Obtaining Your Total Solids Measurement 4. Add 100 mL of your
Contents
1. HA 7 Ay QH CLOSED SYSTEMS 271 Several important points about the pC pH diagram should be noted Figure 23 1 was made for a 0 001 M phosphate system Note the lines represent ing the hydrogen and hydroxide ion concentrations which have a slope of 4 1 and respectively The system points defined as vertical lines at each pK value represent the pH where each chemical species adjacent to these lines is at equal concentration Note that this condition is met at each equilibrium constant Ka or using the negative log scale at each pK value For the phosphate system these values are 107 for Ki 1077 for Ko and 10 12 for Note that at pH values less than the system is dominated by the HPO species at pH values between pK and pK the system is dominated by the H2PO ion at pH values between pK and the system is dominated by the HPO ion and at pH values above pK3 the system is dominated by the PO ion Also note that as the pH increases each time the line describing the concentration of a species approaches a pK value and crosses another pK system point the slope of the line decreases by a whole number value For a diprotic system the equilibrium equations for HA and A are HA R HAT H here 2 where EA 2 7 y H A Ht where ar When these equations are combined with the mass bala2. 0 results in the following governing equation for the transport of an instantaneous input to a stream system Mo Wdv 4nEt 4Et kt 24 1 where C x pollutant concentration mg L or uCi L for radioactive compounds at distance x and time t mass of pollutant released mg or average width of the stream m average depth of the stream m longitudinal dispersion coefficient m s time s d t distance downstream from input m average water velocity m s first order decay or degradation rate constant s SS Il Note that exp represents e the base of the natural logarithm When there is no or negligible degradation of the pollutant k is set to zero or a very small number in Fate The longitudinal dispersion coefficient E is characteristic of the stream or more specifically the section of the stream that is being modeled Values of E can be determined experimentally by adding a known mass of tracer to the stream and measuring the tracer concentration at various points as a function of time Equation 24 1 is then fitted to the data at each sampling point and a value for E is estimated Unfortunately this experimental approach is very time and cost intensive and is rarely used One common CONCEPTUAL DEVELOPMENT OF GOVERNING FATE 281 approach for estimating E values is given by Fischer et al 1979 vw EUM and 4 215 where is
3. What is meant by carbonate and noncarbonate hardness What is the color change for the Calmagite indicator Briefly outline a procedure for titrating a water sample for hardness List the major steps If you titrate 50 0 mL of a sample with 0 100 EDTA and the titration takes 25 75 mL of EDTA to reach the endpoint what is the hardness of the sample in mg CaCO L DATA COLLECTION SHEET PART 7 FATE AND TRANSPORT CALCULATIONS 23 pC pH DIAGRAMS EQUILIBRIUM DIAGRAMS FOR WEAK ACID AND BASE SYSTEMS Purpose To learn to plot and interpret diagrams manually BACKGROUND The concentration of a weak acid or base in a solution e g H COs HCO or CO can be calculated using simple equilibrium expressions at any given pH In some cases it is useful to look at the equilibrium distribution of each of the protonated and nonprotonated species in solution at the same time A pC pH diagram such as those shown in Figures 23 1 and 23 2 is an excellent tool for viewing these concentrations simultaneously As the name implies the con centrations of all chemical species including the hydronium ion are expressed as the negative log of concentration for the hydronium ion the pH To construct a pC pH diagram the total concentration of the acid or base is needed along with the corresponding equilibrium equations a
4. Ca 1 where k Land Cross Section Ez Figure 25 2 Pollutant concentration in a lake undergoing step input Step Pollutant Input The conceptual approach for a step input of pollutant to a lake is similar to that of an instantaneous input First the lake water and the pollutant are mixed completely and evenly However in the step input the pollutant is emitted from a point source such as a chemical plant represented by a W in Figure 25 2 The units of W are mass per time and this mass is divided by the volume V of the lake to yield a concentration mass volume As in the instantaneous example we treat microbial and chemical degradation as well as volatilization and adsorption reactions as first order processes represented by k in the equation Finally we need to know the residence time of water in the lake This is calculated by dividing the volume of the lake V by the volumetric flow rate of water out of the lake Qe which yields t the time an average water molecule spends in the lake Using this approach and the governing equation shown in Figure 25 2 we can calculate the pollutant concentration as a function of time A typical plot of this type is shown in the upper right hand portion of Figure 25 2 Mathematical Approach to a Lake System The first step in developing the governing equations for the fate of a pollutant in a lake system is to set up a mass balance on the system First quanti
5. chemical structure for the disodium salt of EDTA is shown in Figure 22 1 Note the lone pairs of electrons on the two nitrogens These combined with the dissociated carboxyl groups create a 1 1 hexadentate complex with each divalent ion in solution However the complexation constant is a function of pH Harris 1999 Virtually all common divalent ions will be complexed at pH values greater than 10 the pH used in this titration experiment and in most hardness tests Thus the value reported for hardness includes all divalent ions in a water sample Three indicators are commonly used in EDTA titration Eriochrome Black T Erio T Calcon and Calmagite The use of Eriochrome Black T requires that a small amount of Mg ion be present at the beginning of the titration Calmagite is used in this experiment because its endpoint is sharper than that of Eriochrome Black T REFERENCES American Water Works Association Standard Methods for the Examination of Water and Wastewater 18th ed AWWA Denver Co 1992 Harris D C Quantitative Chemical Analysis 5th ed W H Freeman and Company New York 1998 Keith L H Compilation of EPA s Sampling and Analysis Methods Lewis Publishers Chelsea MI 1992 Sawyer C N and P L McCarty Chemistry for Environmental Engineering 3rd ed McGraw Hill New York 1978 Snoeyink V L and D Jenkins Water Chemistry Wiley New York 1980 260 DETERMINATION OF HARDNESS IN A WATER SAMPLE
6. Turbidity measured in nephelometer turbidity units NTUS is a function of particle size shape and concentration Turbidity is only a quick field approximation of total 242 DETERMINATION OF INORGANIC AND ORGANIC SOLIDS IN WATER SAMPLES suspended solids Consult the user s manual and measure the turbidity of your sample Compare this to your TSS measurement Hints for Success e Always always mix your sample completely before removing any solution or suspension The clay particles will settle and bias your results if you do not mix the sample completely every time you remove an aliquot e Normally in this laboratory manual you will not be given data collection sheets but due to the complicated nature of this experiment a data sheet is supplied on your CD Each group should complete the data sheet for the experiments that you conduct and share the results with your instructor and the other groups e Perform all measurements in triplicate e Carefully clean all containers and prewash all filters with deionized water prior to use As the procedure section notes heat all of these to the maximum temperature that you will use before obtaining weights Also as noted in the procedure you must obtain a constant weight generally within 0 5 mg of each other before you end each experiment Fingerprints and dust weigh enough to affect your results significantly e Your balances have been calibrated but for best results you should use the
