Putting It All Together Where Chemistry Enters Into The Modeling Effort

We have covered many important and complicated chemical concepts in Chapters

2 and 3. But where do they all fit into the pollutant fate and transport modeling approach, and when is each important? It depends on the pollutant and the environmental system under study, but we will attempt to summarize the role of chemistry in the modeling effort. We will divide our discussions into a metal pollutant and a hydrophobic (organic) pollutant, and important chemical processes are summarized in Table 3.3. Note that ionizable organic pollutants, such as phenols, will fall in between these two extremes.

Case I: A Metal Pollutant

In our models for aqueous systems, the source of a metal pollutant is largely controlled by Ksp, since the dissolved (mobile) phase of the metal cannot exceed its ther-modynamically determined solubility (if it does, the metal will precipitate). Vapor pressure and Henry's law constants are of little consequence for metals, which are usually not volatile.

Recall that the purpose of fate and transport modeling is to determine the concentration of pollutant reaching a receptor (human), which in turn serves as the input to risk assessment models (Chapter 10). Although chemical speciation, discussed in Section 3.2.2, is not included in even the most sophisticated fate and transport models, it is considered in risk assessment. Many of the parameters discussed in Chapters 2 and 3 influence the speciation of metals. For example, pH can determine a metal's solubility, speciation, and sorption to mineral surfaces. Metals are more readily available in their hydrated free metal form at low pH values. The adsorption of all metals to particles increases with pH of the solution, due to surface charge availability (thus more dissolved metal is present at low pH values). EH can greatly affect oxidation states of transition, lanthanide, and actinide metals and therefore change their solubility, speciation, and degree of sorption. Thus, EH is another important parameter affecting mobility in aquatic systems. As we discussed, increasing ionic strength (salt content) can also have profound effects on metal speciation. A good generalization is that high ionic strength waters exhibit lower toxicity than low ionic strength waters. This is due to the complexation of the toxic free metal ion, generally the most toxic form of the metal, by anions in solution.

Sorption phenomena can greatly influence transport in aquatic systems. Metals adsorbed to mineral surfaces or natural organic matter are less bioavailable than dissolved metal species. Also, adsorbed metals generally share the fate of the particle. In lakes and streams, most particles and the metal ions sorbed to them settle to the bottom of the system and are incorporated into the sediments. Metals adsorbed to dissolved natural organic matter usually stay in the moving water and are transported out of the system under study. Transformation reactions (biological, chemical, and photochemical) are of little consequence to metals, with the exception of radioactive decay for radionuclides. One other rare exception is the methylation of mercury (a biological reaction) that creates a very toxic form of the pollutant.

Case II: Hydrophobic Pollutants

Hydrophobic pollutants represent the other extreme of types of pollutants because these pollutants do not "like" being dissolved in a polar fluid (water). Here, the concentration of pollutants in an aquatic system is controlled by the aqueous solubility and/or Henry's law constant. For atmospheric systems, vapor pressure determines the mass input.

TABLE 3.3. A Summary of Chemical Factors Affecting Fate and Transport for Each Category of Pollutants

Chemical Factor (by section)

Metals

Radionuclides (a Class of Metals)

Ionizable Organics

Hydrophobic Organics

Section 2.4 PH

Solubility Vapor pressure HLC

For inorganics Acid-base Redox Precipitation Section 2.5 Sorption

Section 2.6 (organic redox transformations) Abiotic Photochemical Biological

Very important Very important Not important Not important

Very important Very important Very important

Very important

Very important Very important Not important Not important

Very important Very important Very important

Potentially important Very important Can be important Can be important for uncharged form

Very important Very important

Can be important Can be important Can be important

Usually not important Very important Can be important Usually important

Very important

Can be important Can be important Can be important

The pH and ionic strength of the system have little to no effect on the fate of hydrophobic pollutants. (Of course, pH does have a large effect on ionizable organ-ics, and the presence of a salt would serve to decrease the solubility of these compounds.) Eh, however, can greatly influence biotic and abiotic degradation reactions. Some pollutants are easily degraded in aerobic environments by microbes, while other pollutants are more easily degraded by biotic and abiotic processes under anaerobic or reducing conditions. Thus, biological and abiotic processes can be very important removal mechanisms for organic pollutants. In the atmosphere and in surface waters, photochemical degradations can also be important.

Sorption phenomena are very important for hydrophobic pollutants, since these pollutants would rather be on any surface than dissolved in a polar solvent like water. Thus, sorption to natural organic matter and mineral surfaces is important. In general, Kp values for hydrophobic pollutants are orders of magnitude greater than Kd values for metal pollutants. As with metal pollutants, sorption phenomena will be important in lake, stream, and groundwater systems.

