Computer Methods For Solving Equilibrium Problems

The chemical equilibrium problems presented in this chapter are relatively simple ones involving only a few species and equilibrium expressions. They have been solved using equilibrium constants, mass balances, charge balances, and sometimes proton conditions, and spreadsheets or by making simplifying assumptions and generating quadratic equations or by drawing log concentration diagrams. However, for more complex problems where many species are involved (say more than 15 to 20), where several solids may be present, and where equilibrium between the atmos-

chapter 4 Basic Concepts from Equiiibrium Chemistry

phere and the water must be considered, computer solutions are required. Most available computer programs are based on the principles developed in this chapter. Basically, all use mass balances and equilibrium expressions that must be solved sir multaneously. The numerical methods used for solving the equations are different for different computer programs. Additionally, there may be some constraints that are specific to the system being analyzed (for example, oxidized versus reduced environment, solids likely to be present, open or closed to the atmosphere). Mass balances must be written in a format that the computer program will recognize; these formats are different for the different computer programs. Matrices called tableaus are used by most for input data. Description of these formats is beyond the scope of this text. Most of the available programs come with databases that include equilibrium constants and other thermodynamic data for acid-base equilibria, complex-ion equilibria, and solubility equilibria.

The most commonly used software are based on MINEQL.13 Examples include MINTEQA2,'4 Visual MINTEQ,15 and MINEQL+.16 Some of these software packages can be downloaded (or purchased) from the internet. More detailed descriptions of the format used for these programs is given by Benjamin17 and Morel and Bering.18

PROBLEMS

For the following, assume that the temperature is 25°C. Ignore activity corrections unless otherwise noted.

4.1 Calculate the activity coefficient and activity of each ion in a solution containing 300 mg/L NaNOj and 150 mg/L CaSO„.

Answer: Na* and NOJ, 0.91 and 3.21 X 10""3; Ca2+ and SO2-. 0-69 and 0.76 X 10"3

4.2 Calculate the activity coefficient and activity of each ion in a solution containing 75 mg/L Na\ 25 mg/L Ca2\ 10 mg/L Mg2+, 125 mg/L Cl~, 50 mg/L HCOf, and 48 mg/L SOl".

4.3 A solution is prepared by diluting 10~3 mol of propionic acid to I liter with distilled water. Calculate the equilibrium concentration for each chemical species in the water.

Answer: £H+] = 1.08 X 10~4, [OH"] = 9.29 X HT11, [HPr] = 8.92 X lO'4, [Pr~] = 1.08 X 10~4

4.4 A solution is prepared by diluting 10™2 mol of ammonia to 1 liter with distilled water. Calculate the equilibrium concentration for each chemical species in the water.

"J. C. Westall, J. L. Zachary, and F. M. M. Morel, "MINEQL, A Computer Program for the Calculation of Chemical Equilibrium Composition of Aqueous Systems," Technical Note 18, Parsons Laboratory, MIT, Cambridge, MA, 1976. WU.S. Environmental Protection Agency.

,shttp://www.lwr.fcth.se/english/OurSoftware/vminteq/mdex.htm

is a registered trademark of Environmental Research Software.

I7M. M. Benjamin, "Water Chemistry," McGraw-Hill, New York, 2002.

"F. M. M. Morel and jf. G. Hering, "Principles and Applications of Aquatic Chemistry," Wiley-Interscience, New York, 1993.

4.5 Calculate the equilibrium pH of a solution containing (a) 1G~3 M H2S04; (£>) 10~3 M

h2so4.

4.6 Calculate the equilibrium pH of NaOH solutions containing (a) 10*"4 M NaOH; (b) 10"8 M NaOH.

4.7 Calculate the pH of solutions containing 100 mg/L of each of the following weak acids or weak bases: (a) acetric acid; (b) hypochlorous acid; (c) ammonia; (d) hydrocyanic acid.

Answer: (a) 3.78; (i>) 5.13; (c) 10.50; id) 5.88

4.8 Calculate the pH of a solution containing 50 mg/L of each of the following weak acids or salts of weak acids: (a) carbonic acid; (b) sodium acetate; (c) sodium hypochlorite; (d) phosphoric acid.

