrong ionic product of water during the calculations This phenomenon can be understood by the fact that even very little carbonate concentration changes the shape of the strong acid strong base titratio
117. r function Figure 2 1 summarizes the names of the text files where TASKNAME tid contains all the data required for the calculations the starting values of the parameters the titration curves and the Vm Em or Vm pHm data pairs needed for the Em pHm gt plH calculations The tid extension is the abbreviation of titration data The fully detailed description of the structure of this file is given in Subsection 2 2 1 phcali cfg is the name of the configuration file The operation of the program can be altered in this file The fully detailed description of the structure of this file is given in Subsection 2 2 2 TASKNAME cinis a file written by the program after the calculations Its structure and contents are identical to that of the file TASKNAME tid see Subsection 2 2 1 with the only difference that it contains the changes made during the last run which can be the following e handling of the parameters they are to be fitted or fixed 15 16 Reference Guide Input files Output files TASKNAME tid TASKNAME cin phcali cfg TASKNAME res TASKNAME crv TASKNAME phv phcali msg phcali odr image files TASKNAME ps eps pdf hpg svg jav wmf tif png ppm bmp gif Figure 2 1 Input and output files of pHCali The framed files are required or always created while the others are optional e final values of the fitted parameters and e weighting factors o
118. r of the calculate and point selector buttons 28 12 color of the save amp quit button 29 13 color of the working button 30 11 color of the file exporting buttons 31 FALSE 0 0 0 0 if TRUE then xmin and xmax are given for LR graph 32 FALSE 0 0 0 0 if TRUE then ymin and ymax are given for UL graph 33 FALSE if TRUE then the report of ODRPACK is also written as phcali odr 34 TRUE if FALSE then the image files does not inlcude the UR description 35 FALSE if TRUE then the program returns to the modifying window after calc 36 notepad exe name of the preferred editor 37 1 1 0 0 place of menu windows in pixels x0 y0 xwidth and ydepth 38 1 1 0 0 place of work window in pixels x0 y0 xwidth and ydepth 39 FALSE if TRUE then the menu windows are skipped 40 853 603 width and height pixels of TIFF GIF PNG PPM BMP and SVG images logical value corresponds to the first syntax but now it determines only the default color of the background for transparent PNG and GIF image files see the second line The 2 4 and 5 7 integer values give the intensities of the red green and blue components of the colors for the background and foreground respectively Default white background with black foreground Line 2 determines the background of the PNG and GIF image files FALSE means that the background color is defined in the first line while TRUE means transparent background In t
119. r potential or pH may be measured the program is capable of handling both types of curves The titration data should be put in a text file The program uses these input data and it applies the orthogonal distance regression to determine the data required for further work that are then stored in text and image files More titration curves and their repetitions can be put into a single input file The program can handle up to 10 titration curves 10000 experimental data pairs and 9 protonation constants simultaneously The program has been written in Fortran 77 with the use of GNU Fortran g77 compiler 10 and two libraries the ODRPACK library 11 includes the subroutines for calculations and the DISLIN library 14 provides the graphics and user interface They ensure that pHCali can be run under various operating systems in several modes There are all together seven variants of the executable program in the following modes the names are shown in Table 1 1 At the time of writing this manual the experimental uncertainty of the advanced good quality pH metric instruments are 0 1 mV or 0 002 pH unit 3The precise definition of q can be found in Notations and definitions on page 75 1 3 How to Read this Manual 9 Text mode This variant of pHCali can be used on a character based full screen e g pure DOS It can only be used with keyboard and does not contain menu window before the work window Console mode This variant of pHCal