So, how do we put chemistry into the fate and transport modeling approach? To understand this, we must introduce the concepts of box models and mass balance. In environmental modeling, it is important to define your system, and we do this using boxes. For example, if we are studying the transport of a pollutant in the atmosphere or in a groundwater system, we define the section of the system we are interested in with a box of physical dimensions equal to that of the system under study. Next, we account for all of the pollutant mass entering, reacting in, being retained in, or exiting the system (a mass balance). Of course, this means we use a lot of mathematics, and the second section of this text will deal with the development and use of models to describe the fate and transport of pollutants in lakes, rivers, ground-water, and atmospheric systems.

The basic approach for our mass balance in each of the following chapters will be represented by

Change of mass = sum of + sum of internal - sum of all - sum of all in system with time dC/dt all inputs mass of pollutant input sources any source or generation of the pollutant from within the system outputs internal sinks mass of removal from pollutant the system exiting the by sorption system or degradation reactions

We have already mentioned most of these terms in this book. For example, the "mass of pollutant input" can be controlled by point and non-point sources, pulse and step inputs, and solubility, vapor pressure, and Henry's law constants. The term "any source or generation of the pollutant from within the system" can be illustrated by desorption from the sediments (Kd or Kp) or by the generation of an atmospheric pollutant by photochemical reactions. The "mass of pollutant exiting the system" can be represented by the outflow from a lake or river or by the specific section of an aquifer or the atmosphere. We will show detailed examples of each of these in the fate and transport chapters.

Finally, let's concentrate on the last term in the mass balance equation, the sum of internal sinks. This is where kinetic transformation/degradation reactions come into the equation. Recall that many of our reactions were found to be or were simplified to be first-order reactions. This makes life much easier for the modelers, since if all of the reactions are of the same rate order (first, in our case), we can add the individual rate constants together and have one overall first-order rate constant. Thus, say we have a pollutant that is biodegraded with a rate constant of 0.05 days-1 and is photochemically degraded such that k equals 0.005 days-1. Instead of deriving a much more complicated equation with two kinetic variables, we can simply add the two k values together to obtain an overall rate constant of 0.055 days-1 and have one kinetic term in the equation. Any number of first-order rate constants can be added together. This will become clearer in the fate and transport chapters when we give each general transport equation.

A Closer Look: Calculation of a Partition Coefficient from Experimental Data

A Koc is to be determined for the sorption of 2,2'4,4',6,6'-hexachlorobiphenyl (a PCB congener) on a sediment sample. The organic content of the sediment is 2.05%. A 2.05 mg/L solution of 2,2'4,4',6,6'-hexachlorobiphenyl (HCB) is prepared, and ~40mL of the solution is placed in a vial containing 0.102g of dry sediment. The final solution volume is 40.0mL. The sample is mixed for 3 days, the aqueous and sediment phases are separated with a 1.0-|mm glass fiber filter, and the aqueous phase is measured for 2,2'4,4',6,6'-hexachlorobiphenyl. A concentration of 0.506mg/L is measured in the aqueous phase. Analysis of a blank vial (containing water and HCB but no sediment) measures a concentration of 1.88mg/L of HCB in the dissolved phase. What are the Kp and Koc for the sample?

1

Total mass (mg) of HCB added each flask

0.0820

2

Mass recovered in blank (mg)

0.0752

3

Mass of HCB in water phase (mg) of mixture

0.0202

4

Volume of water (L)

0.0400

5

Concentration of HCB in water phase (mg/L)

0.505

6

Mass of HCB on solid phase (mg) (determined by difference) (1-3)

0.0550

7

Mass of solid phase (kg)

1.02 x 10-4

8

Concentration of HCB on solid phase (mg/kg)

539

9

K

1068

10

Koc (Kp/foc) (L/kg)

51350

Box 1: First we should determine the mass of HCB in each flask. This is done by multiplying the HCB concentration by the volume of solution: (2.05mg/L) x (0.0400L) = 0.0820mg.

Box 2: Note that not all of the HCB added to each flask was recovered during the analysis of the blank (1.88mg/L x 0.0400 = 0.0752mg). This observation is common in laboratory experiments. Thus, we must assume that all of the flasks only have 0.0752mg of recoverable HCB in them. Sources of loss of HCB could include volatilization from the aqueous phase during solution preparation or sorption to the vial walls or vial top.

