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1. Y 17 m E 17 Qoi 19 xij 19 Ceci Dn ee eo ree eee eee 21 SOA ON ER E TE 22 Jplus Consulting Pty Ltd 1 ReactLab EQUILIBRIA 1 1 PORN sn aeesdessaeaesecmne EEE 24 cu 24 BE vies EEEE E saree dione sateen EEEE E AOA E AEE 25 ONE RER OPTIONS EE EE E E N 26 PEOP OPON ee T EA E E E 26 CAN REACTLAD rE OA A 27 9l P 27 ghi PEs 2 00 YX 27 AUXILIARY PARAMETERS ne en en 0 nie 27 NUMERICAL AND OTHER OPTIONS nn nmm nnns 28 HANDLING PROTONATION EQUILIBRIA H OH and KW 30 MODEL ENTRY SYNTAX RULES ane edito u tutt uU Deua ed vetta nsc 31 PARTZ ER AMIS M 33 Example 1 Simple Equilibrium M L ML M L xlsx eere 33 Hoi idet mmm 33 RDA S PO 33 OR A a a tee ee a de 34 COPI Nats ne ERE cs 35 Total Concentrations OF COMPOR NES da en aavosaedaaiviowaptinesbaagauationadbucesancstions 36 D MO OF 5 D C NRI 37 Initial Guesses for the Equilibrium Constant ss 37 Blei cH 38 adc
2. e 39 TAC 0 02 RN uu 40 Measurements at Only One Wavelength sise 41 Example 2 Determination of concentrations of two acids concAH2 xlsx 42 The auxiliary AAA a ee 43 Example 3 Determination of the Protonation Constants of an Indicator Indicator xlsx 45 Simuldtion ba MES re mEn case ne ane AE De inb don end mes mac te 45 TANS TINS T ommmeE 47 Example 4 Ni ethylenediamine Ni en3 xlsx eerte 49 MO de a ot 49 DE m 50 gcc m PP 51 Example 5 Temperature Dependence Of logKy eese 52 Jplus Consulting Pty Ltd 2 ReactLab EQUILIBRIA 1 1 Example 6 Two Acids AH BEEUXISX sean NOE Auk du Y annes ose ss sect E X DE S Edrequ YO rb ah 53 qe ioRelerz iode RR RSR uaeunpstess oparsuteupesuteerned E T 54 Non Negative Spectra ccccssccseccceeccsecoscceusceseceseceseceseceseceseccsecesecsseetseetseetseetseeseeteeeseesetsaeses 55 Example 7 The Complexation of Cu by DANA 3 7 diazanonanedioic acid diamide CU DANA S 55 TSS TEUER 55 Different definitions of the Model OTT TT 56 Example 8 A pH metered titration Cu with PHE 1 9 Bis 2 hydroxyphenyl 2 5 8 tiazanonane CU PIE IG ae EEO da USD EROR UN 58 The experim
3. molar absorptivity CuLOH2 1 0E 03 5 0E 04 0 0E 00 600 650 wavelength Figure 81 a The concentration profiles of the Cu DANA system plotted against pH b the molar absorption spectra of the complexes It is possible to define the model is several different ways one example is shown in Figure 82 Naturally the analysis is equivalent and the concentration profiles and molar absorption spectra are identical Reactio Parameters Reactants Products abel ue Fit ype logKlogg w Figure 82 An alternative definition of the model for the Cu DANA system Cu DANA v2 xlsx What is the relationship between the two definitions of the model The chemical equations used in Figure 82 are shown below Jplus Consulting Pty Ltd 57 ReactLab EQUILIBRIA 1 1 Jolus consulting ivariate analvtical M L zz ML M L H o gt MLH M L 2H z MLH MLH MLH with K ne HM d c lo aaa M L HT M IL H MLH 1 The relationship between the definitions in Figure 80 and Figure 82 is developed below for the first deprotonation Note that the species MLOH and MLH are identical just different notations are used MLA MIHI y MLH 1 M ILIHT ML OH MLOH K K ML Ww xK xK ML or log K log Kuon log K log K 5 048 6 782 12 271 14 The equality between the definitions is not perfect it is only correct within the error limits of the fitted parameters We lea
4. EQUILIBRIA 1 1 Numerical calculation options Equil Speciation Non linear reg Spectra linear reg Measurement options E O O Figure 32 Adjustable options in the Main sheet Numerical Several of the numerical options are included for completeness rather than intended for routine customer use Equilibrium Speciation Conv tol Max Iter Used for speciation calculations by Newton Raphson algorithm Non linear regression Init marpar Initial value for the Marquardt parameter used to determine the nonlinear regression algorithm strategy Can be increased for difficult data or set to zero for faster convergence Num diff Accuracy term used in the numerical partial differentiation of the parameters in the non linear regression algorithm Do not normally adjust Conv limit Reduction in ssq accepted to define convergence Default value 1e or 01 Max iter Maximum number of iterations before exiting non linear regression Default is 50 but can be reduced or increased if preferred Note exit of a fit at this limit means convergence is not valid Spectral linear regression Non neg Switches the normal linear regression algorithm used for spectrum calculation to an algorithm that enforces non negativity from Anderson C A http www models kvl dk source This can be very useful for monopolar data such Jplus Consulting Pty Ltd 29 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate an
5. ReactLab a User Manual Copyright Jplus Consulting Pty Ltd dy multivariate analytical technologies Jolus consulting multivariate analytical techr ReactLab EQUILIBRIA Global Analysis and Reaction Modeling for Chemical Equilibria USER MANUAL Contents RACE D EO UIER c 1 ABOUT THO MANUAL 4 SYSTEM REQUIREMENTS AND INSTALLATION eere nennen nnne nenne 4 CONTACT INFORMATION AND SUPPORT en areae ineo dte deencd 4 PARI T REFERENCE COIDE reece eren UE E E E Ur RC UPEINIDI T DE NIFI EU IR NOMINEE 5 INTRODUCTION e 5 SNL A 5 TORRA TION MODE E 0 7 TITRATION DATA SPECIES AND COMPONENT CONCENTRATIONS eee 8 Automatic TIIRADHONJAMOBDBE store ee EE nn 9 Manual TRATION MODE 10 PH M tered TITRATION T 10 STARTING THE MATLAB PROGRAMI cece cas cotecesteteeraneticosatetrarenesnrcsattemecananecstateesacsesetercantiees 11 Prosram OO na D UN IM DID ee a ta UNES 12 OAC ECS 2 OR eo EE SAA 12 COS SEXES E E eee ee ee 13 VIC NEN DaT a a a ea be en Re tn 13 MODEL ENTRY AID COMPILA TION aE 13 Sens 15 FPARANIETER ENT RS 16 FITUNG THE MODEL TO DATA
6. The Automatic mode is represented in the first column of Figure 2 Equilibrium solutions are prepared automatically by addition of reagent solution from a piston or stepper driven burette into a beaker and the spectra of a sample of the solution is measured after equilibration Often this beaker is the cuvette in the spectrophotometer Knowing the experimental volumes the component concentrations in the burette and initially in the beaker allows the computation of the total component concentrations in the beaker following each addition These calculations are performed by ReactLab based on this initial information which is entered in the Main menu of the workbook Jplus Consulting Pty Ltd 7 ReactLab EQUILIBRIA 1 1 dy Jolus consulting In Manual mode represented in the second column of Figure 2 individual solutions are prepared independently and their spectra measured The total component concentrations for each sample have to be entered by the user in the Data worksheet of the workbook and ReactLab does not participate in these calculations In spectrophotometric titrations spectra are generally recorded as a function of the total component concentrations in the equilibrated solutions The solutions are prepared in either Automatic or Manual mode as described above yielding all participating total component concentrations for each sample These are then used in subsequent ana
7. lt log sqsum ae ssq n aux par Species A H AH AH2 OH non abs non abs apu D 3 4 5 6 iteration LA Update Beaker Burette spectra concn mol Absorbance Numerical calculatio Equil Speciation Non linear reg Graph GUI Restore Options 15 Lot Conv tol Max iter nit marpar Conv lim Max iter 450 500 550 600 D 5 10 wavelength addition ml Figure 56 The result of fitting the component concentrations perfect fits and fitted concentrations with standard deviation Jplus Consulting Pty Ltd 44 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical tech The concentrations A and H in Beaker and Burette and thus in auxiliary parameters are the total concentrations i e A io AH2 AH A and H 2 AH2 AH H OH where on the right hand side of the equals sign we have the actual species concentrations Appropriate interpretation of the above result for the concentrations of the acids in the Beaker would be A 0 100 M and if A has been added as AH the concentration of excess strong acid HCI 0 050 M Of course it is also possible to use the auxiliary parameters to fit any component concentration in the Burette solution provided the concentrations in the Beaker are known Such a titration would be done e g for the standardization of the NaOH solution in the Burette Example 3 Determinatio
8. 17 18 19 Figure 24 the Sim worksheet showing data simulation parameters It is necessary to provide three parameters for each Gaussian spectrum the position of the maximum on the wavelength axis the Gaussian peak half width in wavelength units and its height equivalent to the maximum extinction coefficient for an absorbance spectrum The calculated Gaussian curves will be used as molar absorption spectra for the appropriate species in the simulation Simply leave the Gaussian parameters blank if it is intended that a species be modelled as colourless or set its height to zero The overall wavelength and titration addition ranges and their resolution are entered in corresponding start step and end fields The resulting absorption spectra are shown in Figure 25 The noise parameter will add an overall percentage of Gaussian noise relative to the maximum overall absorbance of the simulated data set J000 450 000 500 000 550 000 600 000 Figure 25 The absorption spectra created by the parameters of Figure 24 Jplus Consulting Pty Ltd 23 ReactLab EQUILIBRIA 1 1 Note When a simulation is calculated all pre existing data and results in the worksheet will be overwritten or removed The model species list is automatically copied to the Sim worksheet at compilation time Initial concentrations of the components for this simulation must be entered in the Main sheet in the usual place No
9. 46 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies Figure 59 Simulated absorption spectra based on the parameters in Figure 58 The volumes of added reagent solution are also defined in the Sim worksheet For the titration 5ml of 0 6 M NaOH are added in 100ul steps The component concentrations of the Beaker and Burette solutions as well as the initial Beaker volume are defined in the normal way in the Main worksheet Spectrum non abs non abs non abs non abs non abs non abs elu Ie d gr M9 dni Figure 60 Definition of the concentrations of the components The Beaker solution contains 0 1 M buffers Ba and Bb and 10 M indicator and an excess of protons 0 25 M The total volume is 10 ml In our example only the indicator components Ind IndH and IndH are colored The result of the simulation is displayed in Figure 61 noce new toolbar buttons data brushing amp inked plots az Cl Pay video 0 3000 m 0 3000 0 2500 0 2500 0 2000 0 2000 0 1500 0 1500 0 1000 0 1000 0 0500 0 0500 0 0000 0 0000 0 0 0500 0 0500 Figure 61 The titration 3 D view collection of spectra and titration curves at the different wavelengths The fitting The fitting is straight
10. If more than 5 wavelengths should appear in the Figure the user is invited to expand the spreadsheet accordingly or to simply copy paste the extra values into a different range of the worksheet and graph them appropriately As this worksheet is produced by excel and not by ReactLab it is not as general as the other worksheets The user might have to change a few cells or ranges of cells to produce the desired outcome Of course the graphics of the Figures can be changed in the usual way colors markers labels legends can be changed using the tools provided by excel Measurements at Only One Wavelength Traditionally equilibrium studies were performed most commonly by measuring the absorption of the solution at one particular wavelength Choosing a good wavelength was important a problem fortunately not relevant today were diode array detectors are very regularly used Here we demonstrate that ReactLab is perfectly able to analyse such one wavelength data sets choosing the wavelength 520nm as a non ideal choice Jplus Consulting Pty Ltd 41 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies 1000 1500 2000 2500 3000 3500 4000 Figure 50 The same reaction but only measured at 520 nm Figure 50 displays the measurement indicating that the first step is probably only poorly defined The result of the fit confirms the suspicion with standard deviations for the two rate constants which are consi
11. Press Brian P Flannery Saul A Teukolsky and William T Vetterling Numerical Recipes in C The Art of Scientific Computing 2 edition Cambridge 1996 E Joseph Billo Excel for Chemists A Comprehensive Guide 2nd edition Wiley VCH 2001 Jplus Consulting Pty Ltd 63 ReactLab EQUILIBRIA 1 1
12. 10 259 4 364E 035 1 366E 02 4 577E 03 229425 00658 0 06553 0 0662 45 10 345 4 824E 03 11926 02 4 340E 03 85319 00675 068r O 0703 1 10 331 4 764E 05 1 2 E D2 4 304E 053 2 4415 0 0658 O 0730 OOTTE 18 10 518 4744E 03 8 492E 03 4 269E 03 2 5551 0 0713 r 0 0844 Od 10 604 4 706E 03 X amp 831E D3 d 234E 03 26691 007534 O00824 0 09535 30 10 650 4 BBSE Q 3 SISTE 05 4 200E 03 26465 OC 0F72 0 08685 0 7025 Figure 88 The Data sheet contains both the original H tot values in column F and for the measured pH values in column M The results of this analysis are of course essentially identical compare Figure 89 with Figure 80 The only significant difference is that the standard deviations of the parameters are clearly smaller in the pH mode Reaction Parameters Reactants a roducts Label Fit Figure 89 The resulting constants and their standard deviations for the Cu DANA system in pH metered titration mode The total concentrations of the protons in column F of the Data worksheet are ignored in this analysis Interestingly if the total concentrations are known as in this example they can be compared with those calculated from the concentrations of all proton containing species in this example it is the sum over the species concentrations H LH 2LH CuLOH 2Cul OH OH Figure 90 demonstrates that the difference of course is not zero but insignificant This can be a valuable test for the correctness of a particu
