## Problems

3.1 Determine the net heat of combustion of ethane gas from standard enthalpies of formation. Give the answer in kilojoules per mole of ethane.

3.2 A small quantity of hydrogen gas is sometimes present in the gas from an anaerobic digester. Determine the net heat value in kilojoules per mole available from burning this gas.

3.3 A waste containing 1 percent sulfuric acid (10,000 mg/L) is neutralized by the addition of a concentrated lime slurry [made by dissolving Ca(OH)2Cr) in water]. If the water temperature is 15°C before neutralization, what is it after neutralization?

3.4 (a)How many kilojoules of heat are required to evaporate 1 liter of water at 1 atm if the initial water temperature is 20°C?

(b) If the water sample in part (a) contained 30,000 mg/L of acetic acid, would sufficient heat be liberated by combustion of the acetic acid to satisfy the heat requirements for water evaporation?

3.5 (a} Using standard free energies of formation, determine the solubility product for zinc sulfide (ZnS(s)) at 25°C. Q>) Which way may the reaction proceed if Zn2+ is 10™3 M and Ss~ is 10~3 M? Ignore activity corrections. Answer: 3.67 X 10~M, precipitating

3.6 (a) MgJ+ is one of the major components of hardness. It can be removed from water by precipitation as Mg(OH)2(i). Using standard free energies of formation, calculate the equilibrium constant Ksp for Mg(OH)2(s) at 25°C. (£>) Is the dissolution of Mg(OH)2(j) endothermic or exothermic? Show calculations necessary to justify your answer.

3.7 (a) Using standard free energies of formation, calculate K,t for CaC03(i) at 25°C. (£>) If a water is in equilibrium with CaC03(j) at a temperature of 25°C, what is the

Cai+ concentration in milligrams per liter if the CO^ concentration is 5 mg/L?

(c) Calculate Ksf for a temperature of 16°C, which is typical of many groundwaters. (¿0 A sample of groundwater with a temperature of 16®C has 100 mg/L of Ca2+ and

10 mg/L of COf". Is this water in equilibrium with CaCO30)? If not, is

CaC03(s) dissolving or precipitating?

Answer 4.99 X 10"', 2.4 mg/L, 5.88 X JO"9, no, precipitating

3.8 (a) Determine the solubility constant (Henry's law constant) at 25°C for hydrogen sulfide gas in water from standard free energies of formation.

(b) Using standard enthalpies of formation and the solubility constant from part (a), estimate the solubility constant for hydrogen sulfide gas at 10°C.

(c) The odor threshold (the concentration at which the average person can detect the odor) for H2S ("rotten-egg" gas) is reported to be approximately 1 ppm (10~6 atm) of H2S. Assuming equilibrium between this gaseous concentration and water, what is the aqueous concentration of H2S at 25°C? At 10°C?

3.9 (a) Determine the solubility constant (Henry's law constant) at 20°C for carbon dioxide gas in water from standard free energies of formation.

(to If the dissolved C02 concentration in a lake at 20°C is 2.2 mg/L, is the lake in equilibrium with atmospheric C02 (partial pressure of 10~3,s atm)? Answer: 23.4 atm-L/mol, volatilizing

3.10 Estimate the ionization constant for acetic acid at 35°C from thermodynamic considerations.

3.11 (a) The following reaction describes the dissociation of ammonium in water:

From standard enthalpies and free energies of formation, calculate the equilibrium (dissociation) constant at 25°C and 10°C. (b) It is the un-ionized form of ammonia (NH3) that is toxic to fish. For a water with a pH of 7.0, what is the ratio of NH3 to NH* at 25°C and 10°C7 Answer: 5.74 X 10"i0,1.90 X 10~10, 5.74 X lO"3,1.90 X 10"3 (NH3 concentration, relative to NH*, decreases by a factor of approximately 3)

3.12 Estimate the first ionization constant for hydrosulfuric acid at 35°C from thermodynamic considerations.

3.13 The oxidation of ferrous iron (Fe2+) to ferric iron (Fe3*) by molecular oxygen can be described by the following reaction:

' 4F e?*(aq) + Oz(g) + 4H *{aq) = 4Fe3"(ag) + 2H,0(/)

(a) Using free energies of formation, calculate the equilibrium constant for this reaction at 25'C.

