Problem Set. Assigned October 18, 2013 Due Friday, October 25, Please show all work for credit

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1 Problem Set Assigned October 18, 2013 Due Friday, October 25, 2013 Please show all work for credit To hand in: Thermodynamic Relations 1. The shells of marine organisms contain CaCO 3 largely in the crystalline form known as calcite. There is a second crystalline form of CaCO 3 known as aragonite. (a) Based on the thermodynamic and physical properties given for these two crystalline forms, would you expect calcite in nature to convert spontaneously to aragonite given sufficient time? Justify your answer. (b) Will the conversion proposed in part (a) be favored or opposed by increasing the pressure? Explain. (c) What pressure should be just sufficient to make this conversion spontaneous at 25 C? (d) Will increasing the temperature favor the conversion? Explain. 2. The temperature of a typical laboratory freezer unit is -20 C. If liquid water in a completely filled, closed container is placed in the freezer, estimate the maximum pressure developed in the container at equilibrium. The enthalpy of fusion of water may be taken as kj kg -1, independent of temperature and pressure, and the densities of ice and liquid water at -20 C are and 1.00 g cm -3, respectively. Free energy of mixing processes 3. Atkins Ch. 5: Ex. 5.2 (b)

4. Atkins Ch. 5: Ex. 5.9 (b) 5. Engel P 6.29 A sample containing 2.25mol of He (1bar, 298K) is mixed with 3.00mol of Ne (1 bar, 298K) and 1.75mol of Ar(1 bar, 298K). Calculate G mixing and S mixing.

2 4. Atkins Ch. 5: Ex. 5.9 (b) 5. Engel P 6.29 A sample containing 2.25mol of He (1bar, 298K) is mixed with 3.00mol of Ne (1 bar, 298K) and 1.75mol of Ar(1 bar, 298K). Calculate G mixing and S mixing. Equilibrium 6. Atkins Ch. 6: Ex. 6.2 (b) 7. Engle P.6.18 Protein denaturing Many biological macromolecules undergo a transition called denaturation. Denaturation is a process whereby a structured, biological active molecule, called the native form, unfolds or becomes unstructured and biologically inactive. The equilibrium is native(folded) denatured(unfolded) For a protein at ph = 2, the enthalpy change associated with denaturation is H = kj mol 1 and the entropy change is S = 1.3 kj K 1 mol 1. a. Calculate the Gibbs energy change for the denaturation of the protein at ph = 2 and T = 303 K. Assume the enthalpy and entropy are temperature independent between and 303 K. b. Calculate the equilibrium constant for the denaturation of protein at ph = 2 and T = 303 K. c. Based on your answers for parts (a) and (b), is protein structurally stable at ph = 2 and T = 303 K?

3 Substance 8. Engle - P.6.25 Pentene isomers At 25 C, values for the formation enthalpy and Gibbs energy and log 10 K P for the formation reactions of the various isomers of C 5 H 10 in the gas phase are given by the following table: H f kj mol 1 G f kj mol 1 log 10 K P A = 1-pentene B = cis-2-pentene C = trans-2-pentene D = 2-methyl-1-butene E = 3-methyl-1-butene F = 2-methyl-2-butene G = cyclopentane Consider the equilibrium A B C D E F G, which might be established using a suitable catalyst. a. Calculate the mole ratios A/G, B/G, C/G, D/G, E/G, and F/G present at equilibrium at 25 C. b. Do the ratios of part (a) depend on the total pressure? c. Calculate the mole percentages of the various species in the equilibrium mixture. 9. Engle P.6.34 Gas reaction Calculate K P at 475 K for the reaction NO(g) + 1/2 O 2 (g) NO 2 (g) assuming that H reaction is constant over the interval from 298 to 600 K. Do you expect K P to increase or decrease as the temperature is increased to 550 K? 10. Engle P.6.40 Calcium carbonate decomposition Ca(HCO 3 ) 2 (s) decomposes at elevated temperatures according to the stoichiometric equation Ca(HCO 3 ) 2 (s) CaCO 3 (s) + H 2 O(g) + CO 2 (g). a. If pure Ca(HCO 3 ) 2 (s) is put into a sealed vessel, the air is pumped out, and the vessel and its contents are heated, the total pressure is bar. Determine K P under these conditions. b. If the vessel initially also contains bar H 2 O(g), what is the partial pressure of CO 2 (g) at equilibrium?

11. Oxides of sulfur are important in atmospheric pollution, arising particularly from burning coal. Use the thermodynamic data at 25 C given in the table below to answer the following questions.

