Thermodynamics. Solutions Identifying Unknowns. 4. What would be the equilibrium ph if gypsum(caso 4 2H 2 O) dissolved in water?

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1 Thermodynamics Solutions Identifying Unknons 1. What ould be the equilibrium p if gypsum(caso O) dissolved in ater? ANSWER: Ca 2+, SO 4 2, +, O, 2 O 2. What ould be the equilibrium p if Al 2 (SO 4 ) 3 ere dissolved in ater? ANSWER: SO 4 2, Al 3+, AlO 2+, Al(O) 2 +, Al(O) 3(s), Al(O) 4, +, O, 2 O 3. What ould be the equilibrium concentration of Cu 2+ in ater at p 7.5 if tenorite (CuO (s) ) ere to dissolve? ANSWER: Cu 2+, CuO +, Cu(O) 2 0, Cu(O) 3, +, O, 2 O Identify equations 4. What ould be the equilibrium p if gypsum(caso O) dissolved in ater? ANSWER: Ca 2+, SO 4 2, +, O, 2 O 5 unknons 1. K { + }{O }/{ 2 O} 2. C T Ca X 3. C T S Y 4. [ + ] + 2[Ca 2+ ] 2[SO 4 2 ] + [O ] 5. { 2 O} 1 5. What ould be the equilibrium p if Al 2 (SO 4 ) 3 ere dissolved in ater? ANSWER: SO 4 2, Al 3+, AlO 2+, Al(O) 2 +, Al(O) 3(s), Al(O) 4, +, O, 2 O 8 unknons 1. K { + }{O }/{ 2 O} 2. K 1 3. K 2 4. K 3 5. K 4 6. C T S X 7. C T Al 2/3X [AlO 2+ ] + [Al(O) 2 + ] + [Al 3+ ] + [Al(O) 3(s) ] + [Al(O) 4 ] 8. 3[Al 3+ ] + 2[AlO 2+ ] + [Al(O) 2 + ] + [ + ] 2[SO 4 2 ] + [Al(O) 4 ] + [O ] 6. What ould be the equilibrium concentration of Cu 2+ in ater at p 7.5 if tenorite (CuO (s) ) ere to dissolve? ANSWER: Cu 2+, CuO +, Cu(O) 2 0, Cu(O) 3, +, O, 2 O (6 unknons) 1. K { + }{O }/{ 2 O} 2. K 1 3. K 2 4. K 3 5. C T Cu [Cu 2+ ] +[CuO + ] + [Cu(O) 2 0 ] + [Cu(O) 3 ] 6. [ + ] + 2[Cu 2+ ] + [CuO + ] [O ] + [Cu(O) 3 ] 1

2 Analytical Solutions Approximations Graphical approach 7. What ould be the equilibrium p if 1 L of 10 4 M N 4 O ere mixed ith 100 ml of M Cl? pka(n 4 + ).2, pk a (Cl) 3.0 The pc p diagram is shon belo. C T for both N 4 + and Cl are about Because Cl dissociates essentially completely, the concentration of Cl is 10 4 M at all p values. The equilibrium point may be found by riting the proton condition: Species ith more protons: Cl, + Proton Reference Level: N 4 +, Cl, 2 O Species ith feer protons: N 3, O Proton condition: [Cl] +[ + ] [N 3 ] + [O ] To find this point, follo the + line don to here it crosses N 3 (see arro). The p is about 6.8. Since e have 10 4 M of both an acid and a base, e should expect that they ill neutralize each other and the p should be around 7. 2

3 8. What ould be the equilibrium p obtained by mixing 0.1 of sodium acetate ith 1 L of 0.01 M NO 3? pk a(acetate) 4.7, pk a(no3) 0. ere e are mixing a lot of a eak base ith a little strong acid, so e should expect the p to be loer than if the base alone ere present, but still above 7. To find the equilibrium p, construct the proton condition: Species ith more protons: Ac, NO 3, + Proton Reference Level: Ac, Na +, +, NO 3, 2 O Species ith feer protons: O Proton Condition: [Ac] + [NO 3 ] + [ + ] [O ] This equation is satisfied here the Ac line crosses the O line (p ~ 8.). What ould be the p of pure ater in equilibrium ith ith pco 2 of 400 µatm? Carbonic acid ( 2 CO 3 ) is a polyprotic acid ith pka 1 of 6.3 and pka 2 of The system is open, and as a result, [ 2 CO 3 ] is constant at all p values to be in equilibrium ith CO 2 (g). [ 2 CO 3 * ] K pco x M The CO 3 line may be computed as a function of 2 CO 3 * : [CO 3 ] K a1 [ 2 CO 3 * ]/[ + ], and the CO 3 2 line may be calculated from this line as: [CO 3 2 ] K a2 [CO 3 ]/[ + ] 3

