Conceptual Problems (each problem is worth 6 points).
Is the Gibbs free energy change for mixing of two ideal gases at constant pressure
positive, negative, zero or impossible to determine?
Answer
Is the enthalpy change for mixing of two ideal gases at constant pressure positive,
negative, zero or impossible to determine?
Answer
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?
Answer
What is the maximum number of phases that can co-exist in a system with 3 components?
Answer
Consider the reaction A + B ß à
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?
Answer
Numerical Problems. Note, express all energies in joules or kilojoules and all entropy
changes in joules per degree K.
(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.
Answer
(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. Answer
(20 points) The reaction A ß à
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, DrG0,
b) the reaction Gibbs free energy, DrG, 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).
Answer
Applied Problem (20 points)
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.
Answer