Box 3: Next the concentration of HCB in the vial containing sediment is calculated: (0.506mg/L x 0.040L = 0.202mg). We will use the concentration in the water to calculate Kp.

Box 4: Next the mass of HCB associated with the sediment is determined by subtracting the mass measured in the dissolved phase from the mass in the blank: 0.0752 - 0.0202 = 0.0550mg.

Box 8: Next the concentration of HCB on the sediment is determined: 0.0550mg / 1.02 x 10-4kg = 539mg/kg.

Box 9: The Koc is calculated from the ratio of sediment-phase concentration to dissolved-phase concentration: 539mg/kg / 0.506mg/L = 1068L/kg.

Box 10: Kp is calculated by multiplying the Koc by the fraction of organic carbon present in the sample: 1068L/kg x 0.205 = 219L/kg.

A Closer Look: Determination of an Average Kd Based on a Set of Kd Measurements

A more accurate determination of Kd or Kp can be made when the parameter is measured over a range of pollutant concentrations. For example, a set of Kd experiments were conducted to investigate the adsorption of Pb on a soil. It is important to note that all of the vials contained the same mass of sediment. This is important because Kd can be a function of suspended solids concentration (sediment). The experiments were conducted in a manner similar to that described in our other examples. The following results were then compiled:

Aqueous-Phase Concentration (mg/L)

0.0500

0.103

0.698

1.50

3.78

Sediment-Phase Concentration (mg/kg)

21.4

35.5

To solve this problem, we must first plot the data and determine the slope of the line (which equals the Kd). The results are shown in Figure 3.12. Note that if all of the data are used, the plot is a straight line, until it levels off at the highest concentration. This is not uncommon in laboratory experiments when excessively high

Aqueous-Phase Conc. (mg/L)

Figure 3.12. Determination of Kd from experimental data.

Aqueous-Phase Conc. (mg/L)

Figure 3.12. Determination of Kd from experimental data.

dissolved metal phase concentrations are used. This phenomenon results primarily from complete coverage of the sorption sites on the sediment and results in an excess concentration in the dissolved phase. When this occurs, it is more accurate to estimate Kd from the lower data points. A linear regression of the first four data points in the table yields a slope, and Kd, of 14.3L/kg.

Exercises

1. Which is a more accurate representation of how toxic a pollutant is, activity or concentration?

2. What is the numeric range of the activity coefficient?

3. Calculate the ionic strength for the following:

(a) a mixture of 0.050M CaCl2, 0.025M NaCl, and 0.045M KNO3

(b) a mixture of 0.097M CaCl2, 0.015M KCl, and 0.405M NaNO3

4. Using your results from exercise 3 and the extended Debye-Huckel equation, calculate the activity of each cation and anion in the mixtures.

5. Acid rain is known to be harmful to the environment for multiple reasons, but few people realize that free Al3+ ions are one of its most harmful products. Ionic aluminum is toxic to fish at levels as low as 6.2ppm. Aluminum forms five ligand complexes with OH- (conplexation constants are given in Table 2.6), but the formation of these is understandably minimized at lower pHs. Draw a speciation plot using a spreadsheet showing the concentrations of each species at pH values ranging from 0-14. Assume that the solution is in equilibrium with the solid phase, Al(OH)3. Ksp values are given in Table 2.5.

6. Mining operations have often been major contributors to groundwater and surface pollution. They introduce toxic metal concentrations as well as increasing the total ion concentration of an aquatic system. An especially troublesome phenomena encountered in mining operations is acid mine drainage (AMD). This occurs when groundwater runs over old mining sites or through old mining tunnels. At these sites, many minerals and metals have been exposed from the surrounding rock and are free to react with the water and the atmosphere. Pyrite (FeS2) is a common mineral found at mine sites that can cause damage to aquatic ecosystems. When pyrite is exposed to air and water, it reacts to form sulfuric acid (H2SO4) and iron hydroxide Fe(OH)3. This not only raises the pH of the stream, but also introduces a solid metal hydroxide which can be toxic to fish and aquatic life. However, the pyrite reaction does not always result in solid iron hydroxide. Consider the following complexation reactions, and produce a speciation diagram (using a spreadsheet) for the various iron hydroxide complexes. Determine what the dominant species will be at a pH of 4.5, a common pH found in streams that suffer from AMD.