7. IN THE LABORATORY Two methods are available for determining the hardness of a water sample The method described and used here is based on a titration method using a chelating agent The basis for this technique is that at specific pH values EDTA binds with divalent cations to form a strong complex Thus by titrating a sample of known volume with a standardized known solution of EDTA you can measure the amount of divalent metals in solution The endpoint of the titration is observed using a colorimetric indicator in our case Calmagite When a small amount of indicator is added to a solution containing hardness at pH 10 0 it combines with a few of the hardness ions and forms a weak wine red complex During the titration EDTA complexes more and more of the hardness ions until it has complexed all of the free ions and outcompetes the weaker indicator complex for hardness ions At this point the indicator returns to its uncomplexed color blue for Calmagite indicating the endpoint of the titration where only EDTA complexed hardness ions are present Safety Precautions e As in all laboratory exercises safety glasses must be worn at all times e Avoid skin and eye contact with pH 10 buffer In case of skin contact rinse the area for several minutes For eye contact flush eyes with water and seek immediate medical advice Chemicals and Solutions Sample Handling Plastic or glass sample containers can be used A minimum of 100 mL
8. M carbonate solution Refer to and use the pC pH simulator which will give color lines on the plot IN THE LABORATORY 253 2 At pH 4 5 dependent on the total alkalinity the H equals the HCO This is the endpoint for mineral acidity and total alkalinity titrations Safety Precautions As in all laboratory exercises safety glasses must be worn at all times Avoid skin and eye contact with NaOH and solutions If contact occurs rinse your hands and or flush your eyes for several minutes Seek immediate medical advice for eye contact Use concentrated in the fume hood and avoid breathing its vapor Chemicals and Solutions Sample Handling Alkalinity is a function of the dissolved CO in solution Thus any chemical or physical manipulation of the sample that will affect the CO concentration should be avoided This includes filtering diluting concen trating or altering the sample in any way Nor should the sampling temperature be exceeded as this will cause dissolved to be released Samples containing oil and grease should be avoided Sampling and storage vessels can be plastic or glass without headspace Sodium carbonate solution 0 025 M Primary standard grade must be dried for 3 to 4 hours at 250 C and be allowed to cool in a desiccator Weigh 0 25 g to the nearest 0 001 g and quantitatively transfer all of the solid to a 100 mL volumetric flask Dilute to the mark with distill
9. as needed 1 2 Why is the slope of the OH and H lines equal to 1 00 and 1 00 respectively Why does the slope of each carbon species shift by one whole number value when the line crosses a second pK value Using graph paper draw a pC pH diagram manually for a closed carbonate system total carbonate concentration of 0 0500 M What is the dominant carbon species at pH 4 0 8 0 and 11 0 Calculate the exact molar concentration of each chemical species at pH 8 00 Using graph paper draw a pC pH diagram manually for an open carbonate system total atmospheric CO concentration of 450 ppm What is the dominant carbon species at pH 8 00 Calculate the exact molar concentra tion of each chemical species at pH 9 50 To Print a Graph from Fate For a PC Select the printable version of your plot lower right portion of the screen Place the cursor over the plot at the desired x and y coordinates Hold the alt key down and press print screen Open your print or photoshop program Paste the Fate graph in your program by holding down the control key and press the letter v Save or print the file as usual For a Mac Select the printable version of your plot Hold down the shift and open apple key and press the number 4 This will place a cross hair symbol on your screen Position the cross hair symbol in the upper right corner of your plot click the cursor and drag the cross hair symbol over the area to b
10. is needed but for replicate analysis of low hardness water 1 L of sample is suggested If you are titrating the sample on the day of collection no preservation is needed If longer holding times are anticipated the sample can be preserved by adding nitric or sulfuric acid to a pH value of less than 2 0 Note that this acidic pH level must be adjusted to above a pH value of 10 before the titration e pH 10 buffer In a 250 mL volumetric flask add 140 mL of a 28 by weight NH solution to 17 5 g of NH4CI and dilute to the mark e Calmagite 1 1 hydroxy 4 methyl 2 phenylazo 2 naphthol 4 sulfonic acid Dissolve 0 10 g of Calmagite in 100 mL of distilled or deionized water Use about 1 mL per 50 mL sample to be titrated e Analytical reagent grade Na EDTA FW 372 25 Dry at 80 C for 1 hour and cool in a desiccator Accurately weigh 3 723 g or a mass accurate to 0 001 g dissolve in 500 mL of deionized water with heating cool to room IN THE LABORATORY 261 temperature quantitatively transfer to a 1 L volumetric flask and fill to the mark Since EDTA will extract hardness producing cations out of most glass containers store the EDTA solution in a plastic container This procedure produces a 0 0100 M solution Glassware e Standard laboratory glassware 50 mL buret 250 mL Erlenmeyer flasks 50 mL beakers Pasteur pipets 262 DETERMINATION OF HARDNESS IN A WATER SAMPLE PROCEDURE Limits of the Method Detection limits depend o
11. molarity of in the water step 4 Finally we calculate the pH of the water based on the equilibrium established between the different species of dissolved carbonate step 4 Step 1 density of air 0 001185 g mL 1000 mL L 1 185 g L CO air 380 mg CO kg air 380 mg air 1 kg air 1000g air 1 185 g L 0 450 mg CO2 L 0 450 mg L 1 2 1000 mg 1 mol 44 g 1 02 x 10 M CO in air Step 2 Using nRT note that n V M gives us MRT 1 02 x 10 mol L 0 08206 L M mol K 298 14 K 2 50 x 107 atm 248 DETERMINATION OF ALKALINITY OF NATURAL WATERS Step 3 Using Kco CO2 y 9 Pco 4 48 x 107 M mmHg yields Pco mmHg 2 50 x 10 atm 760 mmHg atm 0 19 mmHg 4 48 x 10 M mmHg Mco Mco in water 4 48 107 M mmHg 0 19 mmHg 8 52 x 10 Step 4 From step 3 8 52 x 1076 M CO2 g HCO 1 88 H2CO H2CO3 1 88 8 52 x 107 M 1 6 x 10 Step 5 Now solving for pH using the equilibrium expression for gt we obtain H3CO H30 HCO 42 1077 5 H30 HCOj 4 2 x 10 ta H0 H gt CO3 2 aen and using the quadratic equation to solve for x yields x 2 59 x 10 6 pH 5 59 pH of natural rainwater We can also solve for the remaining chemical species using equilibrium equations HCO x a
12. other Obtaining the Total Dissolved Solids Measurement 4 Add 100 mL of your filtered sample to your crucible and evaporate it in the 98 C oven overnight 5 Place your crucible in the 104 C oven the next day and bake it for 1 hour 6 Place the crucible in a desiccator until cool and obtain a constant weight 7 Repeat steps 5 and 6 until you obtain a constant weight within 0 5 mg of each other This will be the total dissolved solids measurement box 5 in Figure 20 1 TDS mg L average crucible weight from step 7 in g average crucible weight empty in g 1000 mg g sample volume in L PROCEDURE 241 Obtaining the Volatile Dissolved Solids Measurements 8 Place the crucible from step 7 in the muffle furnace at 550 C for 30 minutes 9 Obtain a constant weight of the crucibles by allowing the crucible to cool almost completely on a benchtop and then to cool completely in a desiccator weighing to a constant weight and repeating the heating and desiccation processes until you have two weights within 0 6 mg or less of each other This measurement will yield your total volatile solids measure ments box 6 in Figure 20 1 DVS mg L average final crucible weight from step 7 in g average crucible weight from step 9 in g 1000 mg g sample volume in L Additional Procedure If you have a conductivity meter you will also be measuring the conductivity of the entire water sample The conductivity of a samp