4.9 Calculate the ratio of ammonia nitrogen in the NH3 form to that in the NHj form in a solution with a pH of 7.4.

Answer: 0.014

4.10 Calculate the ratio of hypochlorous acid to hypochlorite ion in solutions with the following pH values:

4.11 Un-ionized hydrogen cyanide (HCN) is toxic to fish. Assume that the toxic level of HCN for a given species of fish is 10~6 M. For a total cyanide concentration of 10~5 M, determine at what pH HCN reaches toxic levels for

(a) Ionic strength approximately 0

4.12 What is the pH of a solution containing 10"2 M propionic acid?

4.13 What is the pH of a solution containing 10~2 M sodium propionate?

Answer: 8.44

4.14 A solution is made by adding Ca(OCl)2 to water to yield a concentration of 0,01 M. Using the algebraic approximation method,

(a) What is the pH of the solution if activity corrections are ignored? (,b) What is the pH of the solution if activity corrections are included? Answer: 9.92; 9.83

4.15 A solution is made by adding NH4C1 to water to yield a concentration of 0.02 M. Using the algebraic approximation method,

(а) What is the pH of the solution if activity corrections are ignored?

(б) What is the pH of the solution if activity corrections are included?

4.16 Aspirin is produced from salicylic acid (HOC6H4COOH). This diprotic acid has pKA1 = 2.97 and p= 13.70 at 25°C, A solution is made by adding enough salicylic acid to water to give a concentration of 10~3 M.

(a) Determine the equilibrium pH using a spreadsheet.

(b) Determine the equilibrium pH using the algebraic approximation method.

(c) What do you think this pH does to your stomach? Answer 3.20; 3.20

4.17 Oxalic acid (HOOCCOOH) is a diprotic acid with p/sfAI = 1.25 and pKA2 = 4.28. Using a spreadsheet, determine the equilibrium pH of a solution made by adding enough oxalic acid to water to give a concentration of 10"2 M.

4.18 A solution is made by adding enough sodium phthaiate (Na2C804H4) to water to give a concentration of 10'3 M. Assume the sodium phthaiate completely dissolves. At 25°C, Km = 2.95 and KM = 5.41.

(a) Determine the equilibrium pH using a spreadsheet.

(b) Determine the equilibrium pH using the algebraic approximation method.

4.19 Sufficient Na2C03 is added to water to yield a concentration of 0.01 M.

(ia) What is the pH of the solution at 25°C if activity corrections are ignored? (£>) What is the pH of the solution at 25°C if activity corrections are included?

(c) What is the pH of the solution at 15°C if activity corrections are included? (At 15°C, pKw = 14.34, pKA1 = 6.41, and pKA2 = 10.42. These values were calculated using relationships developed in Chap. 3.)

4.20 Arsenic acid (H3As04) is a triprotic acid with pKM = 2.22, pKA2 - 6.98, and pifA3 = 11.53. KH2AsO„ is added to water to give a total concentration of 0.001 M.

(a) Write the mass balance for this solution.

(b) Write the charge balance for this solution.

(c) Write the proton condition for this solution.

(d) Using the algebraic approximation method, calculate the equilibrium pH.

(e) Determine the equilibrium pH using a spreadsheet.

4.21 Calculate the concentration of each chemical species in a solution made by dissolving enough NaH2P04 in water to yield a concentration of 100 mg/L.

4.22 A solution is made by adding acetic acid to yield a concentration of 0.01 M and sodium acetate to yield a concentration of 0.01 M. Using the algebraic approximation method,

(a) What is the pH of the solution if activity corrections are ignored?

(b) What is the pH of the solution if activity corrections are included? Answer: 4.74; 4.69

4.23 A solution is made by adding HCN to yield a concentration of 0.01 M and KCN to yield a concentration of 0.01 M. Using the algebraic approximation method,

(a) What is the pH of the solution if activity corrections are ignored?

(b) What is the pH of the solution if activity corrections are included?

4.24 (a) Draw a logarithmic concentration diagram for a 10~3 M solution of hydrogen sulfide. Assume a closed system. (6) From the diagram, determine the pH for solutions that contain the following (1) 10™3 M H,S, (2) 10"' M Na,S, (3) 0.5 X 10~3 M HS" and 0.5 X 10~3 M S2~, and (4) 0.5 X 10~3 M H2S and 0.5 X 10~3 M HS". Answer: (1) 5.0; (2) 10.9; (3) 12.9; (4) 7.0

4.25 (a) Draw a logarithmic concentration diagram for a 10~2 M solution of hydrogen sulfide. Assume a closed system. (£>) From the diagram, determine the pH for solutions that contain the following (1) 10"2 M HjS, (2) 10"2 M Na2S, (3) 0.5 X 10~2 M HS" and 0.5 X 10"2 M S2", and (4) 0.5 X 10"J M H2S and 0.5 X 10-2 M HS".

PART 1 Fundaméntate of Chemistry for Environmental Engineering and Science

4.26 Using a logarithmic concentration diagram, determine the pH of a solution containing 10"2 M H2C03 and 2 X 10"2 M Na2C03.