120. r simple In fact the measurement devices always measure potential directly The pH displayed on the screen of the device is only the result of a previous one two or three point adjustment calibration through which the user has taught the device how to calculate pH from the measured potential It isa common procedure that the device is set to a specific pH value of a buffer solution before the measurement of every titration curve Any failure in this operation may cause that not the same pHm Em function describes all the titration curves In this way the basic assumption is not fulfilled for devices calibrated to pH values The measured potential is not influenced by this adjustment so the potential data can still be evaluated The third example of Chapter 3 details how such problems can be identified and in some cases how the pHCali can take the change in the pHm Em curves into account 4 4 How Closely the Titration Points should be Measured In practice the titrant is dosed in two ways 1 The added volume is independent from the measured potential but the added volume portions are approximately constant The reason of this technique is that measured data around the equivalence point carry much more uncertainty in potential or pH than the other data so it is not worth to measure many points here these data would be excluded from the evaluation anyway This method enables the user to carry out the titration faster 2 The principle of
121. r this fitting it is expedient to handle the repeated curves together by pHCali as a single one The reason for this treatment comes from the nature of parameter estimation By fitting the repeated experiments separately more than one value should be fitted for some parameters e g the exact concentration of the strong acid The over parametrization of the task certainly leads to unnecessary correlations It is even more serious problem in case of orthogonal fitting than in the usual parameter estimation procedures see Section 4 1 To avoid this failure it is highly suggested to contract curves 1 3 and 4 6 of apph d tid into one one curve before the final fitting This change has already been made in the aspph e tid file 3The first point of the fifth curve is also omitted on this figure as an erroneous one 3 3 Complete Evaluation of Equilibrium Measurements 49 Number of skipped data Skip S_E S E less at pKw 13 844 m 0 9826 o omitted data e fitteddata initial curve s E curve 1 E curve 2 GENE curve 3 MMMM cirve 4 ME curve 5 6 MO ata ET Do E ouve i i 1 i 1 i ie 2 4 6 8 10 0 01 V cm i 1 i 0 00 0 01 0 02 0 03 0 04 PH PH rn Figure 3 8 The work window of the aspph c tid file in the third example Number of skipped data Skip S E S E c less _at pKw 13 730 m 0 9958 omitted data a ee fitted dat
122. ration curves were measured 1 6 035 cm 0 012 M HCI solution was titrated with 0 025 M KOH solution and 2 6 035 cm 0 1201 M KH phtalate solution was titrated with the same 0 025 M solution of KOH The ionic strength was adjusted to 1 0M with KCI both in the titrant and in the solutions to be titrated The change of the ionic strength during titrations was less than 1 2 Both the potential and the pH were measured during the experiments so the titration curves are available in both Em Vm and pHm Vm formats in the kh2 12e tid and kh2 12ph tid data files respectively These plain text files include all the input data required for the calculation namely the initial values of the parameters and the titration data The structure of the tid files is rather simple it can be understood easily but the detailed description can also be found in Subsection 2 2 1 The goal of calculation based on the two titration curves is to get the calibration param eters of the used instrument E and me from equation A 8 negative logarithm of the ion product constant of water pK as well as the precise concentrations of the strong base in the burette and the strong acid to be titrated cp and c In addition the program fits the two formation constants of KH phtalate Bi and p and also determines the carbonate content of the titrant c lt As it can be seen below pHCali solves these tasks in a single step In order to solve the task of the f