13. point is inversely related to alkalinity with higher total alkalinity corresponding to equivalence at a lower pH value This can be explained by looking at a pC pH diagram of the carbonate system A pC pH exercise is included in this manual Chapter 23 and a pC pH program is included on the accompanying CD ROM Figure 21 1 is for a 0 0010 M total carbonate system The exact equivalence point for the alkalinity titration occurs when the H concentration equals the HCO concentration For the 0 001 M carbonate solution Figure 21 1 this corresponds to the location of the arrow at pH 4 67 As the carbonate concentration increases to 0 10 M Figure 21 2 the carbonate species lines shift to yield an interception at a pH value of 3 66 This is a significant difference in equivalence points but is not reflected in the indicator endpoint As a result the equivalence points described below have been suggested The following endpoints corresponding to total alkalinity concentrations are suggested in AWWA 1992 pH 5 1 for total alkalinities of about 50 mg L pH 4 8 for 150 mg L and pH 4 5 for 500 mg L Two points should be noted about the titration curve again refer to the pC pH diagrams in Figures 21 1 and 21 2 1 At pH 10 7 the HCO equals the OH This is called an equivalence point and is the endpoint of the caustic alkalinity and total acidity titrations At pH 8 3 the H CO3 equals the CO This is the endpoint for carbonate alka
14. same balance for every measurement Even if the calibration on a balance is slightly off the change in weight will probably be accurate ASSIGNMENT 243 ASSIGNMENT Complete the data sheet included with this laboratory procedure In addition to the TS FS VS SVS and DVS calculations you should answer the questions located on the bottom of the data collection sheet on the enclosed CD Based on your results also summarize the mass of particulate matter inorganic salts and organic matter in your 1 00 L sample DATA COLLECTION SHEET 21 DETERMINATION OF ALKALINITY OF NATURAL WATERS Purpose To determine the alkalinity of a natural water sample by titration BACKGROUND Alkalinity is a chemical measurement of a water s ability to neutralize acids Alkalinity is also a measure of a water s buffering capacity or its ability to resist changes in pH upon the addition of acids or bases The alkalinity of natural waters is due primarily to the presence of weak acid salts although strong bases may also contribute in industrial waters i e OH Bicarbonates represent the major form of alkalinity in natural waters and are derived from the partitioning of CO from the atmosphere and the weathering of carbonate minerals in rocks and soil Other salts of weak acids such as borate silicates ammonia phosphates and organic bases from n
15. shown As a plume of pollution is transported down a stream additional mixing occurs and the length of the pollutant plume increases We account for this mixing and dilution of the pollutant concentration with E the longitudinal dispersion coefficient m s This is easy but costly to measure in a stream but we can estimate it accurately by knowing the slope of the stream channel the decrease in elevation with distance from the pollutant input point Next we are concerned with any first order removal of pollutant from the stream and include microbial and chemical degradations volatilization and sorption to river sediments This accounts for all of the major processes in the real world and all of the terms shown in the governing equation A typical concentration distance profile for an instantaneous input is shown in the upper right hand corner of Figure 24 1 below the instant aneous input model equation Instantaneous Input Model ex 14h E Instant a ETE Input Q Conc X distance First Order Degradation Step Input Conc X distance Step Input Model Figure 24 1 Transport equations and conceptualization of a polluted stream system CONCEPTUAL DEVELOPMENT OF GOVERNING FATE 279 Step Pollutant Input The conceptual approach for the step input of pollutant to a river is very similar to that of an instantaneous input All of the terms described above are applicable to the step model However here
16. solution e Metacresol purple indicator solution pH 8 3 indicator Dissolve 100 mg of metacresol purple in 100 mL of water Colors yellow in acidic solution purple in basic solution Mixed bromocresol green methyl red indicator solution You may use either the water or alcohol based indicator solution Water solution dissolve 100 mg of bromocresol green sodium salt and 20 mg of methyl red sodium salt in 100 mL of distilled or deionized water Ethyl or isopropyl alcohol solution dissolve 100 mg of bromocresol green and 20 mg of methyl red in 100 mL of 95 alcohol Glassware e Standard laboratory glassware 50 mL buret 250 mL Erlenmeyer flasks 50 mL beakers Pasteur pipets PROCEDURE 255 PROCEDURE Limits of the Method Typically 20 mg of CaCO L Lower detection limits can be achieved by using a 10 mL microburet Keith 1992 1 First an adequate sample volume for titration must be determined This is accomplished by performing a test titration Select a volume of your sample such as 100 mL and titrate it to estimate the total alkalinity of your sample For best accuracy you should use at least 10 mL but not more than 50 mL from a 50 mL buret Adjust your sample size to meet these criteria Titrate your sample with standardized 0 02 solution Add phe nolphthalein or metacresol purple indicator solution and note the color change around a pH value of 8 3 Alternatively a pH meter can be used to determin
17. the pollution enters the rivers at a constant rate For example industries located along the river have permits for federal and state agencies to emit a small amount of waste to the stream Most industries operate 24 hours a day and 365 days a year and their process waste does not usually change drastically So we can model the introduction of waste to the river as a constant input The resulting concentration of a pollutant down stream is a function of mixing and dilution by the river water described by E and any degradation or removal that may occur described by k A typical concen tration distance profile for a step input is shown in the lower left hand corner of Figure 24 1 above the step input model label Mathematical Approach to a Lake System The governing equation is obtained initially by setting up a mass balance on a cross section of the stream channel as described by Metcalf amp Eddy 1972 When the dispersion term given above is included in a cross sectional mass balance of the stream channel each term can be described as follows Inflow QC At EA SAL x 2 Outflow Q ORA At EA EOE KS At Ox Ox 0x Sinks vkC At where Q is the volumetric flow rate m s C the concentration mg m E the longitudinal dispersion coefficient m s A the cross sectional area m7 x the distance downstream from point source m and v the average water velocity m s The two longitudinal dispersion terms in th
18. two of the few common salts whose solubility decreases with increasing temperature This is due to the removal of dissolved CO as tempera ture increases The advent of synthetic detergents has significantly reduced the problems associated with hard water and the lack of foaming However scale formation continues to be a problem The source of a water sample usually determines its hardness For example surface waters usually contain less hardness than do groundwaters The hardness of water reflects the geology of its source A color coded summary of water hardness in the United States can be found at http www usgs org and if Environmental Laboratory Exercises for Instrumental Analysis and Environmental Chemistry By Frank M Dunnivant ISBN 0 471 48856 9 Copyright 2004 John Wiley amp Sons Inc 257 258 DETERMINATION OF HARDNESS IN A WATER SAMPLE TABLE 22 1 Correlation of Water Hardness Values with Degrees of Hardness mg CaCO L Hardness Degree of Hardness 0 75 Soft 75 150 Moderately hard 150 300 gt 300 Very hard you view this map you will see that hardness values can range from less than 50 mg L to over 250 mg L Therefore depending on your water s source some modifications to the procedure described below may be necessary Carbonates in surface soils and sediments increase the hardness of surface waters and subsur face limestone formations also increase the hardness of groundwaters As indicate
19. 07 7 log Pco 1 47 K1 Pco 10 47 10635 10 147 Ht H log Pco 7 82 pH Kx 10 635 10 147 1071935 10 635 10 147 Ht Ht log Pco 18 15 2pH As mentioned previously and demonstrated by the equations above the con centrations of gt HCO and Co vary as a function of both pH and This means that as Poo has varied naturally over the years during ice ages and periods of warming the concentration of H CO3 and in surface 274 pC pH DIAGRAMS EQUILIBRIUM DIAGRAMS waters has changed It also means that Pco changes caused by global warming will alter the surface water concentrations of these species pC pH diagram for the open carbonate system 380 ppm in the atmosphere is shown in Figure 23 2 REFERENCES Langmuir D Aqueous Environmental Geochemistry Prentice Hall Upper Saddle River NJ 1997 Snoeyink V L and D Jenkins Water Chemistry Wiley New York 1980 ASSIGNMENT 275 ASSIGNMENT Insert the CD ROM or install the pC pH module on your computer the pC pH simulator is included with your lab manual After you have installed pC pH if it does not start automatically open it A sample data set will load automatically Work through the example problem referring to the background information given earlier and the explanation of the example problem included in the pC pH module