4.27 Using a logarithmic concentration diagram, determine the pH of a solution containing 10~2 M acetic acid and 2 X 1CT2 M sodium acetate.

Answer: 5.0

4.28 Using a logarithmic concentration diagram, determine the pH of a solution containing 10"' M acetic acid and 10"3 M hydrochloric acid.

4.29 Using a logarithmic concentration diagram, determine the pH of a solution containing 10"3 M Na2C03 and 10"3 M NaOH.

Answer: 11.1

4.30 Using a logarithmic concentration diagram, find the pH of a solution containing 10"2 M acetic acid and 10"2 M ammonia.

4.31 Using a logarithmic concentration diagram, find the pH of a solution containing 10~! M acetic acid and 2 X 10"11 M sodium bicarbonate.

Answer: 6.4

4.32 Using a logarithmic concentration diagram, find the pH of a solution formed from mixing equal volumes of 10~3 M acetic acid and 10~2 M ammonium bicarbonate.

4.33 Using a logarithmic concentration diagram, find the pH of a solution formed from mixing equal volumes of 10"2 M propionic acid, 10"2 M acetic acid, and 10 1M sodium bicarbonate.

Answer: 7.0

4.34 A solution is made by adding ammonium acetate to water to give a concentration of 0.01 M Using a logarithmic concentration diagram, determine the equilibrium pH.

Answer: 7.0

4.35 A solution is made by adding ammonium carbonate to water to give a concentration of 0.01 M. Using a logarithmic concentration diagram, determine the equilibrium pH.

4.36 The pH of clean rain was calculated to be 5.68 in Example 4.16. Acid rain, defined here as rain with pH less than 5.68, can be formed when sulfur dioxide (S02) is discharged into the atmosphere. Assume that the atmosphere contains 20 ppb by volume of S02 {10"" atm). Develop an equation that will allow determination of the pH of rainwater in equilibrium with CO, in air @ 10"" atm (see Example 4.16) and SOj. Use a spreadsheet to calculate this pH. Comment on the relative impacts of SO, and C02 on the pH of rain. The following should be used.

H2S03(a<?) = SO 2(g) + H20 Kh,SOi = 0.80 atm-L/mol H,SO, = HS03- + H+ PKA!= 1-77 HS03" = SOl" + H* pKA2 = 7.21

4.37 Calculate the pH of the equivalence point in the titration of solutions containing the following concentrations of acetic acid with sodium hydroxide: (a) 100 mg/L; (b) 1000 mg/L; (c) 10,000 mg/L.

4.38 Calculate the pH of the equivalence point in the titration of each of the following concentrations of sodium bicarbonate with sulfuric acid: (a) 10 mg/L; (b) 100 mg/L; (c) 1000 mg/L. Assume a closed system.

4.39 Calculate the equivalence point pH for both ionizations in the titration of 150 mg/L of sodium carbonate with sulfuric acid. Assume a closed system.

4 4Q Calculate the equivalence point pH for both ionizations in the titration of 150 mg/L of sodium sulfide (Na2S) with sulfuric acid.

4.41 A l-Ktw solution contains 100 mg of HCL Calculate the following:

(a) Initial pH of the solution

(b) pH after addition of 1 mL of 1 N NaOH

(c) pH after addition of 2 mL of 1 N NaOH

(d) pH after addition of 3 mL of 1 N NaOH

(e) mL of 1 N NaOH required to reach the equivalence point Answer: (a) 2.6; (b) 2.8; (c) 3,1; id) 10.4; (e) 2.74 mL

4.42 A 500-mL solution contains 100 mg of NaOH. Calculate the following:

(a) Initial pH of the solution

(c) pH after addition of 4 mL of 1 N H2S04

(d) mL of 1 N H5S04 required to reach the equivalence point

4.43 (a) Using the approximating equations developed in the text, sketch the titration curve for titrating a solution of 0.001 M sodium propionate with 0.1 M HCL

(b) At what pH is the buffer intensity (buffer index) maximum? What is the value of the buffer intensity here?

(c) At what pH is the buffer intensity minimum? What is the value of the buffer intensity here?

Answer: (b) 4.89,6.05 X I0~4 M; (c) 3.95,4.71 X 10"4 M

4.44 A solution contains 10"3 M total inorganic carbon and has a pH of 7.2. No weak acids or bases are present other than the carbonate species, but other cations and anions are present. Neglecting ionic strength effects, plot the titration curve for titration of I liter of this water with 0.1 M HC1. Assume no interchange with the atmosphere occurs.

