Exam 3 Key
Conceptual Problems (each problem is worth 6 points). NOTE: You do not need to give an explanation of your answer -- just the answer is fine.
1)Is the Gibbs free energy change for mixing of two ideal gases at constant pressure positive, negative, zero or impossible to determine?
Gmix is negative because mixing is a spontaneous process.
2)Is the enthalpy change for mixing of two ideal gases at constant pressure positive, negative, zero or impossible to determine?
Hmix is zero because at constant pressure the enthalpy change for a process is just the heat and the heat released or absorbed by mixing ideal gases is zero.
3)Dissolving a small amount of sugar in liquid water causes the chemical potential of the water to increase, decrease, remain the same or impossible to determine?
The chemical potential will decrease because the mole fraction of the water will decrease and
4)What is the maximum number of phases that can co-exist in a system with 3 components?
F = 2 - P + C or P = 2 + C - F. F cannot be less than zero. C = 3. Thus the largest P could be is 2 + 3 - 0 = 5
5)Consider the reaction A + B C. If this reaction is in equilibrium and I add a small amount of C to the system, will the equilibrium constant for this reaction increase, decrease, remain the same, or is it impossible to tell?
It will not change. The equilibrium constant is not changed by the addition or removal of components in the reaction.
Numerical Problems. Note, express all energies in joules or kilojoules and all entropy changes in joules per degree K.
6)(15 points) The addition of a certain amount of a solute to water increased the boiling point by 1.0 K. Calculate the decrease in the freezing (melting) point. Cryoscopic and ebullioscopic constants for water are given on the equation sheet for exam 3.
Note that the change in the vaporization temperature is an increase while that in the melting temperature is an decrease.
7)(15 points) Consider a container of volume 10 liters that is divided into two compartments of 3 liters and 7 liters. In the 3 liter compartment there is oxygen at 1 atm and 25 C; in the right compartment there is nitrogen at the same temperature and pressure. Calculate the Gibbs energy of mixing when the partition is removed. Assume that the gasses are perfect.
8)(20 points) The reaction A B has an equilibrium constant of 10 at 25 C. A beaker is prepared with 0.02 M compound A, and 0.01 M compound B in water at 25 C and then allowed to come to equilibrium. Calculate a) the standard reaction Gibbs free energy, rG0, b) the reaction Gibbs free energy, rG, for the initial conditions, and c) the equilibrium concentrations of A and B (in moles per liter). Assume all activity coefficients are 1.0. Also assume that molal and molar concentrations are the same in water (moles per kg water is the same as moles per liter).
a)
b)
c) At equilibrium, . But we know from the chemical equation that as A is converted to B, A will go down in concentration by the same amount that B will increase. Thus we can say that where [A]0 is the initial concentration of A and [B]0 is the initial concentration of B. Solving for alpha gives: . Thus, the final values of [A] and [B] at equilibrium are [B] = 0.01 + 0.0173 = 0.0273 M and [A] = 0.02 - 0.0173 = 0.00273 M
Applied Problem (20 points)
9)You are an engineer and your company is considering building electrical generators at the mouth of a river where it enters the sea. The idea is to use the fact that there is an osmotic difference between fresh water and sea water to drive some sort of a pump. Your job is to figure out how well this might work. A diagram of a test apparatus is given below. Salt water is placed in a piston which is in contact with fresh water through a semipermeable membrane that lets through the water, but not the salt. As water comes in through the membrane, the piston moves up. For your calculation, assume that the amount of fresh water that enters the piston through the membrane is small compared to the total volume of the piston and does not appreciably change the concentration of the sea water (assume sea water has a solute molarity of about 0.3 M). Determine the maximum amount of work that can be obtained per liter of fresh water that comes into the piston. The water is at 15 C.
The extra pressure generated by the osmotic force of the fresh water coming into the salt water at the lower chemical potential is given by:
The max work will occur if we expand the piston reversibly. Thus the external force will also always be 7.09 atm ( in addition to the 1 atm that was already there on both sides due to the atmosphere but cannot be used to drive a generator). Thus the max work per liter of fresh water coming in is just
Note that the 1 atm on both sides is just the atmosphere pushing against itself and I cannot use that pressure to drive my motor so I did not include it.