20. 238 DETERMINATION OF INORGANIC AND ORGANIC SOLIDS IN WATER SAMPLES Obtaining Your Total Solids Measurement 4 Add 100 mL of your sample to your crucible and evaporate it in the 98 C oven overnight 5 Place your crucible in the 104 C oven the next day and bake it for 1 hour 6 Place the crucible in a desiccator until cool and obtain a constant weight 7 Repeat steps 5 and 6 until you obtain a constant weight within 0 5 mg of each other This will be the total solids measurement box 1 in Figure 20 1 TS mg L average final weight in g average initial crucible weight empty in g 1000 mg g sample volume in L Obtaining Your Fixed and Volatile Solids Measurements 8 Place the crucible from step 7 in the muffle furnace at 550 C for 30 minutes 9 Obtain a constant weight for the crucibles by allowing the crucibles to cool almost completely on a benchtop and then to cool completely in a desiccator weighing to a constant weight and repeating the heating and cooling process until you have two weights within 0 6 mg or less of each other This measurement will yield your fixed solids and volatile solids measurements box 2 in Figure 20 1 FS mg L average final weight from step 9 in g average initial crucible weight empty in g 1000 mg g sample volume in L VS mg L average initial crucible weight from step 7 in g average final weight from step 9 in g 1000 mg g sample volume in L Group II Tota
21. ORY To determine the alkalinity a known volume of water sample is titrated with a standard solution of strong acid to a pH value of approximately 4 or 5 Titrations can be used to distinguish between three types of alkalinity hydroxide carbonate and bicarbonate alkalinity Carbonate alkalinity is determined by titration of the water sample to the phenolphthalein or metacresol purple indicator endpoint approximately pH 8 3 Total alkalinity is determined by titration of the water sample to the endpoint of the methyl orange bromocresol green or bromocresol green methyl red indicators approximately pH 4 5 The difference between the two is the bicarbonate alkalinity Hydroxide OH alkalinity is present if the carbonate or phenolphthalein alkalinity is more than half of the total alkalinity American Water Works Association AWWA 1992 Thus the hydroxide alkalinity can be calculated as two times the phenolphthalein alkalinity minus the total alkalinity Note that only approximate pH values can be given for the final endpoint which occurs near a pH value of 4 5 This is because the exact endpoint at the end of the titration the equivalence point is dependent on the total concentration of carbonate species in solution while the indicator color change is referred to as the endpoint The endpoint is subject to the pH value only where the indicator changes color and is not influenced by the total alkalinity in solution whereas the equivalence
22. The model used here accounts for longitudinal dispersion spreading in the direction of stream flow advection transport in the direction of stream flow at the flow rate of the water and a first order removal term biodegradation or radioactive decay Environmental Laboratory Exercises for Instrumental Analysis and Environmental Chemistry By Frank M Dunnivant ISBN 0 471 48856 9 Copyright 2004 John Wiley amp Sons Inc 277 278 FATE AND TRANSPORT OF POLLUTANTS IN RIVERS AND STREAMS CONCEPTUAL DEVELOPMENT OF GOVERNING FATE AND TRANSPORT EQUATION Instantaneous Pollutant Input Before we show the mathematical development of the governing equation we present a conceptual approach that shows how each part of the equation relates to a physical model of a polluted river illustrated in Figure 24 1 The governing equation for the instantaneous model and a typical concentration time profile for this equation are shown in the upper right hand corner of the figure The river is shown flowing from the upper left hand corner to the lower right hand corner The instantaneous source W in mass units is shown upstream in the river as an irregular by shaped object This represents a one time sporadic input of pollutant such as a barrel of waste falling in the river or a shipping accident Upon entry to the river the pollutant is mixed rapidly and evenly across the cross section of the stream Next the velocity gradients v and flow rate Q are
23. a metal is its uncomplexed hydrated metal ion Complexation of this free ion by carbonate species can reduce toxicity THEORY As mentioned previously alkalinity in natural water is due primarily to carbonate species The following set of chemical equilibria is established CO H20 amp 21 3 amp HCO H 21 4 HCO CO 21 5 THEORY 247 where HCO represents the total concentration of dissolved and Reaction 21 3 represents the equilibrium of CO in the atmosphere with dissolved CO in the water The equilibrium constant using Henry s law for this reaction is H2CO3 CO Kco 448 x 107 M mmHg 21 6 The equilibrium expressions for reactions 21 4 and 21 5 are H RBCO 6 37 mo 10 21 7 Sio 101932 21 8 As you can see from equations 21 6 to 21 8 the important species contributing to alkalinity are and each of these reactions is tied strongly to pH To illustrate the importance of these relations we will calculate the pH of natural rainwater falling through Earth s atmosphere that currently contains 380 ppm First we convert the concentration of in the air to mol L step 1 and then calculate its partial pressure for use in equation 21 6 step 2 This enables us to calculate the molarity of carbon dioxide in water H CO term in equation 21 6 step 3 and then the
24. atural organic matter may be present in small amounts Alkalinity by convention is reported as mg L since most alkalinity is derived from the weathering of carbonate minerals rather than from partitioning with the atmo sphere Alkalinity for natural water in molar units is typically defined as the sum of the carbonate bicarbonate hydroxide and hydronium concentrations such that alkalinity 2 CO HCO H30 21 1 Alkalinity values can range from zero from acid rain affected areas to less than 20 mg L for waters in contact with non carbonate bearing soils to 2000 to Environmental Laboratory Exercises for Instrumental Analysis and Environmental Chemistry By Frank M Dunnivant ISBN 0 471 48856 9 Copyright 2004 John Wiley amp Sons Inc 245 246 DETERMINATION OF ALKALINITY OF NATURAL WATERS 4000 mg L for waters from the anaerobic digestors of domestic wastewater treatment plants Pohland and Bloodgood 1963 Neither alkalinity nor acidity the converse of alkalinity has known adverse health effects although highly acidic or alkaline waters are frequently considered unpalatable However alkalinity can be affected by or affect other parameters Below are some of the most important effects of alkalinity 1 The alkalinity of a body of water determines how sensitive that water body is to acidic inputs such as acid rain A water with high alkalinity better resists changes in pH upon the a
25. cross section of the lake First we assume that the input of pollutant is evenly distributed over the entire lake and that the lake is completely mixed Thus the total mass of pollutant added to the lake is divided by the volume V of the lake to yield the initial pollutant concentration Co Next we look at how pollution is removed from the lake Our model assumes that there are two ways of removing pollution from the lake degradation microbial or chemical or other loss processes such as sorption and volatilization described by the first order rate constant k in the governing equation and natural removal out of the lake with the river water represented by Qe Since the lake is completely mixed and the pollutant concentration is equal everywhere in the lake the concentration of pollutant in the exiting river is the same as the concentration in the lake This concentration is represented by C in the governing equation and is the concentration at a specific time after the addition of pollutant to the lake As time passes f increases the concentration of pollutant in the lake and in the exiting water can be calculated using the equation for instantaneous pollutant input This accounts for all the terms in the governing equation A more mathematical approach to our modeling effort is described later in this section CONCEPTUAL DEVELOPMENT OF GOVERNING FATE AND TRANSPORT EQUATION 287 Bird s Eye View mm Step Input