7. You are curious about the speciation of Ni2+ in a solution with OH- ions. Excess Ni(OH)2 salt is added to a beaker with distilled water. Your goal is to determine the predominant species of Ni2+ and OH- complexes based on the OH- concentration. Since there is excess salt in the solution, Ni(OH)2 controls the main species present and its concentration by the Ksp of the salt (5.48 x 10-16). Draw a speciation plot using OH- concentrations from 1.00 x 10-18 to 1.00 x 10-8M and the following log K values for binding between the Ni2+ and OH- ions:

8. Silver bromide is used in photography as a developing emulsion. Given the Ksp values (Table 2.5) and stability constants (Table 2.6) for Br- ligands, determine how the concentration of each Ag species in solution varies as the Br- concentration changes. Construct a graph of the log[Br-] from -1.0 to 6.0 versus log[Ag species] from 0.0 to -35. Include a line for total [Ag] as [Br-] varies.

9. Cobalt is usually emitted during the production of steel and other alloys, and specifically in the production of airline engines and gas turbines. Ionic cobalt can be carcinogenic, but the amount of consumption must be very high in order for cancer to occur. Create a speciation diagram using a spreadsheet for a cobalt hydroxide system without any solid phase present (Case II in this chapter). The total concentration of Co2+ species is 20ppm. The hydroxide concentrations should range from 1 x 10-1 to 1 x 10-14.

Helpful equations

Co2+ + OH fi CoOH K = 5.01187 x 10-5 Co2+ + 2OH fi Co(OH)2 p 2 = 6.30957 x 10-10 Co2+ + 3OH fi Co(OH)3 p3 = 3.16228 x 10-11

10. Mercury sulfate was tested in a renegade agricultural operation as a mildew inhibitor. A few acres were dusted with HgSO4, and then irrigation water and rainfall washed the compound into a nearby holding basin. The EPA caught wind of the illegal activity and sent you in to investigate. Since there is no solid phase present, you will be given the K and beta values for Hg and SO4-ligands. Your assignment is to show how the concentration of each Hg species changes as the SO|- concentration is varied. Create a labeled graph of the log[Hg] from 0.0 to -30.0 versus log[SO42-] from -10.0 to 10.0. Be sure to include how the total [Hg] changes overall.

11. An aspiring restaurateur purchases a cheap plot of land to open a restaurant, complete with a less than pristine pond. In an effort to make the restaurant more scenic, she valiantly undertakes the task of cleaning up garbage in the pond. In doing so, she discovers a 55-gallon drum labeled "Barium Waste." She then hires you, a contractor, to determine what has been chemically disposed of in the pond. You find that the concentration of dissolved barium in the pond is 10.5ppm, with no solid phase present in the sediments. Using the equations in this chapter, determine the concentration of Ba2+ in the water as a function of CO3- concentration. Use CO2- concentrations of 0.000100M, 0.001M, 0.100M, 1.00M, and 5.00M.

12. Ethyenediaminetetraacetic acid (EDTA) is a widely used chemical in industry and is very good at complexing metal ions. We can use EDTA as a com-plexing agent for mercury, which lowers the mercury's toxicity but at the same time increases its mobility by keeping it in solution. Draw a speciation diagram for a closed system (Case II) of 10ppm Hg as a function of EDTA concentration. Use a log[EDTA] concentration range from 5 to -35.

Hg2 + + EDTA2+ fi HgEDTA K = 3.16 x 1023 Hg2+ + EDTA- fi HgEDTA + Pj = 1.00 x 1027

13. Cadmium metal ions form three complexes with SO4- in the absence of a solid. Draw a speciation plot of Cd2+ in the presence of SO42- ions using a Cd2+ concentration of 40.5ppm and a concentration of SO|- ranging from 1.00 x 10-6 to 1.0M. The following binding log K values will be useful:

For CdSO4: 2.3 For Cd(SO4)2-: 3.2 For Cd(SO4)3-: 2.7

14. The leachate from a local landfill has been suspected of containing high cadmium concentrations, and the city downstream from the watershed has begun monitoring the streams for cadmium. In order to better predict transport, they need to determine the distribution coefficient for cadmium between the stream water and the local soil. Two liters of sample water were collected, filtered, and dried. The dried filtered particulate matter weighed 10.0g and was used to determine the total suspended solids (5000mg/L). Sediment samples of the local soil (250mg) were prepared in ~50-mL sample bottles to create the same TSS as the local streams. Cadmium (0.375mg) was added to each of the sample vials, including the blanks, and water was added for final solution volumes of 50.0mL. The solutions were mixed for three days, and then they were filtered with 0.20-|mm filters and analyzed by flame atomic absorption spectrometry. The equilibrium cadmium concentration in of the aqueous phase was 5.00mg/L. Calculate the Kd for Cd2+ on the soil.