(b) For a water in equilibrium with the atmosphere, a pH of 2.0, and a total soluble iron concentration of 1 mg/L, calculate the concentrations oi~P&2+(aq) and

Answer: 1.19 X 103!,4.51 X 10"HM, 1.79 X 10"SM

3.14 Consider the following acid-base reaction:

(a) From thermodynamic considerations calculate the equilibrium constant K at 25°C,

(b) For the value of K you calculated in part (a), if a solution contains 10"4 M Fe3+ and has a pH of 7.5, will Fe(OH),(j) form? Show all calculations necessary to justify your answer.

3.15 Consider the corrosion of elemental iron in anaerobic waters (Fe° oxidized to FeI+) with the reduction of protons (H*) to form hydrogen gas(H2):

(a) From thermodynamic considerations, calculate the equilibrium constant K at 25°C.

(£1) For 7 = 25°C, pH = 10, and [Fe2*] = 10~3 M, at what partial pressure of H2 does this reaction become unfavorable?

3.16 Consider the oxidation of ammonium (NH4) to nitrate (N03") by molecular oxygen:

part 1 Fundamentals of Chemistry for Environmental Engineering and Science

From thermodynamic considerations, calculate the equilibrium constant K at 25°C. Is this reaction thermodynamically favorable? Justify your answer.

3.17 (a) Calculate the standard free energy of the reaction for the biological decomposition of 1 mol of acetate under both aerobic and anaerobic conditions:

Aerobic: CHjCOO"^ + 202(g) -> HCO,"^} + H20CO + C02fe) Anaerobic: CH3COO-(«9) + H20(Q -> HC03~(a<?) + CH4(g) (¿>) For a given quantity of acetate waste, which system would you expect to be capable of supporting the growth of the largest biological population? Why?

3.18 (a) One of the major intermediates in the anaerobic biological degradation of organic matter to methane is propionate (CH3CH2C00~). Propionate conversion to methane can be described by the following reaction:

4CH3CH,COO (aq) + 6H20(/) = 7CH4fe) + C02{g) + 4HC03(ûç) Assuming that reactants and products are at unit activity, is methane production from propionate thermodynamically favorable? (i>) However, it is known that methane is not formed directly from propionate.

Rather, propionate is converted by bacteria to acetate (CH3COO~) and hydrogen as follows:

CHaCHjOXn&ï} + 2H,0(i) = CH3COO"(^) + 3H2(g) + CO ¿g) Show that this reaction is not thermodynamically favorable. In a well-operating anaerobic biological treatment system, propionate is efficiently converted to methane. Offer an explanation how this is possible given that propionate conversion to acetate and hydrogen is not thermodynamically favorable. Answer: (a) Yes, since AG0 = -229.9 kJ has a negative value, (i>) Reaction not possible under standard conditions since AG0 = 71.65 kJ is positive.

3.19 At 1 atm the boiling temperature for isopropanol (isopropyl alcohol) is 82.5t,C and for water is 100°C. A mixture containing 12.5 percent water and 87.9 percent isopropanol by weight has a boiling temperature of 80.4°C, and at this temperature the composition of the vapor is the same as the liquid. If the waste from an industry contained 10,000 mg/L of isopropanol, would it be possible to remove the alcohol from the water by fractional distillation of the waste? Why?

3.20 An industrial wastewater contains 10 percent by weight of an organic solvent and has a boiling temperature of 105°C at 1 atm. The vapor is found to be richer in organic solvent than the liquid waste. The boiling temperature of pure solvent is 80®C. Can pure solvent be obtained by fractional distillation? Pure water? Explain why.

3.21 (a) At 1 atm, n-butanol (n-butyl alcohol) boils at 117.8°C. A binary mixture , containing 2.52 mol of water per mole of this alcohol boils at 92.4°C, and with this mixture the composition of the vapor is equal to that of the liquid mixture. Sketch roughly the temperature composition diagram for the liquid-vapor equilibrium for mixtures of water and n-butanol at atmospheric pressure. (£>) An industrial waste contains 90 percent water and 10 percent n-butanol by weight. What would be the composition of the distillate and the residue from fractional distillation of the waste?

Answer: (b) distillate 0.716 mol fraction H20, residue pure H20

3.22 The boiling temperature for butyric acid at 1 atm is 163.5°C. When wastewaters containing low concentrations of butyric acid are distilled, it is found that the distillate is richer in butyric acid than the wastewater being distilled. In what class would a butyric acid-water binary mixture be placed? Illustrate.

3.23 What approximate osmotic pressure would be created across a semipermeable membrane if water containing 0.01 M Na2S04,0.02 M MgCl2, and 0.03 M CaCl2 were placed on one side of the membrane and distilled water were on the other?