13. also updated numerically in the Main Excel worksheet and the concentration and spectra matrices in the Results worksheet Any Excel graphs linked to these data ranges will be updated accordingly Figure 18 The implementation of such graphs is entirely at the discretion of the user and these can of course be created and manipulated entirely independently of ReactLab Jplus Consulting Pty Ltd 18 ReactLab EQUILIBRIA 1 1 E Jolus consulting multivariate analytical technologies II A B G D E F G H J K L M 1 4 5 Vadd ml M L ML ML2 Spectra M L ML ML2 6 0 000 0 100 0 000 0 000 0 000 400 000 0 146 0 000 0 124 0 025 T 0 200 0 088 0 000 0 010 0 000 410 000 0 275 0 000 0 213 0 044 8 0 400 0 078 0 000 0 018 0 000 420 000 0 459 0 000 0 339 0 078 9 0 600 0 067 0 000 0 026 0 001 430 000 0 672 0 000 0 514 0 125 10 0 800 0 058 0 001 0 033 0 002 440 000 0 867 0 000 0 736 0 195 11 1 000 0 049 0 001 0 039 0 003 450 000 0 985 0 000 1 000 0 291 12 1 200 0 041 0 001 0 044 0 004 460 000 0 985 0 000 1 284 0 419 13 1 400 0 034 0 001 0 048 0 006 470 000 0 867 0 000 1 559 0 582 14 1 600 0 027 0 002 0 051 0 008 480 000 0 671 0 000 1 790 0 779 15 1 800 0 022 0 002 0 052 0 011 490 000 0 459 0 000 1 945 1 000 16 2 000 0 017 0 003 0 052 0 014 500 000 0 276 0 000 2 000 1 236 17 0 120 2500 18 19 0 100 20 2 000 21 0 080 22 M 1 500 4 M 23 0 060 4 24 1 000 25 0 040 ML 26 M
14. auxiliary parameter In this example we wish to determine M o in the beaker This is normally entered in as a static value in cell C37 when it is known Instead a formula K7 is placed in C37 linking its value to the auxiliary parameter in cell K7 Figure 30 When the data is fitted optimisation of this aux parameter and therefore M which is continuously accessed by ReactLab to compute the species concentrations during this process Jplus Consulting Pty Ltd 27 ReactLab EQUILIBRIA 1 1 Jplus consulting multivariate analytical technologies Reaction Parameters Auxiliary E F Reactants type Products Label y kpeta I Parameters oe 5 671E 03 5 173E 05 aa 1 141E 02 v a m m r a r a a WT TTT Ty OT or 127E 04 ssq 784E 06 Species M 1 w w2 1 d 4 1 Spectrum non abs e PR E eee eee eee ee eee PECES CNET Vtot mi Figure 29 Entering a simple auxiliary parameter example Auxiliary Parameters Figure 31 The M o auxiliary parameter NUMERICAL AND OTHER OPTIONS A range of numerical calculation and other options are provided in the Main sheet that can be adjusted These are read by ReactLab when the workbook is loaded and so different workbooks can have customised settings which suit a specific analysis There are also a number of software flags Jplus Consulting Pty Ltd 28 ReactLab
15. for the Beaker and Burette if this is a conventional titration see Automatic TITRATION MODE on page 9 Figure 11 Fields for entering the initial component concentrations and the initial volume in the Beaker Vtot Certain key values are calculated automatically by Excel and are required by ReactLab namely the number of reactions specified in the model for which there is an equilibrium constant field n par the number of individual chemical species in the mechanism n species and the number of auxiliary parameters n aux par Do not overwrite the formulae in these cells they are protected in the templates supplied Figure 12 Model information automatically generated in Excel Note it is not necessary to enter any other species concentrations These are calculated from the total component concentrations of each equilibrium mixture following titrant addition from Burette to Beaker Species headings are also written to the Sim Results and Aux worksheets for subsequent data output Any previous results are cleared at this point Auxiliary parameters are an advanced feature which can be ignored during program familiarisation though this feature can be used for fitting other parameters e g unknown component concentrations See Auxiliary Parameters on page 27 Jplus Consulting Pty Ltd 15 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical PARAMETER ENTRY
16. functionality to process and chart data from elsewhere in the workbook in this specific case for presenting residual plots It is not necessary for ReactLab analysis functionality and can be deleted from all workbooks if it is not required Graph GUI This will launch a standalone GUI figure which allows close inspection of individual fitted spectra and concentration profiles either together or individually The real data can be superimposed on the best fit curves along with separate residual plots A slider control is available for easily scanning through the individual traces Modes for autoscaling are available as well as the ability to plot the y axis logarithmically which can be useful for visualising intermediates occurring at very low concentrations The best fit concentration profiles and intermediate spectra can also be displayed here Again a toolbar provides access to plot zooming Jplus Consulting Pty Ltd 21 ReactLab EQUILIBRIA 1 1 E Jolus consulting multivariate analytical technologies e n es 9 e 2 9 e 9 94 Figure 22 Example displays in the Graph GUI window Right clicking within the display area will open a context sensitive menu allowing the current graph to be pasted to the Windows clipboard for direct transfer to other applications such as Microsoft Word It is also possible to print any plot from this display and a print preview facility is provided to
17. in which a titration can be conducted and consequently there are two modes for the component concentrations in ReactLab EQUILIBRIA see also TITRATION MODES on page 7 for a description This example is a default titration in which a titrant is added to a solution of the analyte The analyte solution is the metal solution and the reagent solution L is delivered by a burette Knowing the concentration of both M and L in the Beaker solution and the Burette solution allows the computation of the total concentration of both in any solution generated during the titration The initial volume of the Beaker solution Vtot ml is also defined here dni M Burette Vtot ml Figure 40 The concentrations of the components are defined for the Beaker and Burette solutions The definition of these concentration and initial volume of the Beaker together with the added volumes of the Burette solution allows the computation of all total concentrations Jplus Consulting Pty Ltd 36 ReactLab EQUILIBRIA 1 1 E multivariate analytical techi Jolus consulting This is done automatically by ReactLab EQUILIBRIA after selecting the Update or Fit options see later Total component Yadd m vtot ml M L 0 0 10 0 0 100 0 000 0 5 10 5 0 095 0 024 10 11 0 0 091 0 045 15 11 5 0 087 0 065 2n 12 0 0 083 0 083 25 12 5 0 080 0 100 3 0 13 0 0 077 0 115 35 13 5 0 074 0 130 4 0 14 0
18. of an acidified solution of Ni and en with a relatively concentrated NaOH solution The ionic strength has been maintained at approximately 1M with NaClO The definition of the concentrations of the components is shown in Figure 67 Spectrum Bri EMEN Er non abs non abs wil e H M 0 0000 0 3140 00000 Vtot ml 10 000 Figure 67 Component concentrations in Beaker and Burette 10 ml of a solution with Ni 0 029M H 0 237 M and en 0 098 M have been titrated with 10 ml of a 0 314 M solution of NaOH in steps of 0 200 ml The added and total volumes as well as the total component concentrations are listed in the Data worksheet The spectral series and absorption profiles at all wavelengths as shown in Figure 68 7 7725 SS 0 08 Y Lc ANS 0 06 fff L i cii cm Figure 68 Series of measure spectra and absorption profiles as executed in Excel and the 3D view in Matlab Jplus Consulting Pty Ltd 50 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies Fit The fitting of this data set is now straightforward the results i e the equilibrium constants and their standard deviations are displayed in Figure 66 Note that the protonation constants have been fixed to their known values These cannot be determined by spectrophotometric titrations as none of
19. protonation equilibria are 8 for the first and 3 for the second protonation Jplus Consulting Pty Ltd 42 ReactLab EQUILIBRIA 1 1 Reaction Parameters Reactants ae Products Label 6 000E 00 3 000E 00 Figure 53 The model for a diprotic acid AH that undergoes two protonation equilibria Compiling the model reveals that we deal with 2 components A and H and 5 species A H AH AH2 and OH The component A and its protonated forms are absorbing the proton and hydroxide ions do not Note that the strong acid is not included in the model as it does not participate in any equilibrium during the titration The hydroxide OH is automatically included in the list of species as described in HANDLING PROTONATION EQUILIBRIA H OH and Kw on page 30 Figure 54 The list of species and their spectral properties The auxiliary parameters In this titration we want to fit the concentrations not the equilibrium constants There is no immediate provision for the fitting of the component concentrations We have devised the auxiliary parameters that allow the fitting of about any relevant constituent of the calculations in this example they are the component concentrations The auxiliary parameters can be fitted in the same way as any of the equilibrium constants How is this organized In the example the entries in the cells for the Beaker concentrations for A is K7 referring to the first auxiliary parameter and the entry for
20. the en species features a useful absorption spectrum in the visible of near UV Thus only the complexation constants can be fitted 0 120 0 100 0 080 0 060 0 040 0 020 0 000 2 000 4 000 6 000 8 000 10 000 0 000 2 000 4 000 6 000 8 000 10 000 12 000 0 035 0 030 0 025 0 020 0 015 0 010 0 005 0 000 0 000 2 000 4 000 6 000 8 000 10 000 0 000 2 000 4 000 6 000 8 000 10 000 12 000 pH Figure 69 Calculated concentration profiles in different modes The results encompass not only the computed equilibrium constants but also concentration profiles which can be displayed in different modes Figure 69 shows in the top panels the complete set of concentration profiles and in the bottom panels only the colored complex species On the left hand side the x axis is given as added volume of titrant solution the right hand side shows the calculated pH as the x axis The spectra of all colored species i e the complexes are also computed and can be displayed Jplus Consulting Pty Ltd 51 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies Figure 70 Computed molar absorption spectra of the Ni complexes Example 5 Temperature Dependence of logK An important property of water is its autoprotolyis its ability to act both as an acid and as a base at the same time The equilibrium can be formulated as H OH gt H O Usually the equilibrium constant is written as K H OH 107 This i
21. the species BH in the Aux worksheet as molar absorptivities Fixed Spectra Lambda A H B AH BH OH 400 000 410 000 420 000 430 000 440 000 450 000 460 000 470 000 480 000 490 000 500 000 510 000 520 000 530 000 540 000 550 000 560 000 570 000 580 000 590 000 600 000 Figure 74 The known spectrum of BH is declared in the Aux worksheet Now the fitting is straightforward and importantly all spectra are correct as displayed in Figure 75 16 000 14 000 12 000 10 000 8 000 6 000 4 000 2 000 0 000 400 000 450 000 500 000 550 000 600 000 Figure 75 Correct spectra after declaring the spectrum of BH Jplus Consulting Pty Ltd 54 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical techi Non Negative Spectra An option we have not discussed so far it to enforce positive spectra i e all molar absorptivities are non negative This done by checking the tick box of cell 146 in the Main worksheet Spectra linear reg Figure 76 Non negative spectra can be enforced Considering the spectra as displayed in Figure 72 where some molar absorptivities are negative this appears to be a good option Unfortunately it is not the case The rank deficiency is not broken and the computations are not reliable However molar absorptivities are of course always positive and it is possible to select this option for any fitting
22. 0 071 0 143 45 14 5 0 069 0 155 5 0 15 0 0 067 D 167 Figure 41 Updated total volume and component concentrations in the Data worksheet Definition of Spectra Next the spectral properties of the species have to be defined The property of each species spectrum can be chosen from three options e colored which means that its spectrum is unknown and will be calculated e non abs which means the species does not absorb in the wavelength region e known which means its molar absorption spectrum has been determined independently and should be fixed during the fitting This feature will be discussed later In our example the metal M and the complex ML are colored the ligand itself is not colored or non abs Figure 42 The spectral properties are defined for all species Initial Guesses for the Equilibrium Constant The fitting of the equilibrium constant s is a non linear process fitting has to be started from a set of initial guesses Naturally the better these initial guesses are the faster and more reliably the best parameters can be computed Initial guesses are allowed to be significantly wrong however if they are completely wrong the algorithm might collapse Where the borders between significantly and completely wrong are is not well defined no general rules can be given as they strongly depend on data set and equilibrium model Trial and Error is the simple answer The initial guess is entered in the
