Useful relations: dG=-SdT+Vdp, (nK/T)_p=H/RT², k=Aexp(-E_a/RT), G=-nFE

R=8.31 J/mol-K, F=96,500 C, 1 atm=1.01 bar=760 torr
 

Useful data at 298 K: G_f(HgO(s)) = -58.54 kJ/mol; H_f(HgO(s))= -90.83 kJ/mol; E_h(Ag₂S(s)+2e^-2Ag(s)+S^2-) = -0.691 V; E_h(Ag⁺ +e^-Ag(s)) = +0.800 V
 

1. (20 points) Indicate whether each of the following statements is true or false. If false, explain why it is false in one sentence.

a) For first order processes like radioactive decays, the process half-life is independent of the initial amount of material, but other "fractional-lives" such as the one-third-life or one-tenth-life do depend on the initial amount.

b) When the chemical constituents of a battery have reached their equilibrium concentrations, no more work can be obtained from the battery reaction (at fixed temperature).

True

c) For a gas phase reaction, increasing the total pressure of the system (at a fixed temperature) increases the equilibrium constant for the reaction.

d) If the S is positive for the chemical reaction occurring in a battery, the standard cell potential E of the battery decreases when the temperature increases.

2. For the reaction 2HgO(s)2Hg(liq)+O₂(g):

a) (12 points) Find the G_react and the equilibrium constant at 298 K.

b) (12 points) Find the equilibrium constant at 700 K.

c) (8 points) What is the pressure of O₂ in equilibrium with this system at 298 K? (Assume ideal gas behavior.)

d) (6 points) When the volume of the container in which this reaction is occurring is halved, how is the equilibrium pressure affected? Explain briefly.

e) (8 points) What is the equilibrium constant at 298 K for the reaction:

HgO(s)Hg(liq)+1/2 O₂(g)? What is the O₂ pressure at equilibrium? Explain briefly.

3. a) (12 points) From the standard half-cell potentials for the reduction of Ag₂S(s) and Ag⁺ to Ag(s), find the equilibrium constant at 298 K for the solubility of Ag₂S; i.e., for the process Ag₂S(s)2Ag⁺(aq) + S^2-(aq).

b) (8 points) What is the equilibrium concentration of Ag⁺ in solution at 298 K when 1.00 g of Ag₂S(s) is added to a flask with 0.500 L of water? (Assume that the solution is ideal.)

c) (4 points) What is the equilibrium concentration of Ag⁺ in solution at 298 K when 1.00 g of Ag₂S(s) is added to a flask with 1.50 L of water? (Assume that the solution is ideal.)

4. (10 points) What is the activation energy, E_a, for the reaction whose rate constant increases by a factor of 10 when the temperature is increased from 400 K to 500 K?