4 11. Oxides of sulfur are important in atmospheric pollution, arising particularly from burning coal. Use the thermodynamic data at 25 C given in the table below to answer the following questions. (a) In air, the oxidation of SO 2 can occur: 1/2O 2 (g)+so 2 (g)=so 3 (g). Calculate the standard Gibbs free energy for this reaction at 25 C. (b) Find the equilibrium ratio of partial pressures of SO 3 (g) to SO 2 (g) in air at 25 C; the partial pressure of O 2 (g) is 0.21 atm. (c) SO 3 (g) can react with H 2 O(g) to form sulfuric acid, H 2 SO 4 (g). Air that is in equilibrium with liquid water at 25 C has a partial pressure of H 2 O(g) of atm. Find the equilibrium ratio of partial pressures of H 2 SO 4 (g) to SO 3 (g) in air at 25 C. 12. What is the pressure of CO(g) in equilibrium with the CO 2 (g) and O 2 (g) in the atmosphere at 25 C? The partial pressure of O 2 (g) is 0.2 atm, and the partial pressure of CO 2 (g) is 3 atm. CO is extremely poisonous because it forms a very strong complex with hemoglobin. Should you worry? Extras practice for exam, do not hand in Thermodynamic Relations 13. Atkins P.3.30 Joule coefficient derivation 14. Atkins P.3.24 Ideal gas derivation 15. Atkins - E.3.22(b) - Free energy of isothermal process

5 16. Engle P.6.23 Glucose breakdown Under anaerobic conditions, glucose is broken down in muscle tissue to form lactic acid according to the reaction: C 6 H 12 O 6 2 CH 3 CHOHCOOH. Thermodynamic data at T = 298 K for glucose and lactic acid are given below. H f kj mol 1 C P,m J K 1 mol 1 S (J K 1 mol 1 ) Glucose Lactic Acid Calculate G at T = 298 K and T = 310. K. Assume all heat capacities are constant from T = 298 K to T = 310.K. 17. Engle P.6.24 Protein denaturing* At T = 298 K and ph=3 chymotrypsinogen denatures with G = 30.5 kj mol 1, H = 163 kj mol 1, and C P,m = 8.36 kj K 1 mol 1. Determine G for the denaturation of chymotrypsinogen at T = 320. K and ph=3. Assume C P,m is constant between T = 298 K and T = 320. K. Free energy of mixing processes 18. Engle P.6.31 Gas mixture* A gas mixture with 4 mol of Ar, x moles of Ne, and y moles of Xe is prepared at a pressure of 1 bar and a temperature of 298 K. The total number of moles in the mixture is three times that of Ar. Write an expression for G mixing in terms of x. At what value of x does G mixing have its minimum value? Calculate G mixing for this value of x. 19. Atkins Ch. 5: Ex (b)* Equilibrium 20. Engle P.6.26 Temperature dependent enthalpy error* In this problem, you calculate the error in assuming that H reaction is independent of T for a specific reaction. The following data are given at 25 C:

H f G f C P,m kj mol 1 kj mol 1 J K 1 mol 1 CuO(s) Cu(s) O 2 (g) 157 130 a. From Equation (6.71), 42.3 24.4 29.

6 H f G f C P,m kj mol 1 kj mol 1 J K 1 mol 1 CuO(s) Cu(s) O 2 (g) a. From Equation (6.71), K P T f K P T 0 d ln K P 1 R T f T 0 H reaction T 2 To a good approximation, we can assume that the heat capacities are independent of temperature over a limited range in temperature, giving H reaction T H reaction T 0 C P T T 0 where C P v i C P,m i. By integrating Equation (6.71), show that ln K P T ln K P T 0 H reaction T 0 R T 0 C P R 1 T 1 T 0 1 T 1 T C P 0 R ln T T 0 b. Using the result from part (a), calculate the equilibrium pressure of oxygen over copper and CuO(s) at 1200 K. How is this value related to K P for the reaction ( ) ( ) ( )? c. What value would you obtain if you assumed that H reaction were constant at its value for K up to 1200 K? 21. Atkins Ch. 6: Ex. 6.3 (b) dt i

2SO 2(g) + O 2(g) Increasing the temperature. (Total 1 mark) Enthalpy data for the reacting species are given in the table below.

2SO 2(g) + O 2(g) Increasing the temperature. (Total 1 mark) Enthalpy data for the reacting species are given in the table below. Q1.Which change would alter the value of the equilibrium constant (K p) for this reaction? 2SO 2(g) + O 2(g) 2SO 3(g) A Increasing the total pressure of the system. Increasing the concentration of sulfur