23. 00 3 892E 03 M Inde2H IndH2 1200E 01 NENNEN EMEN En BbH BH 4 700E 00 T Figure 57 The model for the titration of a diprotic indicator in the presence of two buffers The equilibria in the model are written as in the equations below Jplus Consulting Pty Ltd 45 ReactLab EQUILIBRIA 1 1 dy Jolus consulting Ind H IndH Binar Ind 2Hz IndH Ba H lt gt BaH Bb H gt BbH __ IndH Binan Ind H B IndH IndH Ind HT Upon compilation of the model the species and component lists are written into the relevant worksheets of relevance for the moment is the Sim worksheet wavelength range start 400 added volume from burette ml aa a ae 1 H Ba Bb indH indH2 BaH BbH OH eS Ss ee ee EIE MES Height 10000 f 3000 20000 J Width ee eS ES EUER NE ee Figure 58 The simulation worksheet defining the titration parameters and the spectra of the absorbing species In the example the spectra are measured between 400 and 600 nm in 10 nm intervals All indicator species are absorbing while all other species are non absorbing in this wavelength range A Gaussian profile with defined Position Height and Width as demonstrated in Figure 58 is computed for the colored species These Gaussians are interpreted as molar absorptivities Jplus Consulting Pty Ltd
24. 02 8 0 5 10 5 0 035 0 024 0 0134 0 0411 0 0737 0 1010 08 0904 0 0671 0 0472 0 0312 0 0175 0 0081 0 0028 9 10 11 0 0 091 0 045 0 0122 0 0353 0 0723 0 1030 O112 01024 0 0835 0 0578 0 0327 0 0149 0 0054 10 15 115 0 087 0 065 0 014 0 0323 00671 O46 0 1231 01325 0 1147 0 081 0 0462 00217 0 0079 11 2 0 12 0 0 083 0 083 0 0106 0 0291 0 0525 01043 0 1336 0 1522 0 1346 0 0962 0 0552 0 0255 0 0095 12 2 5 12 5 0 080 0 100 0 0101 0 0274 0 0594 01015 0 1336 0 1542 01376 00988 0 0567 0 02593 0 0037 13 Units 3 0 13 0 0 077 0 115 0 0096 0 0260 0 0568 009380 0 1358 0 1506 0 1348 0 0965 0 0557 0 0255 0 0094 14 addition ml 3 5 13 5 0 074 0 130 0 0093 0 0253 0 0547 00948 0 1311 0 1457 0 1305 0 0937 0 0538 0 0247 0 0094 15 wavelength 4 0 14 0 0 071 0 143 0 0088 0 0241 0 0528 0 0914 0 1270 O00 0 1262 0 0803 0 0520 0 0233 0 0086 16 Absorbance 4 5 14 5 0 053 0 155 0 0086 0 0237 0 0509 0 0884 0 1225 0 1367 01222 0 0874 0 0504 0 0232 0 0085 17 5 0 15 0 0 067 0 167 0 0082 0 0228 0 0494 0 0852 0 1184 0 1323 O78 0 0848 0 0483 0 0224 0 0082 Ey lat D co Figure 3 The Data sheet containing the spectra wavelength range and volumes of added reagent solution There is a distinction between components and species in titration experiments Components are the basic building blocks of the chemical scheme and whilst they are species in their own right also combine to form other species For example in the simple metal ligand scheme M Lz ML Ku ML L
25. 03 7 18E 04 2710 0 0260 0 0259 00256 0 0257 16 Absorbance 0 193 1 59E 03 7 17E 04 2778 0 0261 0 0262 0 0258 0 0259 17 0 213 1 59E 03 7 17E 04 2856 0 0262 0 0263 0 0260 0 0261 Figure 84 Only the total concentrations of the metal and ligand are required the column for the protons is left empty Column M contains the pH values and the entry pH in cell M6 to indicate a pH metered titration 10 000 Figure 85 The measurement here displayed as a series of titration curves at the different wavelengths The ligand PHE has five protonation constants which have to be determined independently The successive logK values are 10 06 10 41 9 09 7 94 and 4 18 Note that in the model of the spreadsheet Cu PHE xlsx the protonations are defined as overall stabilities rather than the successive ones given above refer to MODEL ENTRY AND COMPILATION on page 13 for additional explanations The results The results of the analysis are summarised in the Figure 86 and Figure 87 Again the equilibria for the complex species are defined as formation constants the logK values for the protonation equilibria ML Hz 2MLH and MLH HZ MIH are 8 42 and 3 92 Jplus Consulting Pty Ltd 60 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies Parameters logK logg Reaction t Fit El Products Label 4636 04 ssq 1765 04 Figure 86 The fitted equilibrium constants for the formatio
26. 03 7 19E 04 2 602 0 0256 0 0257 0 0255 0 0254 14 addition ml 0 149 1 59E 03 7 19E 04 2 653 0 0258 0 0259 0 0256 0 0256 15 wavelength 0 171 1 59E 03 7 18E 04 2 710 0 0260 0 0259 0 0256 0 0257 16 Absorbance 0 193 1 59E 03 7 17E 04 2 778 0 0261 0 0262 0 0258 0 0259 17 0 213 1 59E 03 7 17E 04 2 856 0 0262 0 0263 0 0260 0 0261 Figure 5 The Data Sheet from Example 8 showing the inserted measure pH vector in column M with the heading pH in cell M Jplus Consulting Pty Ltd 10 ReactLab EQUILIBRIA 1 1 multivariate analytical tech Jolus consulting In a pH metered titration analysis all the total component concentrations with the exception of H are calculated automatically from the initial component concentrations and beaker and burette volumes in the Main worksheet The H tot vector from which the H free would otherwise be determined is now redundant and ignored All speciation calculations instead use the H tree values derived from the pH vector in the Data sheet Indeed there is no need to provide initial concentrations for H in the beaker and burette as these parameters are redundant in this calculation mode The subsequent calculations will lead to a meaningless H vector in the data sheet of course but this can be ignored Advanced note The H tot column has been left in place since it is possible to compare a volumetric calculation of H to with the apparent total determined by the measure
27. 034 0 0086 0 0085 0 0082 Most of the experimental information is stored in the Data worksheet The vector of added volumes is stored in the column of cells C7 C17 under the heading Vadd ml The vector of wavelengths in the row of cells N6 X6 The matrix of data is stored the array N7 X17 The number of spectra and wavelengths are computed by excel in cells B6 and B7 The yellow headings are pre set in the worksheet The Model The next step is to define the model This is done in the Main worksheet Jplus Consulting Pty Ltd 34 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical techn Reactants DER Products Type Figure 36 Definition of the model K In this example there is one reaction step the reaction M LZ MEL the translation into the spreadsheet is self explanatory At this stage save the workbook under an appropriate name Close the file Compilation In order to perform the next tasks the ReactLab EQUILIBRIA has to be started The empty GUI in Figure 37 appears the excel file is read in after clicking the Load Excel File button ReactLab EQUILIBRIA out Figure 37 The empty ReactLab EQUILIBRIA GUI E ReactLab EQUILIBRIA cii x About DAS Excel filename M L xlsx Load Excel File residual Close Excel File Graph GUI mol conc mol Absorbance Restore Optio
28. 2 ML M and L are components as well as species and solutions of these would be made up for the titration experiment The other species ML and ML are formed according to the equilibrium parameters in the scheme Knowing Mot Ltot and the equilibrium constants allows all the individual species concentrations ML ML M and L to be calculated during fitting During a typical titration a series of additions are made from a Burette to a Beaker The data measurement comprises the spectra of the solution in the Beaker following each addition The initial volume Vio and initial concentrations of the model components in the beaker and burette are provided in the Main worksheet These may be known or can to be estimated as auxiliary parameters page 27 during fitting Figure 4 Initial concentrations of components and the starting volume Vtot are entered in the Main sheet after model compilation Automatic TITRATION MODE In order to calculate the component concentrations in the individual solutions at any point during the titration it is necessary to use this initial information and the Vadd vector to compute the total beaker volume Vtot and total component concentrations compl This calculation is done entirely by ReactLab in Automatic mode during the update and fitting cycle and the results transferred to the Data worksheet for use in subsequent calculations columns E and F in Figure 3 Jplus Consul
29. 34 0 0568 0 0547 0 0528 0 0503 0 0434 g 460 0 0383 0 1010 0 1030 0 1046 0 1043 0 1015 0 0380 0 0348 0 0314 0 0884 0 0852 R 480 0 0671 0 0304 0 1112 0 1231 0 1336 0 1336 0 1358 0 1311 0 1270 0 1225 0 1184 Into S Ti 500 520 0 0278 0 0070 0 0671 0 0472 0 1024 0 0835 0 1325 0 1147 0 1522 0 1346 0 1542 0 1376 0 1506 0 1348 0 1457 0 1305 0 1410 0 1262 0 1367 0 1222 0 1323 0 1178 d 0 0013 0 0312 0 0578 0 0811 0 0362 0 0388 0 0365 0 0337 0 0303 0 0874 0 0848 0 0200 AM 600 A B C D E F G H N 1 4 5 Total component 6 n_spectra Vadd ml Ytot mi 400 n lam 1 0 0 0 0147 8 0 5 0 0134 3 1 0 0 0122 10 15 0 0114 1i 2 0 0 0106 12 25 0 0101 13 Units 3 0 0 0096 14 addition ml 35 0 0093 15 wavelength 4 0 0 0089 16 Absorbance 45 0 0086 17 5 0 0 0082 18 0 1800 0 1800 B 0 1600 4 0 1600 4 20 21 0 1400 0 1400 4 22 0 1200 0 1200 23 0 1000 0 1000 I 0 0800 4 0 0800 4 25 26 0 0600 4 0 0600 4 27 0 0400 4 0 0400 28 0 0200 23 30 0 0000 T T T T T T 0 0000 31 0 0 1 0 2 0 3 0 4 0 5 0 6 0 32 Figure 35 The data arranged in the Data worksheet COpy 0 0001 0 0175 0 0327 0 0462 0 0552 0 0567 0 0557 0 0536 0 0520 0 0504 0 0483 of 580 0 0001 0 0081 0 0143 0 0217 0 0255 0 0253 0 0255 0 0247 0 0233 0 0232 0 0224 the 600 0 0002 0 0028 0 0054 0 0073 0 0035 0 0037 0 0034 0 0
30. 4 000 5 000 6 000 Vadd ml 0 000 0 500 1 000 1 500 2 000 2 500 3 000 3 500 4 000 4 500 5 000 M 0 100 0 084 0 072 0 062 0 054 0 048 0 043 0 038 0 035 0 032 0 029 L 0 000 0 013 0 026 0 040 0 054 0 068 0 081 0 094 0 106 0 118 0 129 ML 0 000 0 011 0 019 0 025 0 029 0 032 0 034 0 036 0 037 0 037 0 038 Spectra M L ML 400 000 0 145 0 000 0 103 420 000 0 451 0 000 0 218 440 000 0 857 0 000 0 609 460 000 1 006 0 000 1 580 480 000 0 754 0 000 2 901 500 000 0 403 0 000 3 708 520 000 0 196 0 000 3 498 540 000 0 104 0 000 2 547 560 000 0 053 0 000 1 472 580 000 0 025 0 000 0 676 600 000 0 009 0 000 0 249 4 000 3 500 3 000 2 500 M M 2 000 1 ML T ML 1 000 0 500 0 000 400 000 450 000 500 000 550 000 600 000 Figure 45 Concentration profiles and absorption spectra in the Results worksheet Jplus Consulting Pty Ltd 38 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical techr Fitting Obviously the fits are not perfect with this starting guess for the equilibrium constant This is clear from the residuals window in Figure 44 and the sum of squares ssq in the Main worksheet in cell G29 Nevertheless the fits are also not hopelessly wrong and we can hit the Fit button in the ReactLab GUI Make sure the fit box M is ticked in column H of the spreadsheet See Figure 43 The progress of the fitting can
31. 521 00963 0 0094 7 25 00101 0 0594 0 15 518009 8 r 3 0 0096 00568 015 9 35 0 0093 0 0547 0 14 0 1600 O Y meas 400 7 4 0 0089 00528 014 l Y_meas 440 11 45 0 0086 0 0509 0 13 93799 n 12 az 0 0082 0 0494 0 13 01200 4 A Y meas300 Les Y meas 540 RAIAN 0 1000 ah D Y_meas 600 ah on 4 0 0800 4 Y calc 400 ac M nm 0 0800 4 Y calc 440 PS ADT IND PRD IM ek ek ab d ek eb eh oh 2 PONI S10 00 i OH Go Ro a ad kaad iad bodd baid Go NO ba ab e co ce nam 0 0400 4 Y calc 500 e 25 20 0 0200 4 X calc 540 26 21 21 22 0 0000 Y calc 600 28 23 d i i g 29 24 _ Figure 49 An overview of the Fit Plots worksheet This worksheet is produced by excel and is completely independent from the ReactLab program This gives the user complete freedom in generating graphs appropriate for their data Its structure is slightly different from the other worksheets and needs a few explanations The default is to present 5 wavelengths spread evenly between minimal and maximal wavelength these wavelengths are produced in row 2 of the worksheet The user can change any of these wavelengths to different values If fewer than 5 wavelengths should be displayed it is sufficient to change some of the wavelengths to values outside the range and the lines disappear
32. 67E 04 6 76E 05 7 31E 05 1 05E 04 3 04E 05 2 45E 04 340E 05 2 19E 05 13 3 50 925E 05 7 27E 05 447E 05 1 58E 04 1 61E 04 2 11E 04 1 50E 05 1 59E 04 1 11E 04 4 35E 05 2 64E 04 14 4 00 343E 05 1 82E 04 3 35E 05 9 96E 06 1 77E 04 1 50E 04 6 61E 05 1 56E 04 6 41E 05 6 55E 05 1 98E 04 15 4 50 1 37E 05 2 85E 04 3 00E 06 1 59E 04 9 42E 05 1 43E 04 6 72E 06 1 30E 04 441E 05 456E 05 1 65E 05 16 5 00 1 63E 04 1 99E 04 1 53E 04 1 17E 04 2 30E 04 1 76E 04 4 05E 04 5 38E 06 1 33E 04 3 04E 05 1 20E 04 17 Figure 48 The Residuals worksheet for the present example More informative than the residuals themselves are plots of measured and fitted curves at one or several wavelengths They are produced in the Fit Plots worksheet see Figure 49 for the present example Jplus Consulting Pty Ltd 40 ReactLab EQUILIBRIA 1 1 E Jolus consulting multivariate analytical technologi A B C D E E G H J K L M N O wavelength 400 440 500 540 600 Y_meas Y_meas Y_meas Y_meas Y_meas Y calc Y calc Y calc Y calc Y calc 1 time 400 440 500 540 600 400 440 500 540 600 2 0 00147 0 0865 00278 00013 0 0002 00146 0 0866 00280 00014 0 0000 3 05 00134 0 0797 00671 00312 0 0028 0 0134 00795 00671 00311 0 0029 4 7 4 0 0122 0 0729 01024 00578 0 0054 0 00123 0 0730 01020 00578 0 0056 5 15 00114 00671 01325 00811 0 0079 00114 00672 01322 00809 0 0079 6 Lr 2 0 0106 0 0625 01522 00962 0 0095 0 0106 0 0625 01
33. A result Thus EFA cannot account for all four species in the simulation and required for the model based ReactLab analysis EFA only sees the colored species This is one of the drawbacks of model free approaches as compared to hard modeling to fundamental reaction mechanisms Jplus Consulting Pty Ltd 25 ReactLab EQUILIBRIA 1 1 E multivariate analytical techi Jolus consulting Fr gi er cui oie X CHAS x EF A Settings 2 Max M ev from SYD 4 x 0 N comp 2N ev 3 ui TS wu Threshold log EFA 3 62288 2 4 SavealtoExcel 0 1 2 3 4 5 addition ml 2 o 01 cda F oa 5 0 05 8 2 2 2 4 0 L 2 3 4 5 400 450 500 550 600 addition ml wavelength 2 1 i j E 1i 1 E 0 5 S 8M 0 0 1 2 3 4 5 0 1 2 3 4 5 addition ml addition ml Figure 27 The EFA GUI Max N ev represents the number of singular values and corresponding eigenvectors selected in the SVD GUI This represents the maximum possible number of components that can be modelled with EFA In fact only significant species should be included in this calculation and any noise vectors in the group excluded This can be adjusted in the N comp edit box The Threshold parameter is adjustable to reject baseline noise so that the C window display reflects as accurately as possible the emergence and disappearance thresholds of the independent species during the progress of the titration An option to sa