3.24 (a) 20,000 mg/L of NaCl would lower the vapor pressure of water at 100°C by about 8.4 mm Hg. Estimate the osmotic pressure across a semipermeable membrane containing a brackish water with this sodium chloride concentration on one side and distilled water on the other, (b) Calculate the theoretical minimum energy requirement to remove the salt from 1000 gallons of the brackish water. Express energy required in units of liter-atmospheres, foot-pounds, and kilowatt-hours.

3.25 Phenol is approximately 12 times more soluble in 1 volume of isopropyl ether than it is in 1 volume of water. How many extractions are required to reduce the concentration of phenol below 100 mg/L in a waste containing 2000 mg/L of phenol if an ether-to-wastewater ratio of 0.2 by volume is used in each extraction?

3.26 The solubility of picric acid at 20°C is 9,56 g per 100 g of benzene, and 1.4 g per 100 g of water. If an industrial wastewater contains 5000 mg/L of picric acid, what concentration would remain after 1 extraction with 1 lb of benzene for each 2 lb of water?

3.27 What is the approximate specific conductance at 25°C of a solution containing 100 mg/L of CaCl2 and 75 mg/L of Na2SO„?

3.28 A standard KC1 solution (0.01 N), when placed in a conductivity cell at 25°C, was found to produce a resistance of 1000 ohms. A MgCl2 solution was then placed in the cell, and the measured resistance at 25°C was 3000 ohms. Approximately what is the concentration of MgCl2 in milligrams per liter?

3.29 The specific conductance of a CaCl2 solution is 200 X 10"s S. Estimate the concentration of CaCl2 in milligrams per liter.

3.30 Ions can contribute to the conductivity of a solution, but un-ionized molecules cannot. On this basis what is the approximate specific conductance at 25°C of a solution containing 1000 mg/L of acetic acid, if the ionization constant for this acid is 1.75 X 10-5?

3.31 What weight of silver will pass into solution from a silver anode by the passage of 0.02 A of current through the solution for 24 h?

3.32 When an electric current is allowed to pass through a dilute sulfuric acid solution, hydrogen gas is evolved at the cathode and oxygen gas at the anode, What volumes of gases, measured at 1 atm pressure and 0°C, will be obtained at the electrodes when 1 A of current is passed through the solution for a 1-h period?

3.33 On the basis of standard electrochemical potentials, which of the following metals could act in a sacrificial manner to protect iron from corrosion: aluminum, copper, lead, magnesium, silver, tin, and zinc?

3.34 A zinc and an iron bar, connected by a copper wire, were introduced into a solution containing 2000 mg/L of Zn2* ions and 5 mg/L of Fe2* ions. What reaction took place?

3.35 Estimate the solubility-product constant for Mg(OH)j(i) at 25°C from standard electrode potentials.

3.36 In a study of the natural die-off of coliforra organisms in a stream, it was found that 36 percent of the organisms died within 10 h and 59 percent died within 20 h. If the rate of die-off followed first-order kinetics and were proportional to the number remaining, how long would it take to obtain a 99 percent reduction in coliform organisms?

3.37 A stream flowing with a velocity of 2 mph contains no BOD, but has an oxygen deficit of 6 mg/L. Ten miles downstream this deficit has been reduced to 4 mg/L through absorption from the atmosphere. The stream conditions are uniform throughout its length. Assuming the rate of aeration is proportional to the deficit, what would be the deficit 35 miles downstream from the original point?

3.38 The radioactive nuclide PM has a half-life of 14.3 days. How long would a waste containing 10 mg/L of this nuclide have to be stored in order to reduce the concentration to 0.3 mg/L?

3.39 The half-life of atrazine (a herbicide) is estimated to be approximately 14 days. What fraction of the initial atrazine will remain after 100 days?

3.40 Laboratory studies with a groundwater sample indicate that trichloroethylene (TCE) is degraded according to first-order kinetics with a half-life of 150 days. If the current groundwater concentration is 15 /xg/L, how long will it take before the TCE concentration is reduced to the drinking water standard of 5 /xg/L? Show your work.

3.41 An experiment was conducted to characterize the rate of a chemical reaction. Concentrations (mg/L) were measured at different times (h) and the data were plotted as follows:

ilt mmmB

ilt mmmB

 ' : ■ & ■ ■ ¡v-riiitj' • V aKtti'-Vli:

Time, hr

Is this a zero-, first-, or second-order reaction? Why? What is the value of the rate constant (include the proper units)? 3,42 The following represents experimental data collected by measuring the disappearance of a compound (concentration in mg/L) with time.