26. d in Table 22 1 hardness values can range from a few to hundreds of milligrams of per liter The divalent metal cations responsible for hardness can react with soap to form precipitates or when the appropriate anions are present to form scale in hot water pipes The major hardness causing cations are calcium and magnesium although strontium ferrous iron and manganese can also contribute It is common to compare the alkalinity values of a water sample to the hardness values with both expressed in mg CaCO L When the hardness value is greater than the total alkalinity the amount of hardness that is equal to the alkalinity is referred to as the carbonate hardness The amount in excess is referred to as the noncarbonate hardness When the hardness is equal to or less than the total alkalinity all hardness is carbonate hardness and no noncarbonate hardness is present Common cations and their associated anions are shown in Table 22 2 THEORY The method described below relies on the competitive complexation of divalent metal ions by ethylenediaminetetraacetic acid EDTA or an indicator The TABLE 22 2 Common Cation Anion Associations Affecting Hardness and Alkalinity Cations Yielding Hardness Associated Anions HCO Mg 01 srt cr Fe NO Mn 51027 REFERENCES 259 CH2 COONa NaOOC CH HH N C C N H H HOOC CH SCH COOH Figure 22 1 Chemical structure for the disodium salt of EDTA
27. ddition of acid from acid rain or from an industrial input We discuss this further when we discuss the relevant equilibrium reactions 2 Turbidity is frequently removed from drinking water by the addition of alum Al SO 3 to the incoming water followed by coagulation floccula tion and settling in a clarifier This process releases H into the water through the reaction Al OH 3H 21 2 For effective and complete coagulation to occur alkalinity must be present in excess of that reacted with the H releases Usually additional alkalinity in the form of Ca HCO3 2 Ca OH 2 or 2 soda ash is added to ensure optimum treatment conditions 3 Hard waters are frequently softened by precipitation methods using CaO lime NasCO3 soda ash or NaOH The alkalinity of the water must be known in order to calculate the lime soda ash or sodium hydroxide requirements for precipitation 4 Maintaining alkalinity is important to corrosion control in piping systems Corrosion is of little concern in modern domestic systems but many main water distribution lines and industrial pipes are made of iron Low pH waters contain little to no alkalinity and lead to corrosion in metal pipe systems which are costly to replacement 5 Bicarbonate and carbonate can complex other elements and compounds altering their toxicity transport and fate in the environment In general the most toxic form of
28. e endpoint pH for the total alkalinity titration Why can we give only approximate pH endpoints for each type of alkalinity To prepare yourself for the laboratory exercise briefly outline a procedure for titrating a water sample for alkalinity List the major steps If you titrate 200 mL of a sample with 0 0200 and the titration takes 25 75 mL of acid to reach the bromocresol green endpoint what is the total alkalinity of the sample The atmospheric concentration of is predicted to increase up to 750 ppm by the year 2100 What will be the pH of rainwater if it is in equilibrium with an atmosphere containing 500 ppm DETERMINATION OF HARDNESS IN A WATER SAMPLE Purpose To learn the EDTA titration method for determining the hardness of a water sample BACKGROUND In the past water hardness was defined as a measure of the capacity of water to precipitate soap However current laboratory practices define total hardness as the sum of divalent ion concentrations especially those of calcium and magnesium expressed in terms of mg CaCO L There are no known adverse health effects of hard or soft water but the presence of hard waters results in two economic considerations 1 hard waters require considerably larger amounts of soap to foam and clean materials and 2 hard waters readily precipitate carbonates known as scale in piping systems at high temperatures Calcium and magnesium carbonates are
29. e printed or saved release the cursor when you have selected the complete image A file will appear on your desktop as picture 1 Open the file with preview or any image processing file and print it as usual 24 FATE AND TRANSPORT OF POLLUTANTS IN RIVERS AND STREAMS Purpose To learn two basic models for predicting the fate and transport of pollutants in river systems BACKGROUND The close proximity to natural waterways of chemical factories railways and highways frequently leads to unintentional releases of hazardous chemicals into these systems Once hazardous chemicals are in the aquatic system they can have a number of detrimental effects for considerable distances downstream from their source This exercise allows the user to predict the concentration of a pollutant downstream of an instantaneous release Examples of instantaneous releases can be as simple as small discrete releases such as dropping a liter of antifreeze off a bridge or they can be more complex such as a transportation accident that results in the release of acetone from a tanker car Continuous step releases usually involve steady input from an industrial process drainage from nonpoint sources or leachate from a landfill Once released to the system the model assumes that the pollutant and stream water are completely mixed i e there is no cross sectional concentration gradient in the stream channel This is a reasonably good assumption for most systems
30. e the inflection point This measurement will be a combination of the hydroxide and carbonate alkalinity Continue the titration to the 4 5 endpoint by adding bromocresol green or the mixed bromocresol green methyl red indicator solution Better results will be obtained by titrating a new sample to the 4 5 endpoint This will avoid potential color interferences between the 8 3 and 4 5 pH indicators Note the color change near a pH value of 4 5 Alternatively a pH meter can be used to determine the inflection point Repeat steps 2 and 3 at least three times excluding the trial titration to determine your sample volume Calculate the hydroxide carbonate bicarbonate and total alkalinities for your samples Report your values in mg CaCO L Show all calculations in your notebook Waste Disposal After neutralization all solutions can be disposed of down the drain with water 256 DETERMINATION OF ALKALINITY OF NATURAL WATERS ADVANCED STUDY ASSIGNMENT In your own words define alkalinity and explain why it is important in environmental chemistry What are the primary chemical species responsible for alkalinity in natural waters Alkalinity can be expressed in three forms hydroxide alkalinity carbonate alkalinity and total alkalinity Each of these is determined by titration but at different pH values What is the approximate endpoint pH for the carbonate alkalinity titration What is the approximat
31. ed or deionized water Calculate the exact molarity of the solution in the 100 mL flask Standardized hydrochloric acid about 0 02 M Add 8 3 mL of concentrated 12 M HCI to a 1000 mL volumetric flask and dilute to the mark with deionized or distilled water This solution has a molarity of approximately 0 10 M Transfer 200 mL of this solution to another 1000 mL volumetric flask to prepare the 0 020 M solution Standardize the dilute solution about 0 020 M against the NaCO primary standard solution This is done by pipetting 10 00 mL of the 0 025 M NaCO solution into 250 mL Erlenmeyer flask and diluting to about 50 mL with distilled or deionized water Add 3 to 5 drops of the bromocresol green indicator more if needed to the Erlenmeyer flask and titrate with 0 02 M solution Bromocresol green changes from blue to yellow as it is acidified The indicator endpoint is intermediate between blue and yellow and appears as a distinct green color Determine the molarity of the solution Remember to wash down droplets of solution from the walls of the flask Bromocresol green indicator solution about 0 1096 pH 4 5 indicator Dissolve 0 100 g of the sodium salt into 100 mL of distilled or deionized water Colors yellow in acidic solution blue in basic solution 254 DETERMINATION OF ALKALINITY OF NATURAL WATERS e Phenolphthalein solution alcoholic pH 8 3 indicator Colors colorless in acidic solution red in basic