34. A 1 1 Jolus consultin multivariate analytical technologies logBi logK logK logK and logK logBin logBin 1 see Maeder and Neuhold Practical Data Analysis in Chemistry Elsevier 2007 in References for further information Jplus Consulting Pty Ltd 32 ReactLab EQUILIBRIA 1 1 PART 2 EXAMPLES Example 1 Simple Equilibrium M L ML M L xisx The Experiment The experiment is aimed at the determination of the equilibrium constant K for the equilibrium K M L ML Absorption spectra of a solution containing the metal M are measured as a function of addition of the ligand L The experimental details are the following the initial solution consists of 10ml of a 0 1 M solution of metal M spectra are measured after additions of 0 5ml aliquots of a 0 5 M solution of L up to total of 5 ml added This results in a total of 11 measured spectra Spectra are acquired in the wavelength range 400 to 600 nm in 20 nm intervals The data set is represented in Figure 34 I se 1 T l 1 7 ARE I I 2 U I I I 7 l J I 6 400 Figure 34 The measurement spectra measured as a function of addition of L The Data The data required for analysis by ReactLab EQUILIBRIA consist of the following 1 Acollection matrix of spectra recorded as a function of titrant addition 2 The total concentrations of metal and ligand components in each solution 3 The vector of wavelengths at which absorption measurement
35. E F G H J K wm M mn u 4 5 Reaction Parameters g Auxiliary a de eee ed E Su 7 Mme ML 3033E 00 8 412E 03 E i HN En 8 A NEN NNNM MEE M yy 3 uM pee ATi OC EE E y NM e e NEN NEN O BEE B yy E a S EN uu B SOR E lu WI A Lo E B EE NEN HB F r 176E 04 ogKw 1 400E 01 I npar 20 ssq 339 06 i n aux par 0l kl 32 33 Species ENT A ERN 34 35 Spectrum non abs 36 ii es ee eee eee ee ee ee ee eee pues 37 Beaker _ MODNA OE EE EE 36 EKTCCERE 7070 791 7 E 3E 3 38 10 0000 40 4 Numerical calculation options 42 m Equil Speciation Non linear reg Spectra linear reg Measurement options 45 46 Convto 1 000E 15 Cell path 1 000E 00 s Max iter 99 Num diff aaa 48 NNNM 1 000E 04 48 ee 2 500E 01 50 O INN 5 NENNEN 52 53 M M Main Data Results Sim Aux About _ 3 A NN 02 1 fi Ready E CI CI go s Us EE Figure 1 The Main worksheet illustrating a simple metal ligand titration Important The workbooks provided have certain areas of each sheet protected These areas include data entry headings generally highlighted in yellow and certain key cells containing Excel formulas used to calculate data ranges for ReactLab generally highlighted in grey It is straightforward to unprotect any sheet using the Excel unprotect c
36. L2 0 500 ML2 27 0 020 4 A anon 0 000 4 30 nis id uon 400 000 450 000 500 000 550 000 600 000 0 500 31 32 33 Figure 18 Results worksheet showing user defined graphs of the concentration profiles and spectra These along with the data are constantly updated during fitting Update Update provides a useful precursor to fitting It allows checking of a model and the starting parameters without actually executing a fit The concentration and absorbance matrices are calculated according to the current model and current parameter values The results of these calculations along with the residuals are shown graphically and will indicate whether the model and initial parameter values are remotely consistent with the current data or indeed have been entered incorrectly If the discrepancy between measured and calculated data is excessive it is improbable that a fit will converge Experiment with different initial guesses until the results of an Update are more reasonable Residuals At the end of the fitting procedure or after an update the residual matrix is copied into the Residuals worksheet A very brief description of the residuals how they are defined and calculated is given below According to Beer Lambert s law the data matrix D can be decomposed into the product of a concentration matrix C and a matrix A of molar absorptivities However due to experimental noise the decomposition is not perfect and the differenc
37. Prior to fitting or simulation numerical parameter estimates or known values if they are available from other work should be entered in the appropriate fields of the Main sheet Figure 13 The log of the Equilibrium or Formation constants must be entered e g 3 for K 10 M The user must decide whether parameters will be either fixed LJ kept constant or fitted II optimised using the tick boxes Reaction arameters ac products Label Parameters Fit v Reactants log K Beta ML ML 3 033E 00 5 538E 03 MW L M2L M2 J 5002E 00 1 118E 02 nr r Figure 13 Labeling and entering parameters and selecting those to fit The spectral status of each species must be assigned colored non abs or known using the corresponding drop down box species m m mz IETENENEN Figure 14 Setting the spectral status of each species Defining a species as coloured means it is predicted to have a spectrum contributing to the measurement i e it absorbs in the wavelength range covered by the measurement Colored spectra will be calculated and optimised during the analysis A non abs species will be fixed as colourless meaning the species is invisible in the measurement Selecting known allows an existing spectrum to be supplied for a species For example this may be for a reagent or product whose spectrum can be measured independently or for a species whose spectr
38. align and size the output graph F oO Print Preview oy StyleSheet defauit Save As sean Overview MIT Rebrash Hep Chose Figure 23 Print preview launched from the Graph GUI window SIMULATION Simulation enables the creation of artificial data sets for model evaluation and comparison with real scenarios It is an extremely useful adjunct to the fitting functionality and very informative when used as a what if tool It also allows an easy route to familiarisation with the ReactLab application The first step in simulation involves provision and compilation of a model as described earlier on page 13 onwards and providing parameter values for the reaction equilibria However instead of calculating the concentration profiles as a precursor to fitting the model Jplus Consulting Pty Ltd 22 ReactLab EQUILIBRIA 1 1 E Jolus consulting ultivariate anal to experimental data these are instead combined with artificial spectra to synthesise a new simulated data set Gaussian curves are used for the artificial spectra The parameters defining these are provided along with a titration addition sequence and the wavelength range required for the simulated data in the Sim Excel worksheet shown in Figure 24 A B C D E F G H 1 Simulation 4 5 6 wavelength range 7 8 40o 10 600 9 added volume from burette ml 0 sat step end 11 0 02 5 12 13 14 15 16
39. alytical techr as absorbance or fluorescence but not for bipolar measurements such as circular dichroism Measurement e Cell Path cm Pathlength of the cell in which the data is measured This is used to allow calculation of correct molar absorption spectra Miscellaneous e logKw This feature allows adjustment of the log of the ionic product of water Kw 1 00x10 M if required LogKw is 14 for pure water at room temperature but changes with mixed solvents and temperature This equilibrium is included when modeling reactions involving protonation equilibria to correctly deal with H and therefore pH Refer to Handling Protonation Equilibria on page30 Status Flags e data comp fit Not for user adjustment These flags are assigned and used by Excel and ReactLab to allow synchronization of a workbook when it is loaded HANDLING PROTONATION EQUILIBRIA H OH and Kw Most equilibrium investigations in aqueous solution include protonation equilibria In such instances the autoprotolysis of water has to be taken into account This is done automatically by ReactLab if any of the components in the system is identified as H which is interpreted as a proton This is one of the very few rules about the names of components or species in ReactLab As a consequence of the presence of protons it is assumed that the titration is performed in aqueous solution and the equilibrium H OH CHO is internally added to the present
40. be observed in the GUI and in the spreadsheet either on the Main or the Results page In Figure 46 we show the final GUI ReactLab EQUILIBRIA Excel filename M L xlsx convergence 2 10 Ze 3 L 10 de c MS i 6S 3 Compile Model 4 d 10 E a Simulate 5 CR 10 VA y 4 8 x i d gt wa p A x 6 10 0 2 4 6 8 10 log sqsum lt m t r g iteration spectra mol Absorbance pui ex 500 1 wavelength addition ml Figure 46 The ReactLab GUI after the fitting random distribution of residuals and good spectra The top left panel shows the progress of the fitting via a graph of the sum of squares The result of the fit includes the concentration profiles and molar absorption spectra as shown in Figure 46 they are also listed in the Results worksheet More important are usually the fitted equilibrium constants and estimates for their standard deviations they appear in the Main worksheet Additional statistical information is the sum of squares and the standard deviation of the residuals all shown in Figure 47 Jplus Consulting Pty Ltd 39 ReactLab EQUILIBRIA 1 1 B Jolus consulting multivariate analytical technologies Parameters logk Beta Reaction Products Type Reactants Label TVW TTT Ty A 9 r Figure 47 Results of the fit rate constants with estimates for the standard deviation also the sum of the squares ssq and standard d
41. constants K s Using the latter format and the same equilibrium constants the model would appear as in Figure 10 Reaction Parameters Reactants Products Label Type log K Beta MeL M 3 000E 00 Ma M2 2000E00 Figure 10 The 2 step equilibrium expressed using the association constant format The two approaches yield distinct parameters though these can be inter converted quite easily In this example logi logK logBi2 logK logK This relationship can be extrapolated for higher coordinations logB logK logK logK One of the merits of the B format is that all complexes can be unambiguously assigned a formation constant with a unique numerical subscript even when further components are involved This is less straightforward with association constants In both cases parameter values are always expressed as a log value which can be positive or negative or indeed zero This simply means the true parameter value i e anti logged is less than or greater than 1 which is permissible for both types of constant A discussion of these alternative representations can be found in Marcel Maeder Yorck Michael Neuhold Practical Data Analysis in Chemistry Elsevier 2007 and in the explanations to Example 7 The key point is that either format will be interpreted correctly by ReactLab Note integers preceding a species letter or string are interpreted as stoichiometry coefficients for the spec
42. d in conjunction with the results of this evolving factor analysis EFA The critical difference between this and the ReactLab model fitting functionality is that these analyses are model free and do not yield reaction mechanism or equilibrium constant information SVD is an incredibly useful algorithm mathematically decomposing a matrix Y into three matrices such that Y U S V Put very simply these matrices comprise the eigenvectors and eigenvalues of the original data matrix These define the data in terms of the linearly independent components along with their significance This correlates with the underlying chemical complexity by a defining the minimum number of species required in a reaction model and b the maximum no of independent coloured species in the model The user is referred to the references on page 55 for further information SVD This opens a new GUI window which graphically displays a reduced subset of the singular value decomposition of the data matrix Jplus Consulting Pty Ltd 24 ReactLab EQUILIBRIA 1 1 multivariate analytical Jolus consulting Bl svp cut AX Singular Values 1 7308 0 49587 0 13271 0 00094516 0 00089662 0 00085205 0 00080412 0 00074471 0 000691 71 o 74 CD Ch 4 Wn Basis Vectors Reduce to first Save all from EFA window 400 450 500 550 600 wavelength Figure 26 The SVD GUI The graphs display the sel
43. d pH This is demonstrated in Example 9 For a Manual pH metered titration the pH measurements are provided in the Data sheet as above Follow the earlier procedure to enforce Manual mode titration analysis and leave the Vtot cell in the Main data sheet blank along with the other initial concentrations Enter the total component concentrations of the equilibrium mixtures in the columns of the Data sheet as for a default manual titration but leave the H tot vector blank The pH entries in column M will be used in all speciation calculations STARTING THE MATLAB PROGRAM When ReactLab is launched it also requires the Matlab MCR to initialise This can take a while and is very much dependant on computer performance after which the ReactLab GUI appears as in Figure 6 B ReactLab EQUILIBRIA eig 3 About BAA Excel filename Load Excel File Figure 6 Matlab GUI control panel at startup This GUI provides the main control interface for the program with a series of pushbuttons on the right hand side for key functions These provide all the ReactLab program commands and their operation is described over the following pages Note depending on the workbook status e g whether a data or model are present some of these functions may be disabled Jplus Consulting Pty Ltd 11 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical techi In addition an About menu item at
