R = 8.31 J/mol-K = 0.0821 L-atm/mol-K, 1 atm = 1.01 bar = 760 torr

dU = TdS - pdV, dH = TdS + Vdp, dA = -SdT - pdV, dG = -SdT + Vdp

dlnP/dT = H/RT², dP/dT = S/V = H/TV µ = µ + RTln a
 

1. (20 points) True or False. If False, explain in one sentence why the statement is false.

a) Because the density of solid methanol is greater than that of liquid methanol, increasing the pressure on the equilibrium solid/liquid system at constant temperature shifts the equilibrium in favor of the liquid.

b) Liquids A and B form a "regular" solution. One finds that after pouring the pure liquids at room temperature into a container at room temperature to make up a solution, the container feels cold. One may conclude that the activity coefficients of the A and B in solution are greater than one.

True.

c) Pure liquid water which is carefully cooled in a clean container to -4C has a vapor pressure which is lower than that of pure ice at the same temperature.

d) A liquid is in equilibrium with its vapor in a closed container at a fixed temperature. If one adds a small amount of the liquid to the container, the vapor pressure should go up to re-establish equilibrium.

False, the equilibrium depends only on the chemical potentials which do not change with more mores of water, in this case.
 

2. The H_vap for CH₃OH(liq) at 298 K is 38.00 kJ/mol. At 273 K, the vapor pressures of pure methanol, CH₃OH(liq), and ethanol, C₂H₅OH(liq) are 32.4 torr and 12.3 torr, respectively, and their molecular weights (molar masses) are 32 g/mol and 46 g/mol, respectively. The normal boiling point of pure methanol is 337.2 K.

a) (15 points) Find the equilibrium vapor pressure of methanol at 298 K. State any assumptions or approximations made.

b) (15 points) A solution of ethanol in methanol is made up by adding 2.3 g of ethanol to 64 g of methanol. If the solution is ideal, what is its G_mix at 273 K?

c) (15 points) If the activity coefficients of both components are actually 0.90, what are the partial pressures of the methanol and ethanol vapors in equilibrium with the solution at 273 K?

d) (8 points) If the solution in (c) is "regular", what is the S_mix at 273 K?

e) (12 points) The Henry's Law constant for ethanol in methanol, K_B, is (hypothetically) 4.1 torr. Calculate the difference in the standard state chemical potentials of ethanol defined in the Raoult's Law limit and in the Henry's Law limit at 273 K? That is, find µ_Raoult's - µ_Henry's at 273 K. (Hint: Remember that the chemical potential of ethanol in solution is independent of the choice of standard states.)

f) (15 points) What is the boiling point elevation constant for methanol and by how much higher should the solution in (b) boil than pure methanol? (Assume that the solution is ideal.)