123. re MR os ME curve 1 SMM curve 20 gg eee L i 1 i L 1 j 1 1 y o 2 4 6 8 10 12 0 015 0 010 0 005 0 000 0 005 V cm5 pHo PHm Figure 2 6 The initial work window of the reference example if pH is fitted last parameter values The scaling and labeling of the axes are done automatically by the program The colors type and size of the symbols together with the thickness of lines can be defined within the phcali cfg file 2 3 Executing pHCali 31 This figure also contains the legend The symbols concerning all curves are written in black in this legend Colored rectangles show the colors of specific curves The order of the curves corresponds to the order within the TASKNAME tid file This legend corresponds to all figures of the work window 2 The lower right figure shows the differences between the calculated and measured poten tials or pHs as a function of the calculated pH pH The figure is rotated by 90 degrees so the pH axis of this figure precisely corresponds to the E or pH axis of the lower left figure The line connecting the points has no specific meaning it only provide better visibility for the trend of the curves The range of the horizontal axis of the figure can be set to arbitrary values by the user in line 31 of the phcali cfg file 3 The upper left figure shows the differences between the calculated and measured volumes as the function of the volum
124. ry on a device with 0 2mV tf the user had modified the kh1 13e tid file before then these modifications must be canceled first 3 3 Complete Evaluation of Equilibrium Measurements 45 Table 3 1 Weak acid strong base titration data in example 3 oe 4 Curve 5 Curve 6 V pHm Em V pHm Em V pHm Em V pHm Em V pHm Em V pHm Em cm mV cm mV_ cm mV cm mV cm mV cm3 mV 0 00 3 842 182 2 4 40 5 708 71 6 0 00 3 852 181 6 4 81 6 433 28 610 00 3 823 183 4 4 82 6 362 33 1 0 42 4 043 170 2 4 60 5 920 59 1 0 40 4 048 170 0 5 12 10 416 206 7 0 43 4 038 170 7 5 00 9 397 4484 0 81 4 223 159 6 4 80 6 295 37 0 0 80 4 228 159 4 0 80 4 212 160 4 5 20 10 565 2415 5 1 21 4 387 150 1 5 00 8 991 46 6 1 19 4 386 150 1 1 21 4 375 150 6 5 40 10 882 234 2 1 40 4 458 145 8 5 21 10 609 218 7 1 64 4 550 140 3 11 227 254 511 60 4 522 141 9 5 63 11 080 245 8 1 60 4 530 141 5 5 40 10 908 236 1 2 00 4 681 132 7 11 322 260 2 1 98 4 655 134 0 5 82 11 196 252 9 1 80 4 601 137 3 5 60 11 092 246 8 2 20 4 745 128 8 11 608 277 3 2 20 4 731 129 6 6 02 11 282 258 2 2 00 4 672 133 1 5 80 11 222 254 4 2 41 4 816 124 7 11 660 280 3 2 41 4 802 125 2 6 47 11 433 267 1 2 19 4 735 129 3 6 00 11 314 259 8 2 60 4 877 120 9 11 726 284 2 2 60 4 866 121 6 6 81 11 517 272 2 2 40 4 806 125 3 6 20 11 422 266 2 2 81 4 950 116 7 11 769 286 9 2 85 4 959 116 2 7 03 11 563 275 0 2 60 4 872 1
125. s but the theoretical grounding of them are the more dubious the more precise the applied measurement devices are For example the applicability of the formulas derived in the Gran method 1 requires the use of a monoprotic weak acid to determine the base concentration The acid should be weightable precisely and must have small dissociation constant In spite of these requirements KH phtalate is used in practice which is a biprotic anion its two protonation steps overlap and the simple buffer formula cannot be applied precisely for the first dissociation step in the frequently used concentration range 2 It is not resolved to take into account or to indicate the carbonate content of the titrant solution only practical advices are known 3 Many methods suppose that the electrode used during the measurements is ideal i e the relationship between the measured signal and the negative logarithm of the hydrogen ion concentration is linear and the slope of the straight line can be calculated from the Nernst equation These methods are not capable of taking either the deviation from the straight line or the deviation from the ideal slope into account only empirical suggestions exist 4 The extension of the calibration range into the non linear range is based on some old measurements 2 4 but their applicability to glass electrodes has neither been proved nor it has been investigated These problems lead to the state that in contrast to
126. sed so far The big advantage of the second method is that it does not hypothesize any relationship for the deviation from the Nernst equation There is also a disadvantage namely that no extrapolation is possible only interpolation is permitted A careful user is able to note that the two methods do not give the same p H values and their difference is larger than the experimental uncertainty The reason of this is not to be searched within the program rather than in the technique of the measurement That is why this problem is discussed deeply in Section 4 8 CHAPTER 3 GETTING STARTED THROUGH EXAMPLES This chapter introduces the abilities of the program through three examples The aim of the chapter is to help the user to gain experience as quickly as possible therefore detailed use of the program is not given here The examples refer to the appropriate parts of Chapter 2 if it is needed Before reading this chapter it is presupposed that the user has studied Chapter 1 and Section 2 1 Additionally the description of an example supposes that the reader has got through the previous ones Since the commands to be used differ due to the various names of the executables the name of the program is denoted with the PROGNAME word from now on The PROGNAME can be one of those described in Table 1 1 3 1 Calibration in the Nernstian Range This example shows how the most common calibration measurement can be evaluated by pHCali The next two tit