44. derably larger than the ones based on the analysis of the complete data set at several wavelengths The two outputs are compared in Figure 51 for the single wavelength fit the fitted values are substantially off the correct values of k 0 003 and k 0 001 but they are just outside the one standard deviation Parameters Reaction Parameters T Products Label Reactants Products Label Fit v Type Type k log K aus D ki 2996E 03 1005E05 F ZEE c o joe 4887 08 P Figure 51 The fitted parameters and their standard deviations for the fit at 520 nm on the left and at 400 800nm on the right Example 2 Determination of concentrations of two acids concAH2 xlsx Titrations can be used to determine equilibrium constants but more common is the analytical application where titrations are used for quantitative analysis of samples of unknown concentration In this example we deal with a solution of two acids of unknown concentrations One is a strong and non absorbing acid e g HCI the other acid is a diprotic acid AH with undergoes two protonation equilibria with known equilibrium constants AH as well as its conjugate bases AH and A are all absorbing 0 1 0 08 0 06 0 04 0 02 02 L 0 5 ie 15 450 Figure 52 Three representations of the data set ConcAH2 xlsx The model for the titration is straightforward shown in Figure 53 The logK values for the two
45. e makes up the matrix R of residuals D CxA R The matrix D is the one stored in the Data worksheet the matrices C and A are stored in the Results worksheet The residuals are computed as D CA and are stored at the end of the fitting or an update in the Residuals worksheet Jplus Consulting Pty Ltd 19 ReactLab EQUILIBRIA 1 1 2 5 n v i Jolus consulting multivariate analytical technologies Figure 19 The residuals as a 3 D plot in the excel format The residuals can be represented in a 3 D plot as demonstrated in Figure 19 in the excel format They are also part of the Jplus GUI as shown in Figure 16 The main purpose is to enable the construction of plots that demonstrate the quality of the analysis in a readily publishable format Naturally the user can also apply any additional statistical analysis to the residual matrix The worksheet Fit Plots has been created for the preparation of plots that compare the measured data points to the fitted curves at a total of five wavelengths The experienced excel user will be able to expand the number of curves wavelengths with little effort 0 1400 0 0800 0 1200 x E d mM R Y_meas 400 0 1000 4 A 0 0400 Z 7 S 6 Y meas 450 O A Y_meas 500 X Y_meas 550 Y meas 600 Y calc 400 Y calc 450 Y calc 500 Y calc 550 Y calc 600 Figure 20 Plot of the measured data differen
46. ected number of concentration and spectral basis vectors of the decomposition essentially the eigenvectors of Y which reside in the columns of U and rows of V and lists the corresponding singular values from the diagonal matrix S The number of significant singular values equivalent to the number of principle eigenvectors n ev over the noise background is equal to the number of linearly independent coloured components in the system The corresponding eigenvectors whilst not representing real spectra or concentration profiles represent the set of linearly independent vectors from which all the data can be re composed by linear re combination The number selected here is used to determine a reduced decomposition to save in the Excel worksheet Saving of SVD and complimentary EFA results is done from the EFA GUI below EFA This opens a GUI window providing basic model free evolving factor analysis of the current data Evolving Factor Analysis provides a model free approach to predicting concentration profiles and spectra of coloured components in the data It results in some indication of spectral shapes and the evolution of independent species during the measurement which can offer useful insight into appropriate reaction models for fitting for example compare the concentration profiles and spectra in Figure 27 with the fitted equivalents in Figure 18 Note that the concentration profile of non absorbing L does of course not appear in the EF
47. ent and data ea 59 Toere a E S E ed es 60 Example 9 The Complexation of Cu by DANA as a pH metered titration Cu DANA PHXISX T 61 RSR cR ETT T OO E TENET 63 Jplus Consulting Pty Ltd 3 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies ABOUT THIS MANUAL This manual is in two parts Part 1 comprises a comprehensive description of the program architecture and functionality and provides a systematic guide to using it Part 2 consists of a series of worked examples demonstrating specific analysis case studies using pre prepared workbooks All these are provided in the Excel examples folder in the application installation package Note when they are installed in the default program files directory they are automatically assigned read only status but can of course be copied or re saved to a suitable working directory SYSTEM REQUIREMENTS AND INSTALLATION Please refer to the System Requirements and Installation Guide available on our website and included with the ReactLab download CONTACT INFORMATION AND SUPPORT support jplusconsulting com www jplusconsulting com Jplus Consulting Pty Ltd PO Box 131 Palmyra WA 6957 Australia ABN 83 135 664 603 Jplus Consulting Pty Ltd 4 ReactLab EQUILIBRIA 1 1 Jolus consulting tivariate analvtical PART 1 REFERENCE GUIDE INTRODUCTION ReactLab EQUILIBRIA provides global analysis for f
48. eviation of the residuals Residuals Judging the quality of the fit by comparing the sum over the squares of the residuals ssq or better their standard deviation with an expected value which might be based on the known performance of the spectrophotometer is possible but visual examination of fitted and measured curves is more satisfactory and might reveal potential problems with a particular model ReactLab computes the matrix of residuals and stores them in the Residuals worksheet see the section Error Reference source not found on page Error Bookmark not defined for more background information A 1 BH C H8 1 E amp l F G H J K L M 4 5 400 00 420 00 440 00 460 00 480 00 500 00 520 00 540 00 560 00 580 00 600 00 6 0 00 5 99E 05 3 00E 05 1 13E 04 2 30E 04 253E 04 2 17E 04 271E 04 4 99E 05 3 75E 05 9 93E 06 1 72E 04 7 0 50 218E 06 1 29E 04 266E 04 1 48E 04 452E 05 147E 06 3 36E 05 3 02E 05 903E 05 6 24E 05 148E 04 8 1 00 1 70E 04 8 11E 05 1 32E 04 1 75E 04 2746 04 362E 04 401E 04 3 26E 05 1 49E 04 277E 04 1 70E 04 9 1 50 6 81E 05 7 32E 05 8 28E 05 2 51E 04 4 82E 04 242E 04 5 31E 04 2 10E 04 1 27E 04 4 09E 04 6 69E 06 10 2 00 1 13E 05 7 12E 05 3 48E 05 1 10E 04 1 98E 04 2 90E 05 1 44E 04 1 03E 04 7 48E 05 1 37E 05 1 44E 04 11 2 50 1 10E 04 2 00E 05 160E 05 2 63E 04 1 69E 04 3 05E 04 2 03E 04 7 19E 05 6 65E 06 2 04E 04 8 02E 05 12 3 00 6 01E 06 1 73E 04 1 07E 04 1
49. example logK 2 Jplus Consulting Pty Ltd 37 ReactLab EQUILIBRIA 1 1 Reaction Reactants Figure 43 Input of initial guesses for parameter s Update Products Type OM m 0wE WIE Label Parameters logK logBet A Jolus consulting multivariate analytical technologies Hitting the Update button in the ReactLab GUI will do the computation of the concentration profiles for the present set of equilibrium constant s as well as the corresponding absorption spectra They appear in the GUI Note also the 3D representation of the residuals the difference between the measured and calculated absorbances ReactLab EQUILIBRIA Excel filename M L xlsx log sqsum mol Absorbance ho coa ED T ex convergence 4 iteration spectra 400 450 500 wavelength 550 mol conc addition ml BITES Graph GUI Restore Options Quit Figure 44 ReactLab GUI after Update absorption spectra concentration profiles and 3D representation of the residuals The Results worksheet will also be updated with the concentration profiles and molar absorption spectra These can be graphed as normal excel plots Figure 45 they of course are the same as the spectra and concentration profiles in the GUI Concentration profiles and spectra 0 140 0 120 0 100 0 080 4 0 060 0 040 0 020 0 000 T T r 0 000 1 000 2 000 3 000
50. forward and the results protonation constants with standard deviations of the analysis are presented in Figure 62 Jplus Consulting Pty Ltd 47 ReactLab EQUILIBRIA 1 1 B Jplus consulting multivariate analytical technologies 3 892E 03 5 825E 03 Reaction Parameters Auxiliary p v a ee cua i ER ONE KU ia n Wy a a 0E 00 ez cse ReactLab EQUILIBRIA About BAN Excel filename Indicator xlsx convergence residual non abs non abs log sqsum 2 4 B iteration co x 10 spectra Num diff e NENNEN mol Absorbance 1 data 1 400 450 500 550 600 wavelength addition ml Figure 62 Result of the analysis of the Indicator xlsx file It is instructive to display the concentration profiles in different modes they can be displayed as a function of the addition of base or as a function of pH which of course is computed as log H in this experiment the pH is not measured This can be done in the Excel Results sheet ndH IndH2 BbH OH 2 0 3 0 ml added ml added Figure 63 Calculated concentration profiles vs volume of added base The first panel displays all concentrations i e the buffer components the second panel only the indicator components which are at a much lower concentration Jplus Consulting Pty Ltd 48 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical
51. here e g Maeder Neuhold Practical Data Analysis in Chemistry Elsevier 2007 see references Fitting progress can be monitored graphically in the ReactLab GUI which displays intermediate concentration profiles and spectra as well as the 3D residual surface of the whole dataset Figure 16 The log of the ssq is also displayed as a function of the number of iterations which indicates progress of the algorithm Iterations stop according to specific convergence limit for a true minimum or if the fit is not converging when a pre set iteration maximum is reached see NUMERICAL OPTIONS page 26 Jplus Consulting Pty Ltd 17 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies B ReactLab EQUILIBRIA Excel filename M L2 xlsx convergence log sqsum 4 iteration spectra mol Absorbance 450 500 3 wavelength addition ml Figure 16 Jplus GUI following fit convergence Note random residual surface Statistical output includes standard deviations for each fitted parameter including auxiliary parameters as well as the sum of squares ssq and the standard deviation for the residuals o Figure 17 Reaction eters Reactants Products Label dessus Fit v WT Ty Ty Ty Ty 4 F n species Figure 17 Main worksheet following fit convergence Note optimized parameters and errors and the final ssq During iterations the intermediate and final best fit results are
52. ies in question e g M 2L ML2 A trailing integer is used to represent higher coordination complexes e g ML ML2 ML3 etc Essentially normal chemical reaction equations can be written For further information on the syntax rules see page 31 In all cases a label for each parameter can be provided This allows easier reference to mechanisms with multiple steps These labels and the parameter values themselves are not required prior to compilation see Parameter Entry below Jplus Consulting Pty Ltd 14 ReactLab EQUILIBRIA 1 1 multivariate analytical tech Jolus consulting Important It is necessary for any new entry in the Excel workbook to be properly completed i e by hitting return or pressing the arrow key to take the focus away from the cell in question once the desired value has been assigned otherwise the Incomplete worksheet entry warning will be raised Failing to enter values properly prevents ReactLab from accessing the worksheet cell through the ActiveX interface Compile Model When model entry is complete press the Compile Model button ReactLab reads in the model and translates it into an internal coefficient form It identifies all the participating species in the model and extracts all the starting components from which all the other species are formed through the model equilibrium relationships These are listed in fields in the Main worksheet Initial total component concentrations are entered
53. ies name That species should be selected as known in the Main worksheet Note Fixed spectra must be provided in units of Molar Absorptivity i e the fictional absorption spectrum of a 1M solution measured in a 1cm pathlength cuvette The easiest way to experiment with this feature is to simulate data to a particular model and copy and paste the simulated spectra from the Result sheet to the Aux sheet species columns These then correspond to the spectra from which the simulated data set was calculated and can be selected as known for species during experimental fitting AUXILIARY PARAMETERS The auxiliary parameter feature is unique to ReactLab and depends on the parallel execution available through the independent Excel process Auxiliary parameters are treated like normal parameters during fitting but can be used to define arbitrary relationships between virtually any of the workbook data or conventional parameters involved in the fitting calculations The feature works using Excel formulas and depends on the fact that at key points of each fit iteration parameters are written out and read back from excel but not before the execution of the any excel cell formula defining relationships between them Thus an auxiliary parameter can be set up to determine the concentration of an unknown component in a titration experiment see Figure 29 This can be achieved by linking the component starting concentration value to an
54. ing another If any changes have been made to the workbook the user must first switch focus to the workbook where he she will be prompted as to whether the changes to the workbook need to be saved Sync New Data Press this to synchronise new or edited data in a workbook with ReactLab without having to save and re load it this was required prior to version 1 1 Build 03 The new or modified data will be displayed in the ReactLab figure window MODEL ENTRY AND COMPILATION Before analysing data or computing a simulation it is necessary to enter a reaction model and compile it All model information is placed in the Excel Workbook in the Main worksheet The scheme corresponding to the example we are using can be represented as in Figure 9 Note each reaction step is entered individually M L ML and M 2L ML which allows for a one to one correspondence of each reaction step to its parameter value in the Parameter column parameters values and labels are not required for the compilation step Jplus Consulting Pty Ltd 13 ReactLab EQUILIBRIA 1 1 Reaction m Parameters qm Products Label log K Beta ML ML 3 000 00 M 2L M X 9 5000E 00 Reactants Figure 9 The 2 step equilibrium expressed using the formation constant format Note for equilibrium fitting the model can be expressed either in terms of formation constants B s as above or in the alternative perhaps more intuitive format of association