15. Aldrin is a chlorinated pesticide that was used to regulate termite populations until the 1970s. After application, this non-biodegradable pesticide found its way into freshwater systems, poisoning organisms. A sample of lake water sediment was taken to determine how well Aldrin adsorbs onto solid sediment. For this experiment, 0.1147 mg of Aldrin was added to a flask containing 100.0mL of water and 4.26 x 10-4kg of lake sediment. Through gas chromatographic-electron capture detection (GC-ECD) the equilibrium concentration of Aldrin in the aqueous phase was determined to be 0.0180ppm. Determine the mass of Aldrin in the aqueous and solid phases and calculate the Kp value for the pollutant Aldrin.

Total mass (mg) of pollutant added to flask

0.1147

Mass of pollutant in aqueous phase (mg)

Volume of water (mL)

100.0

Concentration of pollutant measured in

0.0180

aqueous phase (mg/L)

Mass of pollutant on solid phase (mg)

Mass of solid phase (kg)

4.26 x 10-4

Concentration of pollutant on solid phase (mg/kg)

KP

16. Kepone (chlordecone), a carcinogenic, tan to white crystalline solid or powder that is insoluble in water, was used as an insecticide, fungicide, and larvacide on bananas, tobacco, and other domestic plants. The U.S. EPA banned the use of Kepone in 1975, but the chemical is still used in some countries. Before the termination of its production in the United States, large amounts of Kepone were dumped into the upper James River. This Kepone poses a threat to the fish and other marine animals, as well as to the ground-water supply. Most of the Kepone in the James River has settled into the sand and sediments at the bottom. A Kp needs to be determined for the sorption of Kepone on a sediment sample. A solution of 0.02453mg/L Kepone is prepared. 100.0mL of the solution is placed in a vial with 0.000100kg of dry sediment. The sample is mixed for three days, and the aqueous and solid phases are separated using a 0.20-|mm glass fiber filter. The mass of Kepone in the aqueous phase is measured with gas chromatography. From this, the concentration of Kepone in the aqueous phase is determined to be 0.02108mg/L. Analysis of the blank shows no loss of kepone from absorption onto the vial wall. Find the Kp for the sample using the following chart.

1

Total mass (mg) of kepone added to each flask

2

Mass of kepone in water phase (mg) of mixture

3

Volume (L) of water

4

Concentration of kepone in water phase (mg/L)

5

Mass of kepone on solid phase (mg)

6

Mass of sediment in vial (kg)

7

Concentration of kepone on solid phase (mg/kg)

8

KP

17. The EPA just received a report of a small-scale dumping site of lead-acid batteries in a city under your jurisdiction of investigation. The site contains various car and tractor batteries located on a downhill slope near a stream. It is your job to determine the extent of the contamination of lead pollution in the stream, accounting for the concentration in the aqueous phase as well as the sorption to the solid particles in the stream—in other words, you need to determine the Kd (distribution coefficient) of lead. To determine the Kd, you add 0.100g clay to 0.1000L water and then add 0.04976mg Pb2+ to the sample. After allowing the samples to equilibrate for a minimum of 3 days, you analyze them on a Flame Atomic Absorption Spectroscopy system and find that there is 0.500mg/L Pb in the aqueous phase of each sample. You also run a blank and find that the amount of Pb lost to sorption in the test tubes is 0.01000mg/L. Use these values to complete the table and determine the Kd of Pb in the samples.

Total Pb in sample (mg)

0.04976

Volume water in sample (L)

0.1000

[Pb] aqueous phase of sample (mg/L)

0.5000

[Pb] lost in blank (mg/L)

0.01000

Mass Pb in aqueous phase (mg)

Solid-phase mass (mass of clay) (g)

0.1000

Mass of Pb in solid phase (mg)

[Pb] solid phase (mg/kg)

Kd

18. We have discussed equilibrium in terms of Kd and Kp, and we have discussed kinetics in terms of first-order sorption and desorption rates. Explain how each can be important in determining the fate and transport of pollutants in natural water systems.

19. Select a metal pollutant. Using the information from Chapters 2 and 3, explain all chemical processes that can influence its fate and transport in an aqueous system. Which processes will increase the transport? Which processes will decrease the transport? Limit your discussion to three typed pages. A good place to start is to outline the important processes in each chapter.

20. Select a hydrophobic pollutant. Using the information from Chapters 2 and 3, explain all chemical processes that can influence its fate and transport in an aqueous system. Which processes will increase the transport? Which processes will decrease the transport? Limit your discussion to three typed pages. A good place to start is to outline the important processes in each chapter.

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