127. sition is achieved The table certainly contains the subjective opinion of the authors too but it is definitely informative for the user either if s he is looking for a calibration material or s he is searching a new compound This book shows the usage of pHCali through titrations based on KH phtalate since this compound is the most known During the installation the files belonging to the other possible calibration materials given in Table 4 1 are also installed on the user s computer so they can be studied as well These files can be interpreted in the same way as kh1 13e tid and kh1 13ph tid detailed previously The only exceptions are the files oy1 13e tid and oy1 13ph tid These are created to demonstrate how can the oxalic acid be treated as a monoprotic acid by excluding the points influenced by the second protonation process The denoting convention in these files the values of the relative weighting factors are 1 0 for each point but for the points outside the Nernstian range this value is given in 1 0e 00 while for the ones within the Nernstian range the string is 1 0e 00 4 7 Signs Suggesting the Existence of Experimental or Calculation Problems The practical knowledge accumulated during the evaluation of the measurements detailed in the introduction of this chapter can be summarized in one simple rule Any fitting or experimental problem significantly modifies the fitted value of the negative logarithm of the ion product consta
128. sting 2 6 in case of the reference example after the data omission described in the previous section has been carried out In the following this file is referred to but the line numbers mentioned may change in other tasks The contents of the result file can be divided into sections Every section starts with a title line It begins with five asterisks and then the name of the section comes The TASKNAME res consists of five sections Used version line 1 in Listing 2 6 This section gives the currently used version of pHCali Input file lines 2 5 in Listing 2 6 In this section the name of the input file and some important parameters of the titration curves are displayed For example line 4 says that the first titration curve contains 69 points of which the first 14 and the last 25 have been excluded from the fitting and the fitted data are in the p H 2 2 11 6 range e e Estimated parameter values lines 6 26 in Listing 2 6 In this section the parameters are given One parameter belongs to each line The parameters that were not fitted are marked with the label fixed In case of fitted parameters the initial value before the last calculation and the standard deviation of it is displayed in 2 4 Output Files 35 Listing 2 6 The content of kh1 13e res file corresponding to Figures 2 7 2 8 1 Used version pHCali v1 27a 20051208 2 Input file kh1 13e tid 3 Curve s 4 1 30 fitted data p H 2 2 11 6
129. tants must be taken into account in every titration point Ht OH gt H20 Ky H OHA Ala H A 17 i Ht AT H A17 Be or i N n and A 1b H cof 7 4 2 k 2 j e 3 oo j H CO H CO P ep qcom Oo 12 A 1c where X is the equilibrium concentration of X species H is the hydrogen ion OH is the hydroxide ion Ky is the ion product constant of water defined with concentrations its negative logarithm pK is used more frequently q is the charge number of the completely deprotonated anion of the weak acid A is the completely deprotonated anion of the weak acid HA1 is the i times protonated form of the anion of the weak acid n is the number of protonation steps concerning the anion of the weak acid BA is the cumulative formation constant of the i times protonated anion of the weak acid defined by concentrations C OF is the carbonate ion For the sake of simplicity hydrogen ion will be written everywhere even where hydroxonium ion H30 should be written Just for the sake of unambiguity n does not necessarily equals to q e g q 1 and n 2 for glycinate 67 68 Mathematical Description of Titration Curves H CO ee is the hydrogen carbonate ion j 1 or the carbonic acid j 2 and Br is the cumulative formation constant defined by concentrations of the hydrogen carbonate ion j 1 or the carbonic acid j 2 In the given titration point the equilibrium concen