4.45 A solution contains 10""3 M dissolved inorganic carbon and has a pH of 8.23. Assume a closed system.

(¡i) How much strong acid (HC1 in moles per liter of solution) would be required to titrate this solution to a pH of 6.3? (b) How much strong acid (HC1 in moles per liter of solution) would be required to titrate this solution to its equivalence point? Answer: 5 X 10"4M; 10-3 M

4.46 A water is in equilibrium with the atmosphere (partial pressure of C02 = 5.0 X 10~" atm) at 25°C, and has a pH of 8.1. The total phosphate concentration is 0.001 M. No other weak acids or bases are present. How many milliliters of 0.5 M H2S04 are needed to decrease the pH of 1 liter of this water to 6.0?

4.47 How many milliliters of 1 N NaOH must be added to a 500-mL solution containing 500 mg of acetic acid to increase the pH to 5?

4.48 {a) Draw a logarithmic concentration diagram for a 10~4 M solution of hypochlorous acid (25°C). (b) From the diagram obtained in part (a), determine (1) the equilibrium pH for 10~4 M hypochlorous acid, (2) the pH after 0.5 X 10~4 mol of NaOH has been added to a liter of solution, and (3) the pH after 10"4 mol of NaOH has been added per liter of solution.

4.49 (a) Draw a logarithmic concentration diagram for aIO-4 M solution of propionic acid. (i>) From the diagram obtained in part (a), determine (1) the equilibrium pH for 10~4

M propionic acid, (2) the pH after 0.5 x 10~4 mol of NaOH has been added to a liter of solution, and (3) the pH after 10~4 mol/L of NaOH has been added to the solution.

4.50 Calculate the pH of a buffer solution prepared by mixing 2.4 g of acetic acid (CHjCOOH) and 0.73 g of sodium acetate (CH3COONa) in 1 liter of water (equivalent to buffer solution for amperometric chlorine determination).

Answer: 4.0

4.51 Calculate the pH of a buffer solution prepared by mixing 8.5 g KH2P04 with 43.5 g K2HP04 in 1 liter of water (equivalent to buffer solution for BOD dilution water).

4.52 Calculate the pH (a) before and (b) after adding 20 mg/L HC1 to a buffer solution containing 100 mg/L KH2P04 and 200 mg/L K3HPO+.

4.53 Calculate the pH of a buffer solution prepared with 500 mg/L acetic acid (CHjCOOH) and 250 mg/L sodium acetate (CBCOONa) under the following conditions:

(o) Initially

(f>) After 20 mg/L of HC1 is added to the solution (c) After 20 mg/L of NaOH is added to the solution

4.54 Calculate the pH of a 200-mL buffer solution containing 20 mg/L carbonic acid and 50 mg/L bicarbonate ion, under the following conditions. Assume a closed system.

(a) Initially

(c) After 3 mL of 0.02 N NaOH is added Answer: (a) 6.8; (b) 6.3; (c)8.I

4.55 Find the pH and buffer index for the following: (a) 0.1 M acetic acid plus 0.1 M sodium acetate (¿>) 0.19 M acetic acid plus 0.01 M sodium acetate (c) 0.02 M acetic acid plus 0.18 M sodium acetate

4.56 Find the pH and buffer index for the following:

Answer: (a) 7.5, 5.8 X lO""3; (b) 8.45,2.2 X 10~3; (c) 6.9,1.26 X 10"3

4.57 Draw a curve of buffer index as a function of pH for 0.1 M acetic acid.

4.58 Draw a curve of buffer index as a function of pH for 0.1 M ammonium chloride.

4.59 You wish to develop a buffer that will maintain the pH of a laboratory reactor in the range 7.0 ± 0.3. The biological reaction of interest is nitrification, which is described by the following:

(a) Assume that the nitrogen is initially present as NH„C1 and that no other weak acids or bases exist in the solution. Select an appropriate acid/conjugate base pair to serve as the buffer and calculate the concentration of acid and conjugate base required for treatment of 50 mg/L of N in the form of NH?-

(b) Calculate the buffer intensity of your buffer system.

4.60 A buffer is made by combining monosodium oxalate (NaC204H) and disodium oxalate (Na;>C204) to give concentrations of 0.01 M for NaC204H and 0.02 M for Na2C204. pifA1 is 1.25 and pK/a is 4.28.

(a) What is the initial pH of this buffer?

(b) What is its buffer intensity?

(c) What is the pH of this buffer after the addition of 0.001 M NaOH? Answer: (a) 4.58; (b) 1.54 X 10~2 M; (c) 4.65

4.61 You wish to construct a buffer that will resist pH changes during biological denitrification. During this process 1 mol of OH" is produced for each mole of N03 removed. You wish to remove 10~3 M of NO3 and maintain the pH at 7.5 ± 0.5. Select an appropriate buffer system and calculate the minimum quantities of chemicals required to maintain the desired pH range.