55. ions for the DANA titration NN IN Wi PQQ NY LEE 0 05 CO 450 500 550 600 Figure 79 The measurement collection of absorption spectra DANA has two protonation constants which of course have been determined by potentiometric titrations The value for the first protonation constant is logK 8 4 and for the second is logK 6 55 Different definitions of the model The definition of the ligand protonations and the complexation to form the ML complex is straightforward the definitions for the deprotonated complex species are not There are different possibilities which can all be interconverted The option used in the first spreadsheet example is the following M L gt ML ML OH gt MLOH ML 20H lt gt MLOH MLOH MLOH with K 2H an MLOH ML OH MLOH2 ML OHP These equations translate into the model definition displayed in Figure 80 Jplus Consulting Pty Ltd 56 ReactLab EQUILIBRIA 1 1 d Jolus consulting multivariate analytical technologies Reaction Parameters Reactants mi Products Label Fit V Figure 80 The model according to the definitions above Cu DANA xlsx The calculated concentration profiles are shown in Figure 81 the main species are the metal complexes the small excess ligand is evident from the differently protonated species with a maximal concentration of about 5x10 M 5 0E 03 4 5E 03 4 0E 03 3 5E 03 3 0E 03 2 5E 03 2 0E 03 CuLOH 1 5E 03
56. ition of unknown amounts of acid via formation of carbonate species In oH metered titrations the effect of this impurity is minimal as long as none of the carbonate species interfere with the process under investigation the effect in the default mode can be much more pronounced The price to pay for that advantage is more complex data acquisition as the pH has to be measured and recorded together with the spectra after each addition of reagent The example is the titration of PHE 1 9 Bis 2 hydroxyphenyl 2 5 8 triazanonane with Cu in aqueous solution The structure of the ligand is shown below It forms several complexes ML where the ligand is penta coordinated presumable via all three secondary amine groups as well as the deprotonated phenolates and two partially protonated species MLH and MLH in these complexes one or both of the phenolates are protonated and most likely not or only very weakly coordinated N N N The experiment and data entry In this titration a solution of 7 23x10 M Cu and 1 60x10 M PHE with an excess HCI were titrated with a total of approx 750uL NaOH solution The titration was performed in manual mode where after each addition of the base the pH and the spectrum were measured The total concentrations of the components and the volume of the beaker Vtot are left blank in the Main worksheet The total concentrations of metal and ligand are entered for each sample in the Data worksheet N
57. itting the parameters of chemical reaction schemes to multivariate spectroscopic titration data It also offers extensive reaction modeling and data simulation capabilities The program including all algorithms and the GUI frontend has been developed in Matlab and compiled to produce the final deployable application It requires the Matlab Component Runtime MCR to be installed on the same computer This allows the program to run on computers without standard Matlab installed The MCR is supplied as part of the installation package All raw data model entry and results output are organised in Excel Workbooks which are launched from and dynamically linked to the ReactLab application It is therefore necessary for Excel to be installed on the same computer as ReactLab The use of Excel provides a familiar spreadsheet format for all experimental and analysis data and results and allows the independent application of Excel tools and features for further processing and graphical presentation It also provides the interface for entering reaction models and all fit related parameters and numerical analysis options When a workbook is saved it contains all information and settings associated with the current analysis session as well as the numerical data and results This allows any number of data analyses with different model scenarios and parameter settings to be developed and saved in a self contained format These workbooks can be further ana
58. kbook it should be saved under a suitable name It must be saved first and re loaded into the ReactLab program even if previously opened by it in order for the new data to be recognised by ReactLab pH Metered TITRATIONS In pH metered titrations the pH of each solution is measured using a pH electrode or in manual mode each sample has had its pH adjusted to a known value ReactLab EQUILIBRIA will switch to pH metered analysis mode automatically depending on whether the measured pH vector is provided in the Data worksheet In order to declare a titration as pH metered the column M of the Data worksheet must contain the entry pH in cell M6 The cells below should be populated with the pH values of the different solutions see Figure 5 The entry pH is used by ReactLab to decide whether titration data is to be analysed using the Default computations or utilise the measured pH A B C D E F G H J K L M N Oo R Q 1 4 5 Total component lam 6 n spectra 36 Vadd ml Vtot ml L H Cu pH 750 740 730 720 7 n_lam 25 0 000 1 60E 03 7 23E 04 2 391 0 0249 0 0247 0 0245 0 0245 8 0 021 1 60E 03 7 22E 04 2 411 0 0250 0 0249 0 0246 0 0246 9 0 043 1 60E 03 7 22E 04 2 441 0 0252 0 0252 0 0249 0 0249 10 0 064 1 60E 03 7 21E 04 2475 0 0253 0 0253 0 0251 0 0250 11 0 086 1 60E 03 7 21E 04 2 513 0 0255 0 0255 0 0251 0 0251 12 0 107 1 60E 03 7 20E 04 2 556 0 0256 0 0257 0 0254 0 0254 13 Units 0 129 1 60E
59. lar analysis 1 50E 05 1 00E 05 5 00E 06 a 0 00E 00 1 uu 5 00E 06 2 9 4 0 6 0 8 0 10 0 12 0 1 00E 05 va 1 50E 05 2 00E 05 2 50E 05 3 00E 05 3 50E 05 4 00E 05 Figure 90 Plot of the difference between the total concentrations of protons calculated from the dilutions column F and calculated from all species concentrations Jplus Consulting Pty Ltd 62 ReactLab EQUILIBRIA 1 1 Jolus consulting References Marcel Maeder Yorck Michael Neuhold Practical Data Analysis in Chemistry Elsevier 2007 Equilibria Arthur Martell Robert Hancock Metal Complexes in Aqueous Solutions Modern Inorganic Chemistry Springer 1996 Arthur Martell Ramunas J Motekaitis The Determination and Use of Stability Constants 2nd Edition Wiley 1992 Juergen Polster Heinrich Lachmann Spectrometric Titrations Analysis of Chemical Equilibria VCH 1989 Kenneth A Connors Binding Constants The Measurement of Molecular Complex Stability Wiley 1987 M T Beck Nagypal The Chemistry of Complex Equilibria Van Nostrand Reinhold London 1970 Fitting Philip R Bevington D Keith Robinson Data Reduction and Error Analysis 3rd edition McGrawHill New York 2002 Meloun Milan Jiri Militky and Michele Forina Chemometrics for Analytical Chemistry Vol I II Ellis Horwood 1994 Peter Gans Data Fitting in the Chemical Sciences by the Method of Least Squares Wiley 1992 William H
60. lots e Sim e Aux e SVD e About The principle model and parameter entry interface Location for experimental or simulated data Location for fitted or simulated concentration profiles and spectra Matrix of residuals Measured and fitted curves as a selection of wavelengths Simulation parameter entry interface Used for managing known spectra Dynamically created sheet for storing SVD or EFA analysis results Sheet with contact information and the workbook format version The format of these sheets is important as ReactLab depends on everything being in particular locations Figure 1 illustrates the organisation and model entry fields in the Main worksheet which is the principle sheet of the workbook requiring user interaction The various fields in this sheet will be described later on in this document Ces ido c i M Lxlsx Microsoft Excel EX Cd Home Insert Page Layout Formulas Data Review View Developer x m Xx EEE E J Seinsatr E f e Arial 2 A a S S Ep Wrap Tet General Fa A D Bf Deete g zl Paste IB Z U A E uw amp Center 9 50 99 Conditional Format Cell Ia Sor amp Find amp y U PE Ory A Sali E amp E ad Merge amp Center o lt 68 528 Formatting as Table Styles Format lt 27 Filter Select Clipboard Font Ta Alignment Number Styles Cells Editing L28 v f Y I AE A B c D
61. lysed by ReactLab as required or reviewed independently just using Excel The program requires Excel analysis workbooks to retain a strict format as is provided in the examples and templates The process of analysing a data set using the program involves launching ReactLab and loading a workbook pre populated with measurement data Note the workbook can be saved or reloaded at any time and will re synchronise with the ReactLab program according to the most recent operation A selection of example workbooks accompanies the program in an Excel Examples folder and is described in detail in Part 2 of this manual This guide describes the equilibrium titration implementation of global analysis ReactLab EQUILIBRIA A separate guide describes operation of the complementary kinetic analysis application ReactLab KINETICS Please note that the workbook formats for these applications differ and are therefore not compatible EXCEL TEMPLATES To inspect an Excel ReactLab EQUILIBRIA workbook load it directly into Excel or via the Load Excel button in the ReactLab GUI The workbook is pre formatted containing several worksheets which provide spreadsheet formatted data and results as well as purpose designed model and parameter entry interfaces Jplus Consulting Pty Ltd 5 ReactLab EQUILIBRIA 1 1 E Jolus consulting multivariate analytical technologies Template Worksheets e Main e Data e Results e Residuals e Fit P
62. lytical calculations to determine the equilibrium concentrations of all the species in the model We term this Default mode and it is represented in the first row of Figure 2 In aqueous solutions it is also common but not required to measure the pH of each equilibrated solution on line in automatic titrations using a pH electrode or adjust the pH of each sample to a specific value in manually prepared solutions In this case the protons are treated differently from the other components involved in the process the measured pH is used to compute the free proton concentration which is used subsequently for the analysis of the data in conjunction with the other component total concentrations We call this mode pH metered To prepare the excel workbook to deal with any of these experimental protocols is straightforward and this is described in the following sections along with a general introduction to titration terminology and analysis TITRATION DATA SPECIES AND COMPONENT CONCENTRATIONS When working with new measurements start with an empty workbook template We advise making a copy of ReactLab Equilibria Master Template xls xlsx for this purpose The first step is to populate the Data worksheet with a new measurement matrix Y This will typically comprise spectra of a titration solution as a function of reagent addition see Figure 3 The addition volume vector Vadd is placed in the column C7 C8 and the wavelength vector i
63. model Further the hydroxide OH will be added automatically to the list of species The ionic product Ky is represented as K Ht OH The unionized water is omitted from the expression as its concentration is essentially constant The value of Ky is then 1 00x10 7 M for pure water at room temperature If measurements are taken at a different temperature solvent or ionic strength the value for logKy can be adjusted in cell K28 of the Main worksheet If protons are involved in a process and the autoprotolysis of water should not be implemented automatically an easy option is to call it P or anything but H Jplus Consulting Pty Ltd 30 ReactLab EQUILIBRIA 1 1 J Jplus consulting ultivariate anal In ReactLab it is necessary to define OH component additions as a negative H addition Adding NaOH is the same as removing HCl For example if NaOH is a reagent added from the burette in a pH titration and its concentration is 0 3M this would be represented by entering 0 3 in the init field for the H component see Figure 33 Do not define the NaOH concentration in the OH column OH is a species and only components are defined by their Burette and Beaker concentrations Figure 33 Representing 0 3M OH in the Burette in a pH titration as H Note OH is present as species but is not entered in the model Its concentration will be correctly computed by the speciation calculation This meth
64. mple workbook M 2L xls the graphics are fully restored reflecting the results of fitting the simulated data to the reaction model Figure 7 B ReactLab EQUILIBRIA 8 X About 9 5 Excel filename M 2L xlsx Se Load Excel Fie 1 AE ne Close Excel File Sync new data Compile Model Simulate 0 2 0 4 0 6 0 6 1 spectra Graph GUI mol Absorbance Restore Options 500 Quit wavelength addition ml Figure 7 The ReactLab GUI display reflects the Workbook content when it is loaded This shows the data residuals fitted concentration profiles and spectra of all absorbing species for the Excel M 2L xisx workbook Jplus Consulting Pty Ltd 12 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical techi Note the toolbar top left offers zooming and rotating tools for the plots These are inbuilt Matlab features Right clicking on a graph while in any of these modes provides a number of supplementary options or constraints When data are present in the workbook they are also displayed in a separate Matlab figure window E Figure 1 o 6 x File Edit View Insert Tools Desktop Window Help OGa8 k 880384 8 08 a0 DE 6 400 Figure 8 3D Data display M 2L xIsx Close Excel File This will on confirmation close the current workbook and link prior to open