130. tarted without any parameter but experienced users can use two command line parameters for using the program more efficiently 1 If the value of the optional first parameter is H h H or h then the program displays a brief help in text or console mode or it writes this help into the file phcali msg in windowed mode In all other cases the first parameter can be the TASKNAME or a minus sign If the first parameter is a minus sign or it is not given then the default value i e phcali is used for the TASKNAME If the end of the parameter contains the tid extension i e the user gave the name of the input file the program detaches the extension from the string and uses the remaining characters as the TASKNAME 2 The value of the optional second parameter can be either a minus sign or a colon In case of minus sign the program skips each graphical window it immediately carries out the fitting on the basis of the TASKNAME tid file it creates the result files and finally it stops running This option lets the program to work without any interaction so its usage can be automated with appropriate input files In case of colon the program skips the file chooser and parameter modifier windows and opens the work window directly This will speed up work if the user is sure that no changes are needed in the TASKNAME tid file This parameter has no effect in text mode since the mentioned windows
131. ted with the experimental volumes and the analytical concentrations from equations A 3 the equation A 5 will take its final form n 2 rp E 7 yee Ca Vo i l Ce Vm j 1 O oF e Moo SHH Vo Vin Vot Ving 2 i EES peT 1 gt BS HH 0 j l 2 T Ca Cs Vo Cv Vm Vo Vm Equation A 6 is an implicite equation giving the exact relation between the volume Vm and the concentration of the hydrogen ion H at a point of the titration If the other parameters B4 s Be Kw Vo Ca Cs Ch and ce are known then the H can be calculated from the value of the volume From equation A 6 the hydrogen ion concentration cannot be expressed in an explicit form by any rearrangement therefore numerical methods must be used to solve the equation It can be proved quite easily that the equation has one and only one positive solution for H at a given value of Vm It can be determined with the help of either the bisection or the modified secant method 16 with arbitrary precision H H Kw 70 Mathematical Description of Titration Curves A 3 Calculation of a Point of the Titration Curve A titration curve means measured potentials or measured pH values as the function of the volume of the titrant Em Vm or pHm Vm The potentials or pH values of a calculated titration curve are computed from the experimentally determined volumes E Vm or pHe Vm A 3 1 Various Definitions of pH and Potenti
132. ter Modifier Window The parameter modifier window is shown in Figure 2 4 in case of the reference example The initial values and the fitting state of the parameters can be modified before the calculations 2 3 Executing pHCali 29 ox Quit Help Parameter 1 pKw 1 380000E 01 fitted Parameter 2 E0 3 770000E 02 fitted Parameter 3 In1ORTzF 5 916000E 01 fitted Parameter 4 JH 0 000000E 00 fixed Parameter 6 JOH 0 000000E 00 fixed Parameter 18 C_base 1 900000E 01 fitted Parameter 19 C_CO3 1 000000E 03 fitted Parameter 20 lgB1_CO3 1 020000E 01 fixed Parameter pKw Initial value 1 380000E 01 lv Fitted Figure 2 4 The parameter modifier window in case of the reference example by the help of this window The window contains three buttons a list box an inactive text field an active number field and a check box They can be used either with mouse or with the help of Tab Space and or Enter keys as usual The functions of the OK and Quit buttons are the same as those described in the previous subsection except that pressing the OK button the program goes forward to the work window The Help button outlines the usage of the window In order to modify a parameter the specific item must be chosen in the list For each parameter the list shows the serial number attached by the program the name the initial value and the actual fitting state fitted or fixed By c