4 The equilibrium p occurs at solution of the proton condition: Species ith more protons: + Proton Reference Level: 2 CO * 3, 2 O Species ith feer protons: CO 3, O 2 Species ith 2 feer protons: CO 3 Proton Condition: [ + ] [O ] + [CO 3 ] + 2[CO 3 2 ] This equation is satisfied here the + line crosses the CO 3 line (p ~ 5.7) 10. What ould be the equilibrium p of ater exposed to a large volume of a gas mixture containing 10% CO 2 and 0% 2 S. For CO 2 pk a1 6.3 and pk a2 10.3; For 2 S pk a1 7.0 Open Systems 11. If the concentration of dissolved atrazine in Lake Michigan is 40 ng/l and the concentration of gaseous atrazine in the above the lake is 3 x atm, ill atrazine move from the into the lake or vice versa? P o 3. x atm K 3.3 x 10 5 /L atm Solubility 1.3 x 10 4 /L m g/ 4

5 The reaction involved is ater partitioning, for hich the equilibrium constant is the enry's La Constant (K ). To determine the direction of the reaction, one can calculate Q/K. A( g) A( aq) [ A( aq) ] F ng g Q [ A ] G I L K J F G I ng K J F G I g K J F G 1 I x atm K J ( g) 4 Q 62. x10 Latm x10 Q Latm 01. K x10 Latm Because Q/K is less than one, the reaction ill proceed to the right ith gaseous atrazine dissolving into the lake. b. What ould be the concentration of atrazine in the lake that ould be in equilibrium ith the gaseous concentration given above (3 x atm)? At equilibrium the dissolved concentration of atrazine ould be: [ Aaq ] K [ Ag ] 5 A K A x L atm x 15 [ atm ( aq) ] [ ( g) ] g ng ng [ A( aq) ]. x K g L 12. Air sparging is one method of removing volatile contaminants from polluted ground ater. In this process, the is pumped into the ground ater, and it rises in bubbles through the zone of contaminated ater. The pollutants partition from the ater into the and are removed from the soil. The pollutants can be removed from the stream by passing it through activated carbon to hich the organic compounds ill sorb. Which compound ould be the easiest and hich ould be the most difficult to remove from ground ater by sparging. Explain your anser. Compound Use Sat. Vapor K Log(K o ) Pressure (atm) (/L atm) Trichloroethylene Solvent.8 x x Decane Jet fuel 1.7 x x component Parathion Pesticide 6.0 x x Dieldrin Pesticide 3.3 x Trifluralin pesticide 6.2 x ANSWER: 5

6 In order for the compound to be removed from the groundater, it must not be sorbed strongly to the soil (it must have lo K o ) and it must partition readily from ater into (it must have lo K ). The compound that has the loest K (decane) has the highest K o and hence it ould not be readily removed by sparging. The compound ith the next loest K is TCE, and this compound has the loest K o so it can both partition into from the ater and desorb readily from the soil. Therefore, TCE ould be the easiest compound to remove by sparging. The most difficult compound to remove ill have a high K and high K o. Without doing the calculations in question 6 belo, it is difficult to kno hether Parathion or Dieldrin ill be the most difficult to remove. 13. What concentration of oxygen ould you expect to find in Lake Superior in summer hen the ater temperature is 18 o C and the enry s La Constant for O 2 is /L atm? (.45 mg/l) [ O2 ]( aq) K [ O2 ]( g) [ O2] ( aq) K [ O2] ( g) F I 4 [ O2 ]( aq) atm x G Latm K J b0. 21 g F I g mg x G L K J F G I K J F G 4 3 I mg g K J. 45 L L 14. If the concentration of CO 2(g) in the atmosphere is 3.7 x 10 4 atm, the concentratration of CO 2(aq) in the lake is 4.7 μm, and the enry's La Constant is L 1 atm 1, ould the CO 2 partition into or out of the lake? Back up your conclusion ith the appropriate calculations. 15. You are in charge of reping the seer mains for Ne York City. Before you send a ork cre into the main, you measure the methane (C 4(g) ) concentration and find it to be dangerously high at 0.01 atm. You ish to determine hether the methane is coming from anaerobic decomposition of the seage or from an unidentified gas leak. You measure the C 4(aq) in the seage in the pipe and find it to be 1 μm. Could the elevated C 4(g) be coming from the seage, or is it coming from another source? The enry's La constant for methane is /Latm at 25 o C. (Assume the temperature in the seer main is about 25 o C.) The easiest ay to anser this question is to compute Q/K and thereby determine hether the methane is coming out of or going into the seage. The value of K is given to us as /L atm. No e must calculate Q. C 4(g) <> C 4(aq) 6