4.62 (a) What is the pH of a buffer made by adding 2.91 X 10"2 M NaHCO, and 4.30 X

10~3 M Na2COj to water in a closed system?

(b) What is the pH of the buffer after addition of 10~3 M H2S04? The system is still closed.

(c) If the buffer in part (a) is opened to an atmosphere with PCOt = 10~3,4(i atm, what is the resulting pH? Does C7CO) increase or decrease? By how much?

4.63 From a distribution diagram for Cu-NH3 complexes, what is the predominant Cu(H) species when the ammonia concentration is (a) 0.1 mg/L, (b) 1 mg/L, (c) 10 mg/L, and (d) 100 mg/L?

4.64 Using a logarithmic concentration diagram, determine the concentration of various ammonia complexes of copper if [Cu2+] = 10"5 moI/L and [NH3] = 10~4 moi/L.

Answer: Cu(NH3)2+, 10~s; Cu(NH3)l+, 2.5 X 10"6; Cu(NH3)|+, 10"7; Cu(NHj)r, 10~'2.

4.65 Using a logarithmic concentration diagram, determine the concentration of various ammonia complexes of copper if [Cu2+] = 10~4 moi/L and [NH3j = 10"3 mol/L.

4.66 Draw a logarithmic concentration diagram illustrating the effect of chloride concentration on the relative concentrations of various chloride complexes of mercury, assuming [Hg2+] = 10"7 mol/L. Which complex predominates when the chloride concentration equals (a) 0,1 mg/L, (b) 1 mg/L, (c) 10 mg/L,

Answer: HgCl2 under all conditions

4.67 Draw a logarithmic concentration diagram illustrating the effect of fluoride concentration on the relative concentrations of various fluoride complexes of aluminum, assuming [AI3*] = 10~4 mol/L. Which complex predominates when the fluoride concentration equals (a) 0,1 mg/L, (£>) 1 mg/L, (c) 10 mg/L?

4.68 Draw a distribution diagram for the chloride complexes of mercury,

4.69 Draw a distribution diagram for the fluoride complexes of aluminum.

4.70 From a predominance area diagram, determine which species of Hg(II) is likely to predominate (among hydroxide and chloride complexes oniy) when the chloride concentration is 35 mg/L and pH is (a) 6, (b) 1, (c) 8, and (d) 9.

Answer: (a) HgCl2; (b) Hg(OH)2; (c) Hg(OH)2; (d) Hg(OH}2

4.71 Draw a predominance area diagram illustrating the effect of pH and fluoride concentration on fluoride and hydroxide complexes of Fe(IB). Assume that the Fe(III) concentration is sufficiently low so that precipitation of iron does not

4.72 Mercury (Hg) is a toxic heavy metal. Typically the "free metal ion," Hg2+, is considered the most toxic inorganic form. For a natural water with apH = 7.8 and containing 0.5 mg/L of total soluble Hg(II) and 50 mg/L of total soluble chloride (CD species, calculate the concentration of all soluble Hg(H) species. Which Hg(H) species is most prevalent? Assume there are no solids present, that the major ligands present are Cl~ and OH", and ignore activity corrections. If you make additional assumptions to solve this problem, clearly state what they are and be sure to check to see if they are reasonable.

4.73 Mercury (Hg) and Cadmium (Cd) are toxic heavy metals; it is usually the Hg2* and the Cd2* forms that are considered the most toxic inorganic forms. For a natural water containing 10~6 M of total soluble Hg(II), 10~6 M of total soluble Cd(II) and 10"3 M of total soluble chloride (CP species), calculate the concentrations of all Hg(II) and Cd(II) species. Which Hg(H) species is the most prevalent? Which Cd(Ii) species is most prevalent? For this problem, ignore complexes of Hg(II) and Cd(II) with OH", assume no solids are present, and ignore activity corrections. Use the equilibrium constants given in Table 4.4 for the chloride complexes of Hg(II) and Cd(II).

4.74 Rework Prob. 4.73 with the same assumptions except this time include the OH" complexes of Hg(II) and Cd(II). Assume the pH of the water is 6.5. Consult Table 4.5 for appropriate values of K.

4.75 Calculate the concentrations of all species (i.e., HCN, CN~, Ni2+, Ni(CN)2") in a solution with a pH of 9.0 having a total cyanide concentration of 10~3 M and a total nickel concentration of 2.0 X 10~4 M. State and verify all assumptions. Ignore other Ni complexes. The following equilibrium will be useful:

4.76 From a logarithmic concentration diagram, estimate the minimum pH to which a water or wastewater need be raised to effect the precipitation as a metallic hydroxide of all but 10~4 mo!/L of each of the following (a) Cr3+, (6) Cu2+, (c) Zn2+, (d) Mg2+, and (<?) Ca2+.