133. ters 4 Vc Calculated volumes using the final values of the parameters Ve 5 Ec or pHc Calculated potentials or pH s using the final values of the parameters Ee or pHe 6 Verr Ve Vm Z Eerr or pHerr Ee Em or pHe pHm 8 p H Negative logarithm of H p HI 2 4 Output Files 37 9 Vm This column is the same as the first one but asterisks replace data omitted from the fitting 10 Em or pHm This column is the same as the second one but asterisks replace data omitted from the fitting 11 JH H JOH OH or Extent of the deviation from the Nerst equation Kw JH p H JOH p 0H expressed in potential or pH Ju H Jon mi Kw or I HH 5 2 4 3 The Structure of the pH values File TASKNAME phv The back calculated p H values are stored in the TASKNAME phv file for the titration points given in the third part of the file TASKNAME tid In the reference example the contents of the kh1 13e phv file is shown in Listing 2 7 For this the calculations were carried out according to the point exclusions shown in Figure 2 7 and 2 8 and the values of Jy and Jon have been fixed to 0 0 Listing 2 8 displays the resulted TASKNAME phv file when every point was included in the fitting and the values of Jy and Jon were fitted too together with the previously fitted parameters The structure of TASKNAME phv is rather simple it consists of a total four columns con taining the Vm values the p H val
134. the second procedure is that the bigger the change in the potential is the smaller the next added volume should be At the most steep ranges of the titration curve as dense the measurements should follow each other as the burette is capable for within its technical limitations Using this method certainly more time is required to carry out a titration For pHCali definitely the second method is preferable The orthogonal curve fitting is capable to evaluate the points around the equivalence point too On the other hand the equations on which the program is based do not apply any approximations These two facts together make it possible to evaluate the complete titration curve without any preliminary exclusion Using pHCali experimental data should be excluded only if 1 the data is erroneous or 2 some of the points are in the non Nernstian range It is extremely important to measure around the equivalence point during a calibration measurement Independent experimental information to determine the carbonate content can only be found on the strong acid strong base titration curves near the equivalence point If this range is skipped during the measurement the program is less capable to determine the carbonate content Considering this fact the strong acid strong base titration of the first example in Chapter 3 is a completely suitable one see Figure 3 1 while the curve in case of the third example seems a bit rough and ready around the
135. this behavior The twice protonated anions of the weak acids do not have charge thus the ionic strength is determined by the KCl in the acidic part of all titration curves In basic medium however this fact is not valid If strong acid is titrated then the ionic strength is determined by both the KCI and the excess of KOH In case of weak acid the concentration of its completely deprotonated anion is also significant This anion significantly contributes to the ionic strength with its two negative charges It follows that equation A 9 cannot be generally valid but it may still be applied if the ionic strength is constant and the ionic strength setting salt does not change during titrations This limited validity must be studied next It is generally true in an equilibrium system that the ionic strength setting salt and the value of the ionic strength are the same in the system to be investigated as they were during the strong acid strong base titration of the calibration On the basis of this fact it can be said that Jy and Jon may be fitted but the non Nernstian points at the basic end of the weak acid strong base titration must be omitted from the calibration In case of the reference example the results of the fitting of Jy and Jon are shown on figures 4 4 and 4 5 The first figure belongs to a two step fitting At first only the parameters influencing the Nernstian range were fitted In the second step the previously determined values w
136. thogonal regression depends more on the correct initial values of the fitted parameters and the experimental errors than in case of the usual parameter estimation procedures The reason of this is that the orthogonal curve fitting treats the volume data as to be fitted although with some constraints together with the other parameters Thus the number of the fitted parameters is more than usual This feature greatly increases the correlation between the parameters i e how the parameters can be substituted with each other Moreover the mathematical equations describing the titration curves equation A 6 and equation A 9 or A 12 contain parameters that are already in large correlation with each other From mathematical aspect the fitting of the parameters in such equations is a very difficult task The following advices are able to aid the successful fitting 1 The parameters with already known exact values are not fitted They can be for example the concentrations or cumulative formation constants exactly known from independent measurements 2 The obviously erroneous experimental points must be excluded An example is shown in the first step of the calibration task described in Section 3 3 3 The initial values of the parameters must be estimated with great caution Differences in the order of magnitude are not tolerated by the orthogonal fitting usually A good approximation is satisfactory in most cases but in extreme situations the
