Problem Set #3
Heat Capacities (Cv, Cp)
1. Equal masses of methane at 300 K and ethylene at 600 K are mixed such that the pressure is constant, and no heat can escape. What will be the final temperature? Methane: Cp,m = 35.46 J K-1 mol-1. Ethylene: Cp,m = 42.17 J K-1 mol-1. Hint: Think about DH for the overall process.
2. Considering H2O to be a rigid nonlinear molecule, what value of Cp,m would be expected classically, if we take into account translation and rotation, but not vibration? If translation, rotation, and vibration are all taken into account, what value is expected?
3. Cv° is 28.3 J K-1 mol-1 for HI(g) at 2000 K; and 30.2 J K-1 mol-1 for I2(g) at the same temperature. How do you explain this difference? Numerical calculations are not needed. Hint:
4. The heat capacities of a gas may be represented by , Cp,m is in J K-1 mol-1. How much heat is required to heat 1.00 mole N2 from 300 K to 1000 K at constant pressure. [a = 26.984, b = 5.910 x 10-3, c = -3.377 x 10-7]
5. Starting from , show that . Then, evaluate Cp - Cv for a perfect gas.
6. Predict the standard reaction enthalpy of at 100° C from its value of –57.20 kJ mol-1 at 25° C. Assume that all relevant heat capacities are constant over this range of temperatures, and that Cp,m(NO2, g) = 37.20 J K-1 mol-1 and Cp,m(N2O4, g) = 77.28 J K-1 mol-1.
7. Calculate the enthalpy change for heating 1.00 mole CO2 (gas) from 300 to 1500 K at constant pressure. , where a = 44.22, b = 8.79 x 10-3, c = -8.62 x 105.
8. A gas obeys the equation of state , where the second virial coefficient B is a function of T. Derive the formula , where .
9. Calculate the enthalpy of formation of PCl5 (s), given the heats of the following reactions at 25° C.
10. For the following three questions, please choose one of the three italicized answers for each case:
1. For an ideal gas, the Joule-Thomson coefficient (mJ-T) is negative, zero, positive; and its temperature always decreases, remains constant, increases during a Joule-Thomson expansion.
2. For a real gas, if mJ-T is positive, then dT is negative, zero, positive when dP is negative, and the temperature of the gas decreases, remains constant, increases during a Joule-Thomson expansion.
3. A real gas showing a heating effect above its Joule-Thomson inversion temperature will show a cooling effect, no effect, heating effect below this inversion temperature.
11. A gas obeying the equation of state undergoes a Joule-Thomson expansion. Show that as the pressure drops during the Joule-Thomson expansion, the temperature must increase. Hint: .
Calorimetry: the Bomb Calorimeter
12. A sample of liquid benzene weighing 0.633 g is burned in a bomb calorimeter at 25° C, and 26.54 kJ of heat are evolved. Calculate DUm and DHm.
13. Evaluate the internal pressure for an ideal gas.
14. Derive an expression for the internal pressure of a gas obeying the Berthelot equation of state .
Test for Exactness
15. If z is a state function (therefore, dz is an exact differential) and , then