4.77 From a logarithmic concentration diagram, estimate the minimum pH to which a water or wastewater need be raised to effect the precipitation as a metallic hydroxide of all but 10"5 mol/L of each of the following (a) FeJ+, (£) Fe2+, (c) Mn1+, (d) Al3*, (■?) Mg2+, and (f) CuI+.

Answer: (a) 3.2; (6) 9.2; (c) 10.0; (d) 5.0; (e) 10.8; (f) 7.2

4.78 From a logarithmic concentration diagram, estimate the minimum concentration in moles per liter of CO|~ required to precipitate as a metallic carbonate all but 1G"4 mol/L of (a) Mg2*, (b) Ca2+, (c) Sr2'1", (d) Zn2+, and (e) Pb2+. Ignore complexes.

4.79 From a logarithmic concentration diagram, estimate the minimum concentration in moles per liter of CO2" required to precipitate as a metallic carbonate all but 10~s mol/L of (a) Ca2+, (b) Cu2+, (c) Fe2+, (d) Cd2+, and (e) Pb2+. Ignore complexes.

Answer: (a) 4 X 10~4; (b) 2 X 10"5; (c) 5 X 10"*; (d)5X 10"7; (e) 1.6 X 10 3

4.80 From a logarithmic concentration diagram, determine the minimum pH at which each of the following concentrations of Ca2+ would be at equilibrium with CaCO: precipitate if the total concentration of inorganic carbon in solution equals 10~2 mol/L: (a) 10~3 mol/L, (b) 10~4 mol/L, (c) 10"5 mol/L. Ignore complexes.

4.81 Do Prob- 4.80, but assume that the total concentration of inorganic carbon in solution equals 10-4 mol/L. Ignore complexes.

Answer: (a) 9.1; 10.4; (c) Not saturated with CaC030)

4.82 Construct a logarithmic concentration diagram showing the relationship between pH and the equilibrium concentration of Ca2+ with respect to CaC03(f), assuming that the total concentration of inorganic carbon in solution, C, equals 10™! mol/L. Ignore complexes.

4.83 A water has an initial Ca2+ concentration of 2 X 10"3 mol/L, and the total concentration of inorganic carbon in solution equals 2 X 10~2 mol/L. It is desired to reduce [Ca2+] to 2 X 10~4 mol/L by precipitation of CaCO30). What minimum pH would be required to effect this removal, and what would be the final molar concentration of inorganic dissolved carbon? Ignore complexes.

4.84 Draw a diagram that shows the solubility of Cd(OH),(i) as a function of solution pH, and that also shows the concentration of other cadmium hydroxide complexes in a saturated solution. At what pH does Cd(OH)2(j) have minimum solubility? for Cd(OH)2(,i) = 2 X 10"!4.

4.85 It has been reported that Americans ingest a total of approximately 8 tons/day of lead. The drinking water standard for lead is 0.05 mg/L total soluble lead. One method for removing heavy metals such as lead is pH adjustment to precipitate the metal hydroxide. Using a logarithmic concentration diagram, determine the minimum solubility (S) of lead (in mg/L as Pb) in water. Be sure to include lead complexes with hydroxide. At what pH does the minimum solubility occur? Ksf) for Pb(OH)2(i) = 2.5 X 10-'6

4.86 A common way of removing Cr3+ from solution is precipitation of Cr(OH)3(s). An environmental engineer tells you that adjusting the pH to 8.5 will decrease the total soluble Cr(IIi) to below 1 mg/L- Is this true? In other words, is the solubility of Cr(ni) in the presence of Cr(OH)3(f) at a pH of 8.5 less than 1 mg/L? The pK,„ of Cr(OH)3(j) is 30.22.

4.87 What is the solubility of iron (in mg/L Fe) in a solution in equilibrium with Fe(OH)3(f), 10~2 M total sulfate, and a pH of 7.0?

4.88 An industrial wastewater contains cadmium, ammonia, and chloride, and is in equilibrium with Cd(OH)2(j).

(a) Write the general mass balance equation for soluble Cd.

(b) Write the general mass balance equation for ammonia-N.

(c) Write the general mass balance equation for chjoride.

(d) Write the equation for the solubility (5) of Cd.

4.89 A solution contains 0.01 M of each of the following metals: Ag+, Ba2+, Ca2+, Pb2+, and Sr2+. You are to titrate this solution with Na2S04. Ignore complexes.

(a) Which metal will precipitate first?

(b) Which metal will precipitate last?