7 μmol 6 Q C 1 10 [ 4( aq) ] L μ [ C ] 001. atm 4( g) F I G K J F G I K J 10 4 Latm 4 Q 10 Latm K Latm Because the value of Q/K is much less than one, the reaction has not yet reached equilibrium and ould continue to go to the right. In other ords, the gaseous methane ould dissolve into the seage, and could not be degassing from the seage. There must be another source of methane besides the anaerobic seage decomposition. 16. For orkers in metal plating industries, the greatest danger from cyanide is from breathing CN. The protonated form, CN, is volatile. If the total concentration of cyanide (i.e., CN + CN ) as 10 M, hat fraction of the total ould exist as the volatile form at a p of 12? (0.2%) ANSWER: The fraction that exists as CN equals: [CN]/([CN] + [CN ]) [CN]/10 M Therefore, e must solve for the concentration of [CN] that ould exist at p [ ][ CN ] [ ](10M [ CN]) K a [ CN] [ CN] + 12 (10M ) [ ] (10M )(10 M ) [ CN] 0.02M K + [ ] ( ) 0.02M 10M a % 17. In flue gas desulfurization (scrubbing), the SO 2(g) that is produced by combustion of sulfur in the fossil fuel is removed by alloing it to partition into ater. SO 2(g) <> SO 2(aq) a) What are the name and one set of possible units of the equilibrium constant that governs this reaction? b) The SO 2(aq) reacts ith ater to form 2 SO 3(aq) hich is an acid. Thus, the folloing sequence of reactions is possible. (1) SO 2(g) <> SO 2(aq) K mol/l atm (2) SO 2(aq) + 2 O (l) <> 2 SO 3(aq) K (3) 2 SO 3(aq) <> + + SO 3 K a Would removal of SO 2(g) from the flue gases into the ater be most effective at high or lo p? Explain your anser ith the aid of a pc p diagram. 7

8 18. A pond on an industrial site is found to be saturated ith trichlorethylene. The engineering firm remediating the site pumps one million liters of the pond ater into a holding tank ith a volume of 2 million liters; the opening of the tank is sealed. To eeks later, the liquid is pumped to a bioreactor here the trichloroethylene is to be biodegraded. What ould you expect the concentration of the trichloroethylene to be hen the ater reaches the bioreactor? Assume the temperature is constant at 25 o C. (20 pts) Trichloroethylene C 2 Cl 3 Solubility of trichloroethylene 1100 mg/l K 114 m 3 atm 1 (To receive partial credit, first explain hy the concentration in the ater ill change.) Some of the trichloroethylene (TCE) ill partition from the ater in the tank into the in the headspace. Therefore, the concentration of TCE ill be loer than the original concentration hen it reaches the bioreactor. The total mass of TCE present (1100 mg/l)(10 6 L) 1.1x10 mg M total The total mass of TCE must equal the mass in the ater and that in the headspace: M total M ater + M M ater C L 6 ( 10 L) Mol. t. g Mol. t. 6 g 3 mg ( 10 L) Mol. t C Mol. t. M ( mg) C L g The concentrations of TCE in the ater and in the are related through the enry s La constant. C [ TCE] ater L K [ TCE] P ( atm) L atm P C C TCE ( atm) C K L C K RT ( P atm) TCE TCE 1 RT No, the expression for C and C can be substituted into the expression for M total. M total M ater + M M 10 Mol. Wt. C + 10 Mol. Wt. C M total total 10 Mol. Wt. C Solving for C yields: + 10 mg g C Mol. Wt. K RT C 8

9 M total 1 C Mol Wt K RT The cular eight of TCE 2(12) (35.5) g/ Substituting values in the equation for C e obtain: 1 1.1x10 mg 1 C L g 3 mg mg L g L 1 Of the initial 1100 mg/l, almost one third volatilized into the headspace.

Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 4

Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 4 Economics 2 Spring 2016 Professor Christina Romer Professor David Romer SUGGESTED ANSWERS TO PROBLEM SET 4 1. The demand curve for auto orkers is derived from profit maximization on the part of automobile