137. ties 27 1 000E 02 or 1 000E 03 Vm cm3 for the volume whichever is larger 28 4 000E 03 unit for pH 29 Goodness of Fit statistics 30 Number of iterations 7 31 Number of function evaluations 63 32 Number of Jacobian evaluations 9 33 Rank deficiency 0 34 Average of weighted deviation of volume 1 107074E 02 35 only for curve 1 1 245299E 02 36 only for curve 2 9 639059E 03 37 Average of weighted deviation of pH 2 575632E 03 38 only for curve 1 2 937330E 03 39 only for curve 2 2 198632E 03 e The deviation in the slope of the electrode used from the ideal Nernstian value can be corrected see line 9 in Listing 3 3 e It is not needed to know or to believe the pH range in which the Nernst equation is valid for the electrode used The appropriate range can simply be determined visually by omitting including points at the beginning and at the end of the titration curves It is highly important to know this range when the user investigates the equilibrium system the measuring device should be calibrated for e The possible errors during the experiments can be either corrected see the shift parameter in line 25 of Listing 3 3 or indicated e g the carbonate content of the strong base These errors usually remained hidden using the conventional calibration procedures so far 3 3 2 Determination of Formation Constants If only protonation equilibria are present in the system to be studied by the user another program is not
138. trations of all species can be expressed according to the equations A 1 if the equilibrium concentrations of the components H A97 C OF and the formation constants are known OH Ky HH 7 A 2a HA7 BA HHA i 1 n and A 2b HjCOy Bo a GS Ts 42 A 2c The total concentrations of the components in the titration point corresponding to Vin 1 can be given with the experimental volumes and the analytical concentrations and 2 can also be expressed using the equilibrium concentrations T Ca Cs Vo TE ey E j H co 7 H 0H A 3a kero AT nn and A 3b Ce V c m 2 H A Te TIRA CO2 2N CO A 3c where Ty is the total concentration of the hydrogen ion Ta is the total concentration of the anion of the weak acid Tc is the total concentration of the carbonate ion Vo is the initial volume of the solution to be titrated Vm is the total volume of the titrant base added at a given titration point Cp is the analytical concentration of hydroxide ion in the titrant base Ce is the analytical concentration of carbonate ion in the titrant base Ca is the analytical concentration of weak acid in the solution to be titrated Cs is the analytical concentration of additional strong acid in the solution to be titrated and r is the protonation degree of the weighted form of weak acid 3 Additional strong acid means that this amount of hydrogen ion was not originally c
139. ues the Em or pHm values and the back calculated Ee or pH values from the equation A 8 respectively see equation A 11 on page 71 for the relationship of p H and pH The first three columns need no further discussion Column 4 have no significance if the Nernst equation is valid for the whole calibrated range If it is not true column 4 contains the expected value of the given titration point if the Nernst equation is suspected to be valid The difference between columns 3 and 4 shows the extent of the deviation from the Nernstian behavior pHCali is able to calculate the values of the fourth column in two ways 25 1 If at least one of the values of J and Jon is fitted or one of them is fixed to a nonzero value then the program uses equation A 9 in case of potential is measured or equation A 12 if pH is measured to calculate the values of the fourth column In such case it is not advisable to exclude experimental points because this omission may decrease the experimental information required for the correct fitting of the parameters Listing 2 8 contains the results of the calculation carried out this way 2 The strictly Nernstian range must be found by systematic exclusion of the non Nernstian points The program then will compare the calculated points with the points of the first strong acid strong base titration and it uses interpolation to correct the measured data The data calculated by this interpolation will b