0.06

mmmm^mmm^

(a) Is this a zero-order, first-order, or second-order reaction? Why?

(b) What is the rate coefficient, reported with the correct units?

3.43 Given the following laboratory data concerning the disappearance of a chemical in water, do the data fit a zero-order, first-order, or second-order rate expression? Provide sufficient justification for your answer, and report the correct rate constant in the correct units.

Time, h

Concentration, mg/L

0

100

0.5

61

1

37

2

14

3

5.0

5

3.45

Answer: first order, 1.0 h"1 Bacterial decay has been described by a first-order rate expression. If the first-order rate constant for bacterial decay is 0.10 day"1 at 20°C (typical for aerobic, heterotrophic bacteria), and if an A [Eq. (3.81 )] of 1.035 is assumed to describe the effect of temperature on the rate constant, what is the first-order rate constant at 30°C? What is the value of £„?

Anaerobic biotransformation of chlorinated organics such as chloroform can be modeled using a second-order rate expression. This process is typically called cometabolism, and it is typically assumed that the concentration of bacteria remains constant. If the second-order rate coefficient is 0.005 L/mg-d and the concentration of bacteria is 100 mg/L, how many days will it take for an initial concentration of chloroform to be reduced to 0.01 mg/L (10/ig/L, which represents a 99 percent reduction)?

3.46 Biotransformation of chlorinated organic compounds such as 1,1,1-tricUoroethane can be modeled using a second-order rate expression. Given the following laboratory data for an experiment measuring the biotransformation of 1,1,1-trichloroethane by 100 mg/L of bacteria, determine the pseudo-first-order rate constant and the second-order rate constant. Plot the data using appropriate graph paper or using an appropriate graphics software package.

 Time,h Concentration, mg/L 0 0.50 2 0.48 5 0.45 10 0.41 24 0.30 48 0.18

Answer: pseudo-first-order k = 0.0213 h"1; second-order k = 2.13 X 10^ L/mg-h

3.47 The transformation of 1,1,1-trichloroethane (1,1,1-TCA) by the mineral iron sulfide (FeS) has been shown to be a second-order reaction, depending on the concentration of 1,1,1-TCA remaining (M) and the surface-area concentration of FeS(mJ/L). The transformation of 1,1,1-TCA by anaerobic bacteria is also second-order, depending on the 1,1,1-TCA concentration (M) and the concentration of bacteria (mg/L). It is hypothesized that when FeS and bacteria are combined in one system, total removal can be described by parallel and independent second-order rate expressions.

(a) Write the rate expression describing the total removal of 1,1,1-TCA by the combination of FeS and bacteria,

(b) Convert your answer for part (a) into a pseudo-first-order expression such that removal is first-order with respect to 1,1,1-TCA only and containing a single rate coefficient. What is the equation for the rate coefficient?

3.49 An evaluation of the ability of activated carbon to reduce the odor of a water with a threshold odor of 30 was made, using the Freundlich adsorption isotherm. By plotting the log of odor removed per unit dose of activated carbon versus residual odor, the constants K and n in Eq. (3.84) were found to be 0.5 and 1.0, respectively. What activated carbon dosage in milligrams per liter would be required to reduce the threshold odor to 4 units?

REFERENCES

Adamson, A. W.: "A Textbook of Physical Chemistry," 3rd ed., Academic Press, Orlando, FL, 1986.

Atkins, P. W.: "Physical Chemistry," 4th ed., Oxford Univ. Press, Oxford, Great Britain, 1990.

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

Daniels, F., and R. A. Alberty: "Physical Chemistry," 5th ed., Wiley, New York, 1979.

pean, J- A- (ed-): "Lang's Handbook of Chemistry," 15th ed., McGraw-Hill, New York, 1999.

Levine, I. N.: "Physical Chemistry," 5th ed., McGraw-Hill, New York, 2002. Lide, D-(ed-): "Handbook of Chemistry and Physics," 82nd ed.: CRC Press, Boca Raton, FL, 2001.

Noggle, ^ H.: "Physical Chemistry," 2nd ed., Scott Foresman, Boston, 1989. Snoeyink, V., and D. Jenkins: "Water Chemistry," Wiley, New York, 1980.

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### Responses

• allison markert
How to calculate standard free energy of a biological decomposition?
3 years ago
• cara
What is the approximate specific conductance at 25C of a solution containing 100 mg/L of Ca?
3 years ago
• DEMI
How to use free energies of formation to get solubility constant in a temperature other than 25 C?
6 months ago