32. ese equations ac Oc At EA Mr x were derived from the equation OM EM m AIL Ot Ox where 0M Ot is the mass flow 0C Ox the concentration gradient A the cross sectional area and E the coefficient of turbulent mixing From this equation it can be seen that whenever a concentration gradient exists in the direction of flow 0C 0x a flow of mass OM t occurs in a manner to 280 FATE AND TRANSPORT OF POLLUTANTS IN RIVERS AND STREAMS reduce the concentration gradient For this equation it is assumed that the flow rate is proportional to the concentration gradient and the cross sectional area over which this gradient occurs The proportionality constant E is commonly called the coefficient of eddy diffusion or turbulent mixing Thus the driving force behind this reduction in concentration is the turbulent mixing in the system characterized by E and the concentration gradient The inflow outflow and sink equation given earlier can be combined to yield the pollutant concentration at a given cross section as a function of time This combination of terms is generally referred to as the general transport equation and can be expressed as accumulation inputs outputs sources removal Instantaneous Pollutant Input Model Combining the inflow outflow instantaneous source and sink terms into the mass balance expression and integrating for the equilibrium case where
33. fy all of the mass inputs of pollutant to the system This can be expressed as W QiC Qrib Cuib PAsCp VC 25 1
34. governing equations by assuming that the lake is completely mixed immediately after the addition of a contaminant It is also assumed that the volume of the lake does not change over the time interval of study so that the volume of water entering the lake is equal to the volume of water exiting the lake usually in the form of a stream CONCEPTUAL DEVELOPMENT OF GOVERNING FATE AND TRANSPORT EQUATION Instantaneous Pollutant Input Before we show the mathematical development of the governing equation we present a conceptual approach that shows how each part of the equation relates to Environmental Laboratory Exercises for Instrumental Analysis and Environmental Chemistry By Frank M Dunnivant ISBN 0 471 48856 9 Copyright 2004 John Wiley amp Sons Inc 285 286 FATE AND TRANSPORT OF POLLUTANTS IN LAKE SYSTEMS Bird s Eye View Instantaneous Input Land Lake zh Cross Section um Figure 25 1 Pollutant concentrations in a lake following an instantaneous input a physical model of the lake Figure 25 1 Two views of the lake are shown in this figure The upper figure shows a bird s eye view of the lake with the water entering the lake on the left and exiting on the right The governing equation is shown in the center of the figure The concentration of pollutant in the exiting water is shown in the upper right hand corner of Figure 25 1 as a function of time elapsed since input The lower figure shows a
35. ight by repeating the drying and desiccation steps This procedure will yield the TSS measurement box 3 in Figure 20 1 TSS mg L average weight from step 3 in g average inital weight from step 1 in g 1000 mg L sample volume in L Obtaining the SVS Measurement 4 Place the filters in the pan from step 3 in a muffle furnace at 550 C for 30 minutes Depending on the type of muffle furnace you have you may need to cover the samples with another weigh pan to avoid contamination of your sample by ceramic dust Remove the filters place them in a desiccator and obtain a constant weight by repeating the muffling and desiccation steps This will yield the SVS measurement box 4 in Figure 20 1 SVS mg L average weight from step 3 in g average weight from step 4 in g 1000 mg L sample volume in L Group III Total Dissolved Solids TDS and Dissolved Volatile Solids DVS Boxes 5 and 6 in Figure 20 1 Overview In this procedure you will perform the second most common solids measurement the total dissolved solids This is determined by first performing a TSS measurement but you do not have to weigh the filter as Group II had to do 240 DETERMINATION OF INORGANIC AND ORGANIC SOLIDS IN WATER SAMPLES You are only concerned with removing the filterable solids from your sample and collecting the filtrate In case you do not have a crucible that will hold 100 mL you can add 50 mL of the filtrate dry the sample to dr
36. l Suspended Solids TSS and Suspended Volatile Solids SVS Boxes 3 and 4 in Figure 20 1 Overview In this procedure you will be taking 100 mL of your sample and performing the most commonly used solids measurement the total suspended solids This requires you to filter a known volume of sample through a preheated and pretared glass fiber filter The difference in weights final initial divided by the volume of sample will yield the TSS The TSS measurement accounts for all solids that do not pass through the filter typically 0 45 to 1 um in size weighed after drying at 104 C When the filter is further dried to 550 C you will oxidize any organic matter present in the solids and can obtain a suspended volatile solids measurement Thus you will be completing boxes 3 and 4 in Figure 20 1 PROCEDURE 239 Step by Step Instructions Preparing the Filters 1 Rinse three filters with 20 to 30mL of deionized water to remove any solids that may remain from the manufacturing process Place each filter in a separate labeled aluminum weight pan dry them in a 550 C muffle furnace for 30 minutes place them filter and pan in a desic cator and obtain a constant weight by repeating the oven and desiccation steps Obtaining the TSS Measurement 2 Filter 100 mL of sample through each filter 3 Place each filter paper in the aluminum weight pan in the 104 C oven for 1 hour Cool the filter and pan in a desiccator and obtain a constant we
37. le is a measure of the dissolved salt concentration TDS but the conductivity depends on type of ions monodivalent divalent etc their concentration and the temperature In general TDS conductivity mmhos cm x K where K is a constant ranging from 0 55 to 0 90 depending on the ions in solution and the temperature Calibrate the conductivity meter using the 0 00100 M solution This solution should have a conductivity of 146 9 mS cm and the 0 00500 KCI solution should have a conductivity of 717 5 mS cm at 25 Make sure that the meter s automatic temperature compensation function is turned on 1 Measure and record the conductivity of the sample If the conductivity of the sample is nearer to 700 mS cm than to 150 mS cm recalibrate the meter with the higher concentration standard 2 Change the meter from conductivity to TDS mode and measure the TDS of your sample Note that this meter uses a K value of 0 5 to estimate TDS from conductivity This assumes that the only ions present in solution are Na and Cl The TDS value reported by the meter has units of mg L 3 Compare your conductivity value to your measured TDS value If you have a turbidity meter you will also be measuring the turbidity of your original sample Turbidity is a measure of the light scattered by suspended particles especially the clay particles in the sample Turbidity is measured by a photoelectric detector aligned at a 90 angle from the light source
38. linity and CO acidity titrations In the alkalinity titration virtually all of the CO has reacted thus the term carbonate alkalinity and half of the HCO has reacted at the endpoint 252 DETERMINATION OF ALKALINITY OF NATURAL WATERS pH 0 1 2 3 4 5 7 9 10 11 12 13 14 0 T T T 1 2 pC pH of a Closed System 3 4 5 6 4 643 pc Approximated 9 10 11 12 13 14 0 00000001 and 1 M Concentration 0 001 pK 1 6 35 pK 2 10 33 pK 3 12 Enter the concentration and pK s Concentrations must be between J Non Printable Molar concentration of species at cursor A 1 00e 14 9 80e 4 2 03e 5 4 41 11 Figure 21 1 pC pH diagram for a 0 001 M carbonate solution Refer to and use the pC pH simulator which will give color lines on the plot 9 10 11 12 13 14 pH 0 1 2 3 4 5 6 7 0 T T T T T T 1 d PC pH of a AL Closed System pH 2 3 640 74 8 9 10 F 11 F 12 13 F 14 L L L 0 00000001 1 Concentration 0 01 pK 1 6 35 pK 2 10 33 pK 3 18 Enter the concentration and pK s Concentrations must be between Molar concentration of species at cursor Non Printable A 1 00 14 0 0998 1 95 4 397e 11 2 Figure 21 2 pC pH diagram for 0 10
