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.
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?
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 .
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?