65. n of the ML MLH and MLH complexes The concentration profiles are represented in two different modes the left part has the measured pH as the x axis and only the metal species are shown the right part shows all species concentrations as a function of the added volume of base This figure reveals that a substantial excess of acid has been added to the initial solution and the first 0 2 mL of base are used to neutralise this excess Cu CuL CuLH CuLH2 added NaOH mL Figure 87 The concentration profiles as a function of pH and volume of added base Example 9 The Complexation of Cu by DANA as a pH metered titration Cu DANA pH xlsx Here we return to example 7 the analysis of the complexation of Cu with DANA this time analysed as a pH metered titration The only difference between this spreadsheet and the earlier version Cu DANA xlsx is the population of the column M of the Data worksheet with sample pH s and the entry pH in cell M6 Figure 88 recall it is this entry which defines a titration as a pH metered titration Jplus Consulting Pty Ltd 61 ReactLab EQUILIBRIA 1 1 D EN G H M T F Data and Component concentrations Total component limi Vtot ml L H Cu pH Fo 735 T20 oo 10 000 4 330E 03 LIWE 02 4 490E 03 2 0034 0 0644 0 0614 0 0579 BB 10 036 4 34TE 03 1726E 02 d d52E 03 20756 O06d2 0 0626 0 0593 T3 10 173 4 905E 035 1544E D2 4d didE 05 2 1557 0 0648 0 0636 0 0620 53
66. n of the Protonation Constants of an Indicator Indicator xlsx Indicators are large aromatic molecules that have very high molar absorptivities and usually are not very soluble in water Thus it is not possible to simply titrate a solution of an indicator of sufficiently low concentration The process of deprotonation from fully protonated to fully deprotonated indicator would happen within one very small volume of added base or if the base solutions is as dilute as the indicator the pH would only be very poorly defined The trick is to add one or two appropriate buffer components to the solution The buffers do not absorb in the visible and thus higher concentrations can be used In this way the pH values of the solution are well defined around the buffer regions of the buffers and if the buffers are correctly chosen the pH values are well defined where the indicator protonation equilibria occur In our example the indicator protonation constants are logK 7 for the first protonation and logK x5 for the second protonation The buffers used in the process are Ba with a pKa value of 7 2 and Bb with a pKa value of 4 7 Simulation of a measurement We will use this example to demonstrate how to utilize the simulation capability of ReactLab First the model has to be entered in the usual way for this titration it is a bit more complex Reaction Parameters Reactants Products Label Fit V log KiBeta w ind H IndH 7000E
67. ns 400 450 500 550 600 0 5 Quit 1 2 3 wavelength addition ml Figure 38 The ReactLab EQUILIBRIA GUI after the excel file has been opened The next step is to Compile the model Compilation is the translation of the chemical model into the code required by the numerical computation software that calculates the concentration profiles of all reacting species as a function of the titration Compilation is initiated by pressing the Compile Model button in the ReactLab GUI Jplus Consulting Pty Ltd 35 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical techn The ReactLab compiler recognizes M L as components and M L and ML as the complete set of the species These are introduced as labels in row 33 for the species and in row 36 for the components in the Main worksheet and also in the Results and Sim worksheets more on them later Reaction Reactants Type Beaker Buette Y 10 0000 Figure 39 The list of components and species is automatically introduced Note the entries n species number of species and n par which equals the number of reactions are automatically updated n aux par will be discussed later Total Concentrations of Components The concentrations of the components M and L in the example in each solution for which a spectrum has been measured need to be known There are two different ways
68. od of dealing with protonations may appear somewhat confusing but allows pH and related effects to be correctly modeled Note also pH titrations will not require any H info other than pH MODEL ENTRY SYNTAX RULES e The parameter associated with is an equilibrium association constant K or formation constant B e The participating reactants must always appear on the left with the single product or complex to the right e Each equilibrium can only have one product e No two equilibria can have the same product e Reactants participating in a particular step are combined using the symbol e Species names can be single or multiple characters e The stoichiometries of species in a particular step are indicated by an integer to the left of the species or component name no integer is assumed to mean a stoichiometry of 1 e The parameter is entered as log10 of the equilibrium constant logK or formation constant logB Note this means it can be negative or positive depending on whether the equilibrium or formation constant itself is less or greater than 1 e In protonation equilibria use of the component name H for the participating proton will enable the automatic incorporation of calculations to account for the autoprotolysis of water OH will automatically be added to the species list and the Kw equilibrium modeled correctly Note the relationships between logB s and logK s Jplus Consulting Pty Ltd 31 ReactLab EQUILIBRI
69. ommand to be found under the Review tab But please be aware that corrupting the layout or formulae will prevent the correct interaction of the spreadsheet with ReactLab Exceptions are the red coloured Expand tabs on certain worksheets as in Figure 1 These provide an Jplus Consulting Pty Ltd 6 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical techi increased cell range for complex models if required To activate these tabs first unprotect the sheet and then expand or contract the cell ranges as required We suggest re protecting the sheet afterwards It is up to the user whether to include a password for re protection To get a practical demonstration of ReactLab capabilities quickly refer to the Example workbooks and the corresponding descriptions in Part 2 of this manual What follows here is a systematic overview of the whole program TITRATION MODES ReactLab EQUILIBRIA supports the analysis of titration data gathered by a number of experimental protocols and provides analysis modes to suit These are illustrated in Figure 2 nat en oO QU i QU de QU L Figure 2 Illustration of the different experimental protocols supported by ReactLab for equilibrium investigations We distinguish two primary titration protocols Automatic or Manual each of which can be performed in either Default or pH metered configurations and the data analysed accordingly
70. ote that the columns for the total concentration of the protons is left empty the measured pH in column M is defining the free proton concentration which in turn is used to compute all species concentrations in conjunction with the total concentrations of in this case the metal ion and the ligand provided In order to declare a titration as a pH metered the column M of the Data worksheet contains the entry pH in cell M6 and the cells below contain the pH values of the different solutions refer also to the next example for additional clarification Wavelengths and absorption measurements are arranged in the same cells as in default titrations Jplus Consulting Pty Ltd 59 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies A a C D G J K L M N o P a 1 Expand 4 5 Total component lam 6 n spectra Vadd ml Vtot ml L H Cu pH 750 740 730 720 7 n lam 25 0 000 1 60E 03 7 23E 04 2391 0 0249 0 0247 0 0245 0 0245 8 0 021 1 60E 03 7 22E 04 2411 0 0250 0 0249 0 0246 0 0246 9 0 043 1 60E 03 7 22E 04 2441 0 0252 0 0252 0 0249 0 0249 10 0 064 1 60E 03 7 21 04 2475 0 0253 0 0253 0 0251 0 0250 11 0 086 1 60E 03 7 21E 04 2513 0 0255 0 0255 00251 00251 12 0 107 1 60E 03 7 20E 04 2556 0 0256 0 0257 0 0254 0 0254 33 Units 0 129 1 60E 03 7 19E 04 2602 0 0256 0 0257 0 0255 0 0254 14 addition ml 0 149 1 59E 03 7 198 04 2653 0 0258 0 0259 0 0256 0 0256 15 wavelength 0 171 1 59E
71. problem Computations can be more robust but usually the difference is not noticeable Additionally calculated negative spectra can be indicative of a problem Nevertheless it is possible to analyse ESR or CD titrations with ReactLab and these spectra of course can be negative Example 7 The Complexation of Cu by DANA 3 7 diazanonanedioic acid diamide Cu DANA xlsx This real example has been chosen to demonstrate some of the subtler issues of coordination equilibria DANA 3 7 diazanonanedioic acid diamide is an interesting ligand as it has 2 secondary amine groups that can coordinate to the metal ion in the normal way as well as 2 amide groups that can coordinate as the intact amide presumably via the carbonyl oxygen or as the deprotonated amide via the negatively charged nitrogen of the amide Figure 77 displays the structure of DANA and of its complexes with Cu O O HN N N NH 2 H H 2 a Cu2 Cu E cu ENS ra E P ENS uU EN b E HN O O NH HN O H O O N N O H H Figure 77 DANA and its complexes with Cu The experiment The titration is a standard spectrophotometric titration where 10 ml of a solution of the metal and a small excess of the ligand at low pH is titrated with up to 1 6 ml of a more concentrated hydroxide solution Jplus Consulting Pty Ltd 55 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies Spectrum E A Vtot ml Figure 78 The concentrat
72. s acceptable as the concentration of water can be assumed to be constant logKw is then 14 and pKw 14 And as a result of the value for this equilibrium constant the pH of pure water is 7 However for all equilibrium constants the value is temperature dependent and only at 25 C is the value of Kw as given above If measurements are taken at different temperatures the appropriate values for logKw have to be used its value is defined in cell K28 As an example we return to the diprotic acid AH only this time we have different protonation constants We attempt to analyze a titration measured at 50 C ignoring that fact that at this temperature the correct value is logK 13 262 The results of the fit appear to be perfect only the first protonation constant is wrong it should be 13 its fitted values is 12 74 instead the second protonation constant with a value of logK 3 is not affected Jplus Consulting Pty Ltd 52 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies Reaction Parameters l Reactants I Products Label kK log K Fit v 2 476E 03 4 036E 03 VW TT TT Ty Ty Tp pT x n_species 5 Figure 71 Incorrect first protonation constant when wrong logKy is used Setting logKwy to the correct value of 13 262 and subsequent fitting results in correct protonation constants of 3 and 13 Example 6 Two Acids AH BH xlsx While this example is somewhat artificial it is useful as it can be
73. s placed in the row starting at N6 O6 The data are placed in an array corresponding to the intersection of the addition and wavelength coordinates The total number of spectra n spectra and the number of wavelengths n lam are calculated automatically from the data range pasted into the worksheet see Figure 3 Important when using Excel 1997 2003 compatible workbooks the maximum number of wavelengths permitted is 253 due to the column number restriction in this version of Excel For Excel 2007 ReactLab can in principle handle 17000 wavelengths the program currently resolves 3 letter column headings 26 combinations Note therefore that saving an xlsx workbook in xls format can lead to truncation of large data sets Note the columns from D to L are reserved for total volume and total component concentration data These are either calculated by ReactLab in Automatic mode or entered by the user in Manual mode In this example ReactLab calculates the Vtot vector and the total component concentrations in Automatic mode during the fit cycle Jplus Consulting Pty Ltd 8 ReactLab EQUILIBRIA 1 1 E Jolus consulting multivariate analytical technologies A B C D E r NNNM H N o F Q R S T Uu V W m Y 1 4 5 Total component 6 n spectra Vadd ml Vrot m M L 400 420 440 460 480 500 520 540 560 580 600 7 n lam 11 0 0 10 0 0 100 0 000 0 0147 0 0453 00865 0 0983 0 0671 0 0278 0 0070 0 0013 0 0001 0 0001 0 00
74. s were taken There are two modes in which titrations can be performed Jplus Consulting Pty Ltd 33 ReactLab EQUILIBRIA 1 1 E Jolus consulting multivariate analytical technologies a Solutions of the components M and L in the example are prepared manually in individual volumetric flasks and spectra are taken after equilibration These total concentrations are transferred into the columns E and F of the Data worksheet b More commonly titrations are done by computer controlled additions of a solution of one or more components e g L from a Burette into the solution of the other component s e g M in a Beaker or often the cuvette in the spectrophotometer In this mode the added volumes of the Burette solution are organised in the Data worksheet the initial volume in the Beaker and the concentrations of the components in these solutions are defined in the Main worksheet concentrations are computed by ReactLab and filled into the appropriate columns of the Data worksheet The total Having the cell Vtot ml in Main C39 empty indicates that the manual mode is in use The example used here is an automatic titration The parts of the complete data set are 0 420 0 0459 0 0411 0 0363 0 0323 0 0231 0 0274 0 0260 0 0253 0 0241 0 0237 0 0228 transferred Master ReactLab Equilibria template xlsx or xls spreadsheets P 440 0 0865 0 0737 0 0723 0 0671 0 0625 0 05