39. lso so HCO 2 59 x 107 M HCO H CO3 1 6 x 10 total carbonic concentration 2 59 x 107 1 3 x 10 M HCO H20 amp K 48x10 C037 4 8 x 10 M REFERENCES 249 Summarizing yields 2 59 x 10 5 59 H2CO3 1 6 x 10 HCO 2 59 x 10 4 88 107 M Thus a pH value of less than 5 6 for a rain snow sample is due to mineral acids from atmospheric pollution or volcanic emissions Interaction of less acidic precipitation with soil minerals usually adds alkalinity and raises the pH value which counteracts the use of carbon dioxide by algae during daylight hours If the consumption rate of CO is greater than its replacement rate from the atmosphere as can occur when acid precipitation is input the dissolved CO concentration in the surface water and groundwater will fall and result in a shift to the left for the corresponding equilibrium reactions CO aq H20 HO H3O This will also result in an increase in the pH of the water As the pH continues to increase the alkalinity changes chemical species to replace the CO2 consumed by the algae Note the equilibrium shifts toward increased concentrations which is illustrated in the following reactions 2HCO CO CO e 20H It should be noted that even though we are creating hydroxide alkalinity the total alkalinity has no
40. n the volume of sample titrated 1 Pipet an aliquot of your sample into a 250 mL Erlenmeyer flask The initial titration will only be a trial and you will probably need to adjust your sample volume to obtain the maximum precision from your pipetting technique use more than 10 mL but less than 50 mL Increase or decrease your sample size as needed Add 3 mL of the pH 10 buffer solution and about 1 mL of the Calmagite indicator Check to ensure that the pH of your sample is at or above pH 10 Add additional buffer solution if needed Titrate with EDTA solution and note the color change as you reach the endpoint Continue adding EDTA until you obtain a stable blue color with no reddish tinge incandescent light can produce a reddish tinge at and past the endpoint Repeat until you have at least three titrations that are in close agreement Calculate the hardness for each of your samples Express your results in mg CaCOj L If you made the EDTA solution exactly according to the procedure 1 00 mL of EDTA solution is equal to 1 00 mg CaCO L Confirm this through calculations Waste Disposal After neutralization all solutions can be disposed of down the drain with rinsing ADVANCED STUDY ASSIGNMENT 263 ADVANCED STUDY ASSIGNMENT amp In your own words define hardness What are the primary cations typically responsible for hardness In what unit of measure is hardness usually expressed
41. nce equation and solved for H5A HA and A in terms of Cr H and the equilibrium constants three equations are obtained Cr 5 L 1 Cr 14 A7 T H K2K2 H K2 1 If a pH dependent constant is defined as pec er ce K K gt Ky 272 pC pH DIAGRAMS EQUILIBRIUM DIAGRAMS the previous equations for the diprotic system can be simplified to 2 Gl K Koay HA Cu 27 57 AH For a monoprotic system the governing equations are considerably simpler since only pK is involved and Ane H Ka The utility of a pC pH diagram is that all of the ion concentrations can be estimated at the same time for any given pH value This computer simulation in the pC pH computer package included with your manual allows the user to select an acid system enter the pK values and draw the pC pH diagram After the diagram is drawn the user can point the cursor at a given pH and the concentrations of each ion will be given Additional discussions of pC pH diagrams can be found in Langmuir 1997 and Snoeyink and Jenkins 1980 OPEN SYSTEMS The pC pH diagrams for open systems are similar to those described for closed systems The primary difference is that in an open system a component of the system exists as a gas and the system is open to the atmosphere In other wo
42. nd constants K CLOSED SYSTEMS All pC pH diagrams have two lines in common the line describing the concentration of hydroxide OH as a function of pH and the line describing Environmental Laboratory Exercises for Instrumental Analysis and Environmental Chemistry By Frank M Dunnivant ISBN 0 471 48856 9 Copyright C 2004 John Wiley amp Sons Inc 267 268 pC pH DIAGRAMS EQUILIBRIUM DIAGRAMS pH 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 T T i T T T T T T T 3 pC pH of a Closed System 3r i J 4 Za 5 r E 6r i 1 pC 7r 8r i i 9p NS 10r i 11 J 12 i h 4 IL Bc 14 1 L 1 1 1 1 L L 1 i L een 1 Enter the concentration and pK s j Concentrations must be between 0 00000001 and 1 Molar concentration of species at cursor Concentration 0 01 HA7 HA A 7 pK 1 2 15 1 00 14 1 00 14 1 00 14 1 00 14 pK 2 7 2 L pK 3 12 35 J Figure 23 1 pC pH diagram for a triprotic system pCpH Help pH 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 nm T T T T T 1 T T T T 7 l T E 2 ral pC pH of a Open System 7 3 4 a 5 6 pC 7 8 9 10 11 12 13 14 Non Printable Current system type aerobic Enter the concentration of atmospheric or H5S Concentration 380 ppm Molar concentration of species at curso
43. ns you must use a mass that will be soluble or miscible with water An important assumption in the governing equation for all fate and transport models is that no pure solid or pure nonmiscible liquid phase of the pollutant is present Construct a pollution scenario for your simulations This will require you to input data on a specific river such as flow rates background pollutant concentrations and any pollutant decay rates most are given in the table of first order decay rates included in Fate The U S Geological Survey maintains a Web site of stream flow rates in the United States These can be accessed at http www usgs org Perform a simulation using your basic input data and evaluate the effluent pollutant concentration for the step and pulse pollution scenarios Next perform a sensitivity test by selecting and varying several input variables such as mass loading flow rate to reflect an unusually wet or dry season and first order decay rate those given in the table are only estimates the actual value can depend on factors such as volatilization the present of different bacterial communities temperature chemical degradations photo chemical degradations etc Write a three to five page paper discussing the results of your simulations Include tables of data and or printouts of figures from Fate A copy of your report should be included in your lab manual To Print a Graph from Fate For Select
44. r H amp CO4 HCO COs 1 29 5 6 31 324 330 Figure 23 2 diagram for an open carbonate system CLOSED SYSTEMS 269 the concentration of hydronium ion H as a function of pH These are based on the equilibrium relation H20 H where H loH 1 x 10 By rearranging and taking the negative log of each side we obtain log log H logjOH 14 pH The slope of the diagonal line representing the change in OH and is ApOH _ ApH and when pH equals 0 the pOH equals 14 This results in a line from pH 0 0 pC 14 0 to pH 14 0 pC 0 0 Similarly a line can be drawn representing the hydronium ion concentration as a function of pH By definition log H pH Therefore A log H pH 1 When the pH equals 0 log H equals 0 This results in a line from pH 0 0 pC 0 0 to pH 14 0 pC 14 0 The next line or set of lines normally drawn on a pC pH diagram is the one representing the total concentration of acid or base Cr When pC pH diagrams are drawn by hand is drawn as a straight horizontal line starting at on the y axis This line is actually a combination of two or more lines depending on the number of protons present in the acid At the first pK the negative log of the Ka two lines intersect one with a negative whole number slope and one with a positive whole number slope For diprotic and triprotic system
45. rds the system can exchange matter and energy with the atmosphere The most important environmental example of such a system comprises carbon dioxide CO2 carbonic acid H5CO3 bicarbonate ion HCO and carbonate ion CO in lakes rivers and oceans The reactions occurring in this system are CO H5CO H HCO lt gt CO Ht H2O o OH OPEN SYSTEMS 273 The equilibrium relationships for this system are H OHT 107 CM 10 147 rae H HCO3 _ 10 635 H5COj H CO3 10 33 ky 10 2 where Pco is the partial pressure of CO in the atmosphere Open system diagrams contain lines describing the concentration of hydroxide and hydronium ion H identical to those for closed systems However because open systems can exchange matter with the atmosphere the total inorganic carbon concentration is not constant as it is for a closed system but varies as a function of pH Still the total inorganic carbon concentration is the sum of all inorganic carbon species as it was for closed systems In this case Cr H5CO HCO C037 The concentration of HyCO3 and COi as a function of pH and Poo can be calculated from the equilibrium relationships given previously The equations for these lines are H CO log HCO log HCO coy log COj Kco Pco Pco 1
