(10 points) Calculate the pl work when a gaseous system expands from 1.0 L to 2.0 L against a constant external pressure of 10 bar. 1 bar = 10' Pa; 1 L = 10 3 m3 V1 = 1.OL W = PV A. -1 x 103 J V2 = 2.OL 1 atm N = 9. 87 ( V F - Vi ) B. +1 x 103 J P = 10 barx - 10 Pa, bar 1. 01 325 x10 Pc 2 9. 87 ( 2.0 - 1.0 ) C. -1 x 10 3 J D. +1 x 10 3 J = 9. 869 atm = 9. 87 1 atm x 101. 325 J W = 100OJ 2 (10 points) Calculate the heat, in joules, when the temperature of 0.100 kg of liquid water increases from 25.0 C to 75.0 C at ambient (1 bar) temperature. The molar heat capacity of 0.100 kg liquid water is 75.4 J.mol-.K- and is nearly independent of temperature. T , = 25+ 273.15 = 298.15 Cp = AH AT A. +2.09 x 103 J T2 = 75+ 273- 15 = 348.15 AH = (75.4 3/DADT.K)(34 8.15- 298.15)14 (6.1) B. -2.09 x 103 J P = 1 bar JH - 3770 J C. +2.09 x 104 J 0 . 100 kg D. -2.09 x 104 J Com = 75. 4J/mol-k 3. (10 points) What are the signs of AS for the system, surroundings, and universe when a sample of ice melts at 5 .C? sustem 2f A. ASsystem > 0, ASsurroundings > 0, ASuniverse > 0 dsur = loses heat B. ASsystem 20, ASsurroundings 0 duni = + C. ASsystem 0, ASuniverse > 0 D. ASsystem Sm,solid > Sm,gas B. Sm,solid > Sm, liquid > Sm,gas C. Sm,gas > Sm, liquid > Sm,solid D. Sm,gas > Sm,solid > Sm,liquid E. None of the above - at a given T, P entropy is equal in all phasesDR: (gsfoma 9'8 '60 5. (10 points) Consider the dissociation reaction of water below: 2H20(g) '' 2H2(g) + 02(g) The standard Gibbs energy of reaction is ArG" = 453.14 kJ'mol'l. (a) Determine the value of K , the equilibrium constant, at a temperature of 298. 15 K. (b) Write an expression for the equilibrium constant in terms of the partial pressures of each species. The only variables that should appear are pHZO, pHZ, p02, and p. 6. (10 points) A molecule can adopt one of two distinct congurations: a low-energy state and a high-energy state. At 298 K, the number of molecules in the low-energy state, N1, is exactly double the number of molecules in the high-energy state, N2. (N 1 = 2N2). You may assume that this system obeys Boltzmann statistics, so that N is proportional to e'EmT), (a) What is AB, the energy difference between the two states? (b) What will the ratio of molecules in the low energy state (N UN 2) at T = 310 K? 7. (20 points) When 6.? mol C02(g) is heated at a constant pressure of 3.25 atm, its temperature increases from 287 K to 315 K. The value of CW1 for C02 is 37.11 J'mol'l'K'l. (a) Calculate g (1)) Calculate AH (c) Calculate AU ((1) Calculate AS 8. (20 points) A vessel is loaded with liquid benzene and liquid methylbenzene, then sealed and maintained at a constant temperature of 298. 15 K. Each substance partially vaporizes until it is in equilibrium with its vapor phase. The final composition of the liquid phase is 60% benzene (by mole). You may assume Raoult's Law applies for both species, and that the vapor pressures at 298.15 K are p; = 0.103 bar, pg\