75. t markers and fitted curves lines in the Fit Plots worksheet Figure 20 shows the default format in the Fit Plots worksheet Markers line styles and colours can be adapted by the user to any preferred format in the usual excel way Jplus Consulting Pty Ltd 20 ReactLab EQUILIBRIA 1 1 E Jolus consulting multivariate analytical tech wavelength 400 450 500 550 600 Y meas Y meas Y meas Y meas Y_meas Y calc Y calc Y calc Y calc Y calc time 400 450 500 550 600 400 450 500 550 600 Q0 0 0147 0 0984 0 0277 0 0002 0 0002 0 0147 0 0984 00277 0 0003 0 0001 7 02 0 0143 00966 00435 0 0099 0 0011 0 0142 00966 00436 0 0099 0 0012 i 0 4 0 0135 00947 00584 0 0192 0 0028 0 0136 00947 00584 0 0192 0 0026 annn solo N Mion amp o h 1 49 CO hO annn mama Figure 21 Section of the Fit Plots worksheet the user can select the wavelengths in the blue cells D2 H2 The worksheet is populated by a selection of five wavelengths covering the complete wavelength range in the blue cells D2 H2 The user can change the wavelengths to any other values the rest is done automatically by excel Invalid wavelengths results in removal of the trace thus if the measurements at only one wavelength should be displayed the remaining four entries are set to an invalid number i e outside the measured range Please note the Fit Plots worksheet is provided by the authors to demonstrate the use of Excel
76. te however the spectra status settings in the Main sheet colored known etc are ignored in the simulation calculation Simulate Selecting Simulate will create a synthetic dataset and populate the Data and Results worksheets with the results of the simulation Data created by simulation can subsequently be analysed in the same way as experimental data using the fitting procedures already described above This allows different model scenarios to be tested as candidate mechanisms in particular providing a means of testing for the resolvability of the data model combinations Simulation also provides an invaluable general educational tool for learning and understanding the behaviour of linked equilibrium processes For example it provides an easy route to investigating the importance and use of known spectra in the determination of complex models since the Gaussian spectra used in the simulation and which now appear in the Results sheet can be simply cut and paste to the Aux sheet for experimentation Simulation does not produce pH metered titrations If required simulate default volume titrations and extract pH to put into pH column FACTOR ANALYSIS Factor analysis is provided as an additional tool that can be used to estimate the number of coloured components in any data set thereby providing insight into process complexity The two principle algorithms used are singular value decomposition SVD an
77. technologies nd IndH2 IndH2 BaH Figure 65 A selection of graphs available in the Graph GUI option measured and fitted curves at one wavelength at all wavelengths and a 3D representation Example 4 Ni ethylenediamine Ni en3 xlsx The model This example is based on a real process the formation of the 1 1 1 2 and 1 3 complexes of Ni with ethylenediamine en in aqueous solution Thus there are 3 complexation equilibria with the appropriate equilibrium constants K Ni en z Ni en 2 Km 2 Ni en en Ni en 2 Kms 2 Ni en en Ni en In aqueous solution the ligand en is also involved in 2 protonation equilibria Ben en Hz enH Dent en 2H 4 enH Again with the appropriate equilibrium constants Translation into the ReactLab model is straightforward Jplus Consulting Pty Ltd 49 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical technologies Reaction ar ter Reactants Ru MEIN UE Fit v Type Figure 66 The model for the interaction of en with Ni Note that in the notation of the model shown in Figure 66 we have used the formation constants for the protonation of the ligand as given in the equations above and the step wise equilibrium constants for the complex formations as also shown in the equations above ReactLab allows both notations The data The data set is a titration
78. the concentration of H is K8 which refers to the second auxiliary parameter The worksheet is shown in Figure 55 Jplus Consulting Pty Ltd 43 ReactLab EQUILIBRIA 1 1 E3 Jolus consulting multivariate analytical technologies Auxiliary Parameters UM Reaction Parameters Reactants Type Products Label logK Beta TOO OUT TW TTY TTT Tp RI nspecies 5 rr 883E 04 a ssq 302E 03 Burette Figure 55 The definition of the component concentrations of A and H in the Beaker they are defined as auxiliary parameters A 0 2 M and H 0 3 M The entries in the component concentration cells are referring to the aux parameters in the Beaker for A the entry is K7 for H it is K8 Hitting the Update button reveals that the guesses for the two concentrations are not correct but also not completely out of range and thus the Fit button can be pushed naturally the fit boxes for the auxiliary parameters have to be ticked M The result of the fitting procedure is shown in Figure 56 the fitted concentrations for A and H with their standard deviations are given in the list of auxiliary parameters Reactants 9c boquets Label s Fit v Auxiliary Parameters 2 127E 04 M aui K pr 2 152E 04 F Li T si r a C a ReactLab EQUILIBRIA BAR About DAR Excel filename ConcAH2 xlsx A convergence residual 10 il EFA 5 9 83E 04
79. the top left provide details of the ReactLab version and licensing information Program Operation Load Excel File Press Load Excel File in the ReactLab GUI to select and link to an Excel Workbook This will launch a new instance of Excel and load the requested workbook independent of any other open Excel workbooks Only Equilibrium workbook templates can be loaded into this version of ReactLab Important Excel is launched as an ActiveX server in an independent process linked to ReactLab which communicates with it through its Microsoft component object model COM interface The launch of Excel and ActiveX server linkage is initiated by the Matlab program Linking to an already open workbook in Excel is NOT supported If a workbook is prepared for analysis following the steps above it should first be saved and re opened from the running ReactLab application Note all Excel functionality is available to manipulate the workbook as normal while it is linked to ReactLab We will use a simulation of a reaction scheme M L ML and M 2L ML in the following sections to illustrate ReactLab features The workbook M 2L xlsx contains this example and the simulated data has been in turn used to illustrate the fitting process by optimising the parameters of the model used to create it When a workbook is first loaded various displays of data or fitted results are created in the Matlab GUI depending on its contents On loading this exa
80. ting Pty Ltd 9 ReactLab EQUILIBRIA 1 1 E multivariate analytical Jolus consulting Manual TITRATION MODE In Manual titration mode the automatic calculation of comp io is not performed by ReactLab In particular when a series of separate solutions have been made up manually their equilibrium spectra measured and the compl values recorded during preparation Such data do not necessarily form an automatic series like a conventional titration and can be completely arbitrary mixtures of the reaction components These can still be fitted to an equilibrium model using ReactLab EQUILIBRIA The data are placed in the spreadsheet as normal but the Vadd vector should now be replaced with a simple index vector 1 n to act as a default x axis for ReactLab and other plots Once the required reaction model has been compiled the known compl values should be entered under the appropriate component headings in the Data sheet To select Manual analysis mode it is necessary to disable the Automatic mode re calculation of these comp io values by ReactLab To do this leave the Vig field in the Main sheet blank When ReactLab identifies a blank in this field it will use the supplied complot data for the speciation calculations Note all the other Beaker and Burette fields as well as the Vtot column in the Data sheet are also ignored Once the data is in place the wor
81. um is known from other work It must be pasted under the corresponding species name in the Aux sheet prior to an Update or Fit otherwise an error will be raised It is essential it is in a compatible format to the experimental or simulated data with the same number of wavelengths and in correct Molar extinction units for further information see FIXED SPECTRA on page 27 Jplus Consulting Pty Ltd 16 ReactLab EQUILIBRIA 1 1 Jplus consulting multivariate analytical technologies ss Reaction A Parameters I Reactants m Products Label log KiBeta Fit v TW TP TY TY TP Tp TT Td 4 ncspedes 4 npar 2 n aux par 0 non abs a I Figure 15 Main sheet model entry area ready for fitting Having completed these steps the Main worksheet will look like the example in Figure 15 and is now fully prepared for model fitting FITTING THE MODEL TO DATA Fit Selecting Fit initiates the data fitting algorithm which proceeds to attempt to minimise the residual square sum or ssq which is a measure of the difference between the real data and that predicted by the current model and prevailing parameters It does this by iteratively refining the free parameters of the model using an adaptation of a Marquardt Levenberg algorithm and adjusting the coloured spectra according to a least squares criterion The details of the Marquardt Levenberg algorithm are described elsew
82. used to demonstrate a few fundamental issues of data analysis It is a titration of two monoprotic acids AH and BH The interesting aspect is the fact that the rank of the data matrix Y as well as of the matrix C of concentration profiles is only 3 rather than 4 As a result it is not possible to calculate all 4 absorption spectra of the species A AH B and BH This fact can be ignored and the fit can be done anyway the result is usually a set of correct equilibrium constants but always wrong spectra 25 000 20 000 15 000 10 000 5 000 gt 0 000 5 off RE 0 550 000 600 000 10 000 BN ST 15 000 20 000 Figure 72 Nonsensical spectra resulting from rank deficiency The rank deficiency can create problems in the fitting and there is no guarantee that the equilibrium constants are correct An option is to declare any one of the species as non absorbing This removes the rank deficiency and the fitting will proceed to the correct equilibrium constants Jplus Consulting Pty Ltd 53 ReactLab EQUILIBRIA 1 1 Known Spectra B Jplus consulting multivariate analytical technologies A more correct option to break the rank deficiency is to determine one of the spectra independently and declare it as known e g the spectrum of BH as in Figure 73 known non abs eo Izd se Burete Figure 73 The spectrum of BH is declared as known This requires the definition of the spectrum of
83. ve all to Excel is provided here An SVD worksheet is created if it doesn t exist already and the current SVD U S and V matrices truncated to N ev vectors and singular values and the EFA results are all saved here see Figure 28Error Reference source not found for an overview for an example of this worksheet If a pre existing SVD EFA worksheet exists the user is prompted whether or not to overwrite a previous output TE ru te Figure 28 Overview of the SVD worksheet NUMERICAL OPTIONS A number of numerical and measurement options may be pre set in the Main worksheet See page 28 for details Restore Options This will restore the program default options if they have been adjusted in a workbook Jplus Consulting Pty Ltd 26 ReactLab EQUILIBRIA 1 1 Jolus consulting multivariate analytical QUITTING REACTLAB Quit This will ask for confirmation before both closing the Excel workbook and then ReactLab FIXED SPECTRA In addition to the option to define species as colourless the known spectrum feature allows predetermined spectra to be assigned to species prior to model fitting During the fitting the fixed spectra are not adjusted The benefits of using fixed spectra are significant and discussed in the context of worked examples in Part 2 When a model is compiled a corresponding species list is created in the Aux worksheet Known spectra should be cut and pasted under the appropriate spec
84. ve it to the reader to verify the equivalence of the definitions for the second deprotonation And to make the picture more complete or confusing here a still different but equivalent definition of the model Reaction Parameters Reactants Products abe Fit v Type hog Kho B Wi ceea cura es ooo P Figure 83 A third way of defining the model for the Cu DANA system Cu DANA v3 xlsx Again we leave it to the reader to confirm the equivalence between all three model definitions presented here There are more ways of defining the model for this system or for most of the other applications of this manual The important thing is to always obey the rules for model development stated on page 31 Example 8 A pH metered titration Cu with PHE 1 9 Bis 2 hydroxyphenyl 2 5 8 triazanonane Cu PHE xlsx In this example we demonstrate the analysis of pH metered titrations a mode of titration that is common in for the investigation of equilibria in aqueous solution In this titration Jplus Consulting Pty Ltd 58 ReactLab EQUILIBRIA 1 1 mode the independent variable is the pH rather than the added volume of reagent as has been the case in all previous examples As before the measured spectra are the dependent variables An important rationale for pH metered titrations is the fact that it is often difficult to completely exclude CO during the whole titration Unknown amounts of CO result in the add

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