46. s as one species line crosses a second line or pK the slope of the line shifts from 1 or 1 to 2 or 4 2 respectively These lines represent the concentration of each chemical species Three cases are given below a triprotic system the phosphate system a diprotic system the carbonate system and a monoprotic system a generic system 270 pC pH DIAGRAMS EQUILIBRIUM DIAGRAMS For a triprotic system the lines for each individual chemical species can be represented by I5A H H3A lt HA here K 3 9 where HA HA HA Ht h ED 2 where Ay H A A H HA AX where K3 all The total concentration of the acid or base is a sum of all protonated and nonprotonated species such that Cr HA HGA A7 When the equilibrium expressions above and the Cr equation are combined and solved for the concentrations of HA and in terms of Cr H and the equilibrium constants four equations are obtained H3A Cr 1 Ki H KiKo H P i Ko Ks H 7 Cr H Ki 1 o H KoKs H Cr 5 KiK2 H K2 1 K3 H A Cr 3 B KxKoK5 KoK3 H K3 1 If a pH dependent constant is defined as B m mj 1 Kj KoK5 the previous equations can be simplified to K Ko K30y4 2 DA
47. t changed merely shifted in chemical form We define hydroxide alkalinity later as alkalinity in excess of a pH value of 10 7 Algae can continue to consume CO until the pH of the water has risen to between 10 and 11 when a growth inhibitory pH is reached and algae consumption of is halted This can result in a diurnal shift in the pH of the photic zone of a water body In waters containing significant calcium concentrations the set of reactions above can result in the precipitation of CaCO on leaves and twigs in water and in the long term can lead to the formation of marl deposits in sediments Thus even algae can produce the industrial sounding hydroxide alkalinity REFERENCES American Water Works Association Standard Methods for the Examination of Water and Wastewater 18th ed AWWA Denver CO 1992 250 DETERMINATION OF ALKALINITY OF NATURAL WATERS Harris D C Quantitative Chemical Analysis 5th ed W H Freeman New York 1998 Keith L H Compilation of EPA s Sampling and Analysis Methods Lewis Publishers Chelsea MI 1992 Pohland F G and D E Bloodgood J Water Pollut Control Fed 35 11 1963 Snoeyink V L and D Jenkins Water Chemistry Wiley New York 1980 Sawyer C N and P L McCarty Chemistry for Environmental Engineering 3rd ed McGraw Hill New York 1978 Stumm W and J J Morgan Aquatic Chemistry 3rd ed Wiley New York 1995 IN THE LABORATORY 251 IN THE LABORAT
48. the average water velocity m s w the average stream width d the average stream depth m g 9 81 m s the acceleration due to gravity and s the slope of the streambed unitless From these equations it can be seen that the downstream concentration of a pollutant in the absence of degradation is largely a function of the longitudinal dispersion which in turn is determined by the mixing in the system and the slope of the streambed Step Pollutant Input Model Combining the inflow outflow step source and sink terms into the mass balance expression and integrating for the equilibrium case where 0C Ot 0 results in the following governing equation for the transport of a step input to a stream system Vx 4kE 14 1 2E y where C x pollutant concentration mg L or uCi L for radioactive compounds at distance x and time t rate of continuous discharge of the waste kg s or Ci s stream flow rate m s longitudinal dispersion coefficient m s distance downstream from input m average water velocity m s first order decay or degradation rate constant s Cx W ex Q 1 4 4kE v x DOS The positive root of the equation refers to the upstream direction x and the negative root what we use in Fate refers to the downstream direction 4 x When there is no or negligible degradation of the pollutant k is set to zero or a very small number in Fate The longi
49. the printable version of your plot lower right portion of the screen Place the cursor over the plot at the desired x and y coordinates Hold the alt key down and press print screen Open your print or photoshop program Paste the Fate graph in your program by holding down the control key and press the letter v Save or print the file as usual 284 FATE AND TRANSPORT OF POLLUTANTS IN RIVERS AND STREAMS For a Mac e Select the printable version of your plot e Hold down the shift and open apple key and press the number 4 This will place a cross hair symbol on your screen Position the cross hair symbol in the upper right corner of your plot click the cursor and drag the cross hair symbol over the area to be printed or saved release the cursor when you have selected the complete image A file will appear on your desktop as picture 1 e Open the file with preview or any image processing file and print it as usual 25 FATE AND TRANSPORT OF POLLUTANTS IN LAKE SYSTEMS Purpose learn two basic models for predicting the fate and transport of pollutants in lake systems BACKGROUND Lakes and human made reservoirs serve as valuable drinking water resources Although many small lakes remain pristine most human made lakes suffer from overdevelopment and large lakes are subject to contamination from local industrial sources and shipping accidents Regardless of the size of the lake most introductory modeling efforts simplify the
50. tudinal dispersion coefficient E is characteristic of the stream or more specifically the section of the stream that is being modeled Under these conditions the governing equation reduces to C x E W vx Wie 3722302 As in the instantaneous input model values of E are estimated using the approach outlined by Fischer et al 1979 282 FATE AND TRANSPORT OF POLLUTANTS IN RIVERS AND STREAMS From these equations it can be seen that the downstream concentration of a pollutant in the absence of degradation is largely a function of the longitudinal dispersion which in turn is determined by the mixing in the system and the slope of the streambed REFERENCES Fischer H B J List R C Y Koh I Imberger and H Brooks Mixing Inland and Coastal Waters Academic Press New York 1979 Metcalf amp Eddy Inc Wastewater Engineering Collection Treatment Disposal McGraw Hill New York 1972 ASSIGNMENT 283 ASSIGNMENT Install Fate on your computer Fate is included with your lab manual Open the program and select the river step or pulse module A sample data set will load automatically Work through the example problem referring to the background information above and the explanation of the example problem included in Fate as needed 1 Select a pollutant and conduct the simulations described below for a step and instantaneous pollution scenario In selecting your pollutant and input conditio
51. yness and add another 50 mL aliquot You will first evaporate the sample filtrate to dryness in a 98 C oven to avoid boiling or splattering which could result in a loss of sample Next you will take the dried filtrate and crucible and dry it at 104 C to obtain the mass of dissolved solids in your sample Finally you will bake the sample at 550 C to oxidize the organic matter and obtain a dissolved volatile solids measurement Step by Step Instructions Preparing the Crucibles 1 Wash and clean at least three crucibles You only need three crucibles but some of these may crack in the preparation steps so it is wise to have more prepared than are needed Some residue may remain from previous experi ments 2 Label each crucible if they are not already labeled A good way to label crucibles is to paint a number on the bottom using an iron oxide paste When you bake the crucible the iron will bind permanently to the crucible Allow the crucibles to dry completely prior to placing them in the muffle furnace After air drying dry the crucibles in the muffle furnace at 550 C for 30 minutes the 30 minutes refers to the total time at 550 C 3 Obtain a constant weight of the crucibles by drying at 550 C allow the crucible to cool almost completely on a benchtop and then to cool completely in a desiccator weigh to a constant weight and repeat the heating and desiccation processes until you have two weights within 0 6 mg or less of each
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