140. uped in two columns are connected to one titration curve The frames vertical divider lines and the serial numbers of the buttons are colored according to the appropriate curve settings Clicking on one of the buttons put the connected curve into the focus so every further change affects this curve The background color of the active curve is by default while the others are light gray If less than ten curves are present in the actual task e g there are only two ones in the reference example the buttons of the unavailable curves have black lines and background Every button contains two numbers The left one indicates how many points are to be excluded from the beginning of the curve The right number indicates the number of data to be excluded at the end of the curve These numbers change if the user excludes or includes points for the next fitting Points cannot be excluded from the center of curves using the operation panel Such changes have to be made manually by modifying the weighting factors within the TASKNAME tid file The interpretation of the relative weighting factors is described in Subsection 2 2 1 see the description of lines 22 80 e By clicking on the buttons in the third column having yellow background by default the number of those points can be changed which are taken into account in the fitting The topmost start button adds previously excluded points if there is any to the beginning 32 Reference Guide of t
141. ven Line 1 contains the the experimental uncertainty of the measured potential pH o expressed inmV orin pH units This value is around 0 1 mV 0 002 pH unit in case of high end devices The next line number references will refer to the kh1 13e tid data file but the line numbers may differ in other systems 2 2 Input Files 19 Listing 2 1 Reference Data File with Potentials Part I kh1 13e tid 1 0 1 uncertainty of Em curve 1 HCl 2 0 002 0 0003 uncertainty of Vm curve 2 KH phthalate 3 1 38000E 01 1 pkw arameter 1 4 3 77000E 02 1 EO arameter 2 5 5 91600E 01 1 m 1n 10 RT zF arameter 3 6 0 00000E 00 JH arameter 4 7 0 00000E 00 O JoH arameter 6 8 1 90000E 01 1 cO in mol dm3 for the base solution arameter 18 9 1 Q00Q0Q00E 03 1 cC C032 in mol dm3 for the impuritites arameter 19 10 1 02000E 01 0 log beta_1 for C032 arameter 20 i 1 63000E 01 0 log beta_2 for C032 arameter 21 12 2 number of given formation constants lt 9 13 4 60000E 00 1 log beta_1 for the weak acid arameter 22 14 7 30000E 00 1 log beta_2 for the weak acid arameter 23 Using low end devices this value can be as high as 1 mV 0 02 pH units Line 2 gives the experimental uncertainty of the volume 0 which may be considered either to be absolute or relative depending on the type of burette used Two real numbers must be given here The first one gives the absolute value of uncertainty in cm s wh
142. ximum values of the horizontal axis in the lower right figure of the graphical window A logical value and two real numbers must be given here If the first data is FALSE then the program automatically determines the minimum and maximum values regardless of the given real numbers If both reals are zero the same happens independently of the logical value If the value of the logical variable is TRUE and at least one real number is different from zero then the real numbers determine the minimum and maximum respectively Default the program calculates the limits Line 32 is analogous to the previous line except it corresponds to the vertical axis in the upper left figure Default the program calculates the limits Line 33 determines whether the original messages of the ODRPACK library used for the 26 Reference Guide orthogonal regression are to be available for the user A logical value is required here In case the value is TRUE the program stores the messages in the phcali odr file In case of FALSE this file is not created The messages of the ODRPACK library are much more detailed than those of pHCali so those users who are interested in orthogonal regression are suggested to let this file created This manual does not explain the ODRPACK library itself in detail so the document given in 11 should be downloaded from the InterNet in order to interpret the content of phcali odr Default phcali odr is not created Line

User's Guide of pHCali

Contents

Download Pdf Manuals

Related Search

Related Contents