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CH 342 Physical Chemistry II

Hour Exam II March 20, 2003

This examination consists of 10 short answer/multiple choices questions and four problems. For the problems, you must show your work and all answers must include units.

Useful Constants

c = 2.99792 x 108 m/s

me = 9.109389 x 10-31 kg

g = 9.80 m/s2

h = 6.626 x 10-34 J-s

k = 1.380658 x 10-23 J/K

R = 0.082057 L-atm/mol K or 8.3145 J/mol K or 0.0831451 dm3-bar/mol K

L = 6.022137 x 1023 /mole

Useful Conversions

1 atm = 760 torr = 101325 Pa =1.01325 bar

101.325 J = 1 L-atm

100.00 J = 1 L-bar

Questions

1) Give a brief statement of the third law of thermodynamics

2) For the reaction of C2H4 (g) + H2 (g) to form C2H6 (g), would you expect the standard state entropy change to be positive or negative? Why?

3) Which of the following statements is true

a) the chemical potential of a pure substance decreases if you raise the temperature at constant pressure

b) the chemical potential of a pure substance decrease if you raise the pressure at constant temperature

c)At 1 atm and 373 K, the chemical potential of water vapor is larger than that of liquid water

d) a, b, and c are all true

e) a, b, and c are all false

4) Which of the following statements is true

a) For a spontaneous process, DS must be positive

b) For a spontaneous reaction, DH must be negative

c) For spontaneous freezing to occur at 1 atm, DG for the transition must be negative.

d) The Helmholtz energy will increase for a spontaneous process at constant T and V

5) Sketch a phase diagram for hexane which like most substances has a more dense solid and less dense liquid. Identify on the diagram the critical point, the triple point, the normal freezing and boiling points

6) What is the second law of thermodynamics?

7)Which of the following statements is true:

a) For a chemical reaction to be spontaneous, DG° must be negative

b) For a chemical reaction to be at equilibrium DG° must be zero

c) For a chemical reaction to be at equilibrium the free energy of the system must be a minimum

d) For a gas phase chemical reaction, Kp and Kc refer to the same standard state

8) Consider the gas phase synthesis of ammonia from nitrogen and hydrogen. If the system was at equilibrium and we increased the volume of the container at a constant temperature. What would happen to the amount of ammonia in the vessel? Explain

9) What are the natural variables of the Gibbs function?

10) What Maxwell relationship can we derive from the total differential, dG?

Problems

1) A sealed container was filled with 0.250 moles of hydrogen gas, 0.350 moles of iodine gas, and no HI. The initial total pressure was 1.00 bar and the temperature was 870 K. The following reaction takes place. with an equilibrium constant of 870. What are the equilibrium partial pressures of the three species

2) Start with the total differential for U and derive an expression for . The final answer should contain only constants, typical lab variables; T, P, V, and their derivatives.

b) Evaluate for a non-ideal gas whose equation of state is

where the virial coefficient B is a function of temperature but not pressure or volume.

3) Carvone (oil of spearmint) has a heat of vaporization of 52.00 kJ/mol with a normal boiling point of 502.1 K? What is the entropy of vaporization? Using the values for DH and DS, what is the free energy of vaporization at 508 K? What is the physical implication of the sign of DG at this temperature?

b) The absolute entropy of carbon disulfide is 150.7 J/mol K under standard conditions and the heat capacity of the liquid is 75.48 J/mol K. What would the absolute entropy of the liquid be at 165.0 K which is just above the melting point. Recall that

4) One method for producing iron from the oxide is to heat the oxide in the presence of CO. . At 523 K, Kp is 100.0 while at 1273 K the equilibrium constant is 0.0721. Using the van't Hoff equation and assuming DH is constant, what is the heat of reaction for this process?

b) Based on your answer from part a, what are DG and DS at 523 K ?

c) At what temperature would DG be zero? What can you say about the equilibrium partial pressures of CO and CO2 at this temperature?