Be sure to give adequate justification for your answers. The pA"sp for Ag2S04(j) is 4.80, for BaSO„(i) it is 9.96, for CaS04(i) it is 4.70, for PbS04(r) it is 7.80, and for SrS04(y) it is 6.55.

4 90 A water is in equilibrium with Ca3(P04)2(i). The solution contains other cations and anions, but no other weak acids or bases or sources of Ca and P04, and has a pH of 8.6. Ignore complexes.

(a) What is the solubility (5) of Ca in this water? j

(b) Will S increase, decrease, or remain constant if HCl is added to this water?

4 91 An industrial wastewater has the following characteristics: temperature = 2S°C, pH = 2 8 total soluble ammonia = 2000 mg/L as N, total soluble nickel - 490 mg/L as Ni, total inorganic carbon = 0. Using a logarithmic concentration diagram, | to what pH must this water be adjusted to reduce the total soluble nickel (5) to 1 mg/L? After the pH has been raised, is the solution well buffered? Why? 4.92 Consider a water in equilibrium with Ca3(P04)2(s). Assume there are no other solids | and no complexes. Develop an equation that will allow you to solve for the pH of this water; that is, your equation will have only one unknown, [H+]. Solve this equation for equilibrium pH using a spreadsheet. Answer: pH = 9.59

4 93 A water is in equilibrium with COj in the atmosphere (partial pressure is 3.16 X 10~4 atm) and with CaC03(s). The pH is 8.1. Ignoring Ca complexes, what is the solubility (S) of Ca?

4.94 Consider a water in equilibrium with CaC03(i) and 10"4 M NH4C1. Assume the system is closed and ignore complexes.

{a) Using a spreadsheet, determine the equilibrium pH of this system. (b) How many milliliters of 0.1 M HCl will be required to decrease the pH to 6.0? Answer: pH = 9.72; 0.32 mL

4.95 Pure water is brought into equilibrium with Mg(OH)2(j) and CaC03(s) in a closed system at 25°C.

(a) Using a spreadsheet, determine the equilibrium pH of this water. j

(,b) The solids are removed by filtration and the system is opened to an atmosphere and allowed to come to equilibrium with Pcot = 10"" atm. How many milliliters of 0.1 N HCl are required to reduce the pH of this water to 7.0? 4 96 Iron oxide will adsorb radium ions (Rai+) to form a 1:1 surface complex. Calculate as a function of pH the percent of radium that will be adsorbed by 10 mg/L of iron , oxide. Plot your results for pH values of 3 to 11. Assume no competition with other metal ions (other than protons). You might want to compare the total soluble radium concentration with available surface sites on the iron oxide to see if appropriate, simplifying assumptions can be made. The following data are to be used.

Surface site density = 10~4 mol/mg of iron oxide 1

This problem, with minor modifications, was contributed by Prof. Richard Valentine j of the University of Iowa. 4.97 Draw a logarithmic concentration diagram showing the relationship between [C02]

and [CH4] as a function of pE for pH = 7 and [C02] + [CH4] = 1 atm. , chapter 4 Basic Concepts from Equilibrium Chemistry

4 98 Draw a logarithmic concentration diagram showing the relationship between [SO2-] and [H2S] as a function of pE for pH = 7 and [S0|"] + [H2S] = 10~3 molTL.

4.99 Draw a p£-pH diagram illustrating predominant iron forms (Fe3+, Fe2+, Fe) in an aqueous system.

4.100 Draw a p£-pH diagram illustrating predominant manganese forms (Mn2+, Mn02l Mn04) in an aqueous system.

4.101 From a p£-pH diagram, estimate the pE range for aerobic conditions in an aqueous system at pH equal to (a) 4, (b) 7, and (c) 10.

Answer: (a) 16.0 to 16.8; (b) 13.0 to 13.8; (c) 10.0 to 10.8

4.102 From a p£-pH diagram, estimate the pE range that is typical for sulfide and methane production in an aqueous system at pH equal to (a) 4, (b) 7, and (c) 10.

4.103 Develop the p£-pH equation for the SO|"/H2S line in Fig. 4.20.

4.104 Develop the p£-pH equation for the C02/CH4 line in Fig. 4.20.

4.105 Consider the oxidation of Mn2+ to Mn02(y) by molecular oxygen [02(g)].

(a) Using appropriate half reactions in Table 2.4, write the p£-pH equations for reduction of MnOj(i) to Mn2< and the reduction of Oj(g) to H20. (ib) For a pH of 7.0 and a total soluble Mn concentration of 10"2 M, what partial pressure of oxygen (in atm) is required for Mn2+ to be the dominant form of Mn in the system?

