Homework assignment 4 (due Wednesday Mar 25)
1. At P = 1 bar, liquid nitrogen boils at Tb= 77.4 K. Its heat of vaporization is
ΔHvap = 5577 J/mol and it can be assumed to be temperature independent. Estimate Tb
that would be measured for nitrogen at Longs Peak, CO (4,345 m). Assume that
temperature of the atmosphere does not depend on the elevation and is equal to 25°C.
Gaseous N2 can be considered to be an ideal gas.
2. Will the ice be melting under a skater whose mass is m=100 kg if the ice temperature
is –5°C? Assume that the surface area of a skate that is in contact with the ice is equal to
A = 0.05 cm × 20 cm and that the heat of melting is 6 kJ/mol. The density of ice is 0.9
g/cm3 and that of liquid water is 1 g/cm3.
3. The equation of state of a material is given by P(V − b) = RT , where b is a constant.
Derive the equation for the change of the chemical potential of this material,
µ ( P, T ) − µ ( P0 , T ) , when its pressure is raised from P0 to P.
4. n1 moles of compound 1 form an ideal mixture with n2 moles of compound 2. The
process is performed at constant P and T. Let V10 and V20 be the molar volumes of the
(a) What is the total volume of the mixture? Is it larger, smaller, or the same as the
total volume of the pure compounds?
(b) What is the change of the Gibbs free energy, ΔG, upon mixing?
(c) What is ΔA?
(d) What is ΔU ?
5. Three kilograms of H2O at T=10°C are mixed with 1 kg of D2O at T=30°C and form
an ideal solution. Assuming that the Cp value of D2O is the same as that of H2O (1 kcal
kg-1 K-1), calculate ΔS in this process.
6*(10). Strictly speaking, phase transitions can only take place in macroscopic objects
containing infinite number of particles. Protein or RNA folding can be loosely viewed as
phase transitions. However because RNA and proteins are microscopic objects, their
thermodynamic functions do not change abruptly, as expected in a true phase transition,
but rather in a continuous manner. The “protein folding” transition can often be detected
as a spike in the temperature dependence of the protein’s heat capacity as shown in the
Assuming that this dependence is described by the formula:
⎡ kJ ⎤
CP = 1 + 15exp ⎡ −0.16(T − 320)2 ⎤ ⎢
⎦ mol K ⎥ ,
estimate the change of the enthalpy ΔH and entropy ΔS upon protein folding.