CHEM 341. Fall 2000.  Next PS   Previous PS   Answers   PS#6.doc (Word 97)   

 

Problem Set #6

DG for Ideal Gases

1. Calculate the change in the molar Gibbs energy of hydrogen gas when its pressure is increased isothermally from 1.0 atm to 100.0 atm at 298 K.

2. When 2.00 mol of a gas at 330 K and 3.50 atm is subjected to isothermal compression, its entropy decreases by 25.0 J/ K. Calculate the final pressure of the gas and DG.

3. One mole of a perfect gas at 27° C expands isothermally and reversibly from 10 to 1 bar against a pressure that is gradually reduced. Calculate q, w, DU, DH, DS, DA, and DG.

4. For each of the following processes, state if DU, DH, DS, DA, or DG equals zero, or if none of these equals zero. No explanation is needed.

  1. Isothermal reversible expansion of an ideal gas
  2. Adiabatic reversible expansion of a non-ideal gas
  3. Adiabatic expansion of an ideal gas through a throttling valve (Joule-Thomson expansion)
  4. Adiabatic expansion of an non-ideal gas through a throttling valve (Joule-Thomson expansion)
  5. Vaporization of liquid water at 80° C and 1 atm pressure
  6. Vaporization of liquid water at 100° C and 1 atm pressure
  7. Reaction between H2O and O2 in a thermally insulated bomb calorimeter
  8. Reaction between H2SO4 and NaOH in dilute aqueous solution at constant temperature and pressure.

5. A mole of an ideal gas expands reversibly and isothermally at 298 K from 1 bar to 0.1 bar. What is DG? What would be DG if the process occurred irreversibly?

 

Maxwell Relations

6. Derive the equation . Use the Maxwell relation .

Hint: and .

7. In problem #6, you were asked to use the Maxwell relation . Show that this relation is valid, starting from and .

 

DG for Real Gases

8. The molar Helmholtz energy of a gas is given by , where a and b are constants and f(T) is a function of temperature only. Find the equation of state of the gas.

 

Temperature Dependence of DG

9. Derive the Gibbs-Helmholtz equation .

Hint:

 

Chemical Potential

10. Calculate the change in chemical potential of a perfect gas when its pressure is increased isothermally from 1.8 atm to 29.5 atm at 40° C.

 

DG for Mixing

11. Calculate DG, DS, DH, and DV for the mixing of mol oxygen and mol nitrogen at 298 K assuming ideal gas behavior.

 

An Interesting & Challenging Practice Exercise: Fugacity

12. For a real gas, at temperature T the chemical potential is given by . For a van der Waals gas it may be shown that to a first approximation so that . What is the corresponding relation for Sm?

Hint:

 


PLEASE NOTE

  • The work you hand in should be neat and well organized, and it should show the strategy and steps you used in solving the problems, as well as the bottom-line answers (or solutions). In grading the problems, both your work-up and your final answers/solutions will be examined and evaluated.
  • The work handed in for grading must carry a pledge that the work is entirely yours and was done without any collaboration with other persons (except for the course instructor and TA's). You are encouraged to work with others in doing the exercises and problems found in the textbook, but all work handed in for grading should be done independently.