(c) For a pH of 7.0, which form of Mn [Mn2+ or Mn02(j)] is thermodynamically favored under normal atmospheric conditions (oxygen partial pressure of 0.21 atm)?

4.106 Using data in Table 2.4, construct a balanced half reaction for the reduction of HOC1 to cr. What is £° for this half reaction?

4.107 Using data in Table 2.4;

(a) Construct a half reaction for the reduction of thiosulfate (S202~) to elemental sulfur (SO)).

(b) Generate the p£-pH equation for this half reaction for a pH of 7.0,

4.108 Can ozone [03(g)] be used to oxidize NH4 to NO3 ? Show all calculations necessary to justify your answer. The following is useful:

Answer: Yes

4.109 Some engineers are recommending addition of the strong oxidant potassium permanganate (KMn04) for remediating aquifers contaminated with chlorinated solvents such as TCE. In many of these sites, we also find trivalent chromium (Cr(lH)), which is the less toxic, less mobile form of Cr. Addition of KMn04 may oxidize Cr(HI) to its more toxic, more mobile hexavalent form (Cr(Vl)). Using the data given, answer the following question: Under standard conditions, can MnOJ oxidize Cr(III)? Give justification for your answer.

HCrOi + 4H+ + 3e~ = Cr(OH)3(j) + H20 = 1,20 volts Mn04 + 8H* + 5e~ = Mn2* + 4H20 = 1.491 volts

4.110 Consider the possibility of oxidation of Fe2+ to Fe3+ with aqueous chlorine. J

(a) Write a balanced equation for this overall reaction in water. |

(b) Is this reaction thennodynamically possible? Justify your answer. |

4.111 Consider the following expression: ; J

(а) Pure gold [Au(s)] is placed in water with a pH of 7.0 and in equilibrium with the f atmosphere (partial pressure of 02 = 0.21 atm). What will be the concentration , of Au3+ at equilibrium?

(б) Given your answer to part (a), what volume of water would be required to | dissolve 1 g of gold? For comparison, the entire volume of the earth is approximately 1024 liters.

(This problem courtesy of Dr. James Gossett of Cornell University.) Answer (a) 6.04 X 10-32 M; (t>) 8.4 X 1028 liters

4.112 A "globule" of elemental mercury (Hg°, which is a liquid at room temperature) is placed in water that is in equilibrium with an atmosphere containing 10 2 atm 02 and : has a pH of 7.0. What will be the concentration of Hg2+ under these conditions? Assume the Hg° is in equilibrium with the water. Use data available in Table 2.4.

4.113 The major species of lead (Pb) that are dominant in natural systems include Pb02(s), ; Pb2+, Pb(OH)3", and PbV).

(a) What are £°, p£°, and AG0 for the reductive dissolution of Pb02(s)? Pb02(i) + 4H+ + 2e~ = Ph2'1" + 2H20 log K = 49.2

(b) Given the reaction for the dissolution of Pb02(s), derive the pJE-pH equation for ; the reduction of PbOa(i) to PbO(s).

(c) What is the concentration of Pb2+ in a lake that has a pH of 6.0 and is in equilibrium with Pb02(j) and atmospheric oxygen?

(This problem, with minor modifications, was contributed by Prof. Michelle Scherer of the University of Iowa.) Answer: (c) M

4.114 Chlorinated solvents such as carbon tetrachloride (CC14) can be degraded in a process called reductive dechlorination where CI atoms are removed and replaced with H atoms (see Chap, 6). For example,

In in-situ bioremediation an electron donor such as acetate is typically added and is oxidized to provide the elections for the reduction of CO,. In groundwaters devoid ; of oxygen, nitrate typically serves as the elctron acceptor. Using data from Table 2.4, ; (a) Is it possible that CC1„ could serve as an electron acceptor for acetate? (£>) Which electron acceptor, CC14 or N03, would be thermodynamically preferred j if both were at the same concentration?

4.115 The following describes the equilibrium between Fe2+ and Fe(OH)3(j):

Fe(OH)3(i) + 3H+ + e" = Fe5+ + 3H20 E° = 1.06 volts j

(a) Develop a p£~pH equation for this half reaction assuming a total soluble iron j concentration of 10~7 M. ■

CHAPTER 4 Basic Concepts from Equilibrium Chemistry

| i (b) Many Midwestern groundwaters are devoid of oxygen but contain significant concentration of NO3". Using the equation developed in part (a) and Fig. 4.20, what is the predominant form of iron present at neutral pH in groundwaters devoid of oxygen but containing NOj ?

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  • jukka-pekk
    How to get a change in total carbon as function of ph using mineql?
    9 months ago
  • brigitte
    How to calculating ph level environmental engineering?
    9 months ago

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