V25.0109: General Chemistry I: Honors

Problem set #8: due 11/20

Practice problems from Chapter 8: 3,4,11,17,19,35,49
Practice problems from Chapter 9: 11,17,23,25,35,36,49,81 \

Additional practice problem:

Suppose n moles of an ideal monatomic gas are compressed or expanded isothermally at a constant temperature T from a volume to a volume . Show that the change in the Gibbs free energy is given by

Graded problems

1.

A monatomic ideal gas initial having a pressure , temperature and volume is taken around a complete, reversible thermodynamic cycle along a four-step path. The steps of the path are as follows:

i.

An isochoric (constant volume) process, in which the gas is heated from to at constant volume.

ii.

An isobaric (constant pressure) process, in which the gas is allowed to expand from to at constant pressure.

iii.

Another isochoric process, in which the gas is cooled at constant volume.

iv.

Another isobaric process, at the end of which the gas is in its initial thermodynamic state.

All processes are carried out keeping the number of moles of gas constant.

a.

Draw the thermodynamic cycle in the P-V plane.

b.

For each of the four steps, determine the heat absorbed by the gas, the work done on the gas, and the change in its internal energy.

c.

Show that the total change in energy for the cycle is 0.

d.

If the process is stopped after step iii, show that the total change in energy for steps i,ii, and iii is the same as that for the reverse of step iv.

2.

In problem set # 4, we showed that the number of microscopic configurations for the positions of particles in an ideal gas is if the particles are distinguishable.

a.

Suppose, now, that the particles are indistinguishable. By dividing the containing volume in to M cells of volume v, show that the number of microsocpic configurations for the positions is , so that the total number of microscopic states is

where c is an arbitrary constant.

b.

An ideal gas containing N molecules in a volume V is initially divided into two separate compartments by a partition such that the number of molecules in one of the compartments is the same fraction as the subvolume is to V, i.e., . The same is true of and , the number of molecules and volume of the second compartment, i.e., . Using the number of microscopic states defined above, show, using Boltzmann's definition of entropy, that the change in entropy before and after the partition is removed is 0. You might find it useful to use the following approximation for factorials of large numbers: .

3.

Problem #50 from Chapter 8

4.

The average energy of n moles of a van der Waals gas at temperature T in a volume V is given by

Calculate the net work done in a Carnot cycle by a van der Waals gas. You may assume that the constant volume and constant pressure molar heat capacities are 3R/2 and 5R/2, respectively and that the adiabatic part of the process can be analyzed assuming that the quantity is negligible.

5.

For each of the following reactions, use the given equilibrium constant and the data in Appendix D of the book to determine the free energy of formation for the compound X:

6.

The activity coefficient of a nonideal gas is defined to be a correction factor, which, when multiplied by the observed pressure of the gas gives the pressure it would have if it were an ideal gas.

Consider the gas phase reaction:

whose equilibrium constant at a high temperature is K=115.00. Suppose that H , F and HF gases are to be treated as nonideal gases with activity coefficients 1.111, 1.180 and 1.250, respectively. A 50 L vessel contains HF gas at an observed partial pressure of 2.4 atm and H gas at an observed partial pressure of 4.5 atm.

a.

It is desired to add enough fluorine gas to the vessel to obtain a total ideal gas pressure of 10 atm. To what observed partial pressure must fluorine gas be added?

b.

What will be the observed partial pressures of each gas in the vessel after equilibrium is established?

c.

What will be the total ideal gas pressure in the container at equilibrium?

d.

Suppose the volume of the vessel is doubled. What effect does this have on the equilibrium? (Think carefully about this one!)

7.

Consider the reaction:

The equilibrium constant for this reaction at 900 K is 0.345. Suppose a sample weighing 0.800 g of SO is at a temperature of 900 K in a 0.1 L vessel.

a.

What will be the partial pressures of SO , SO and O gases at equilibrium?

b.

What will be the partial pressures of each gas at equilibrium if the reaction is carried out at 1100 K (you may wish to consult the data in Appendix D)?

c.

What will be the partial pressures of each gas at equilibrium if the reaction is carried out at 750 K (you may wish to consult the data in Appendix D)?

• About this document ...