CHEM 341. Fall 2000.  Next PS  Previous PS  Answers  PS#3.doc (Word 97)     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. Enthalpy 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 . Hint: . 9. Calculate the enthalpy of formation of PCl5 (s), given the heats of the following reactions at 25° C. Joule-Thomson Coefficient 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. Internal Pressure 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   . 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.