CHEM 341. Fall 2000. Next PS Previous PS Answers PS#3.doc (Word 97)
Problem Set #3 Heat Capacities (C_{v}, C_{p}) 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: C_{p,m} = 35.46 J K^{1} mol^{1}. Ethylene: C_{p,m} = 42.17 J K^{1} mol^{1}. Hint: Think about DH for the overall process. 2. Considering H_{2}O to be a rigid nonlinear molecule, what value of C_{p,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. C_{v° } is 28.3 J K^{1} mol^{1} for HI_{(g)} at 2000 K; and 30.2 J K^{1} mol^{1} for I_{2(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 , C_{p,m} is in J K^{1} mol^{1}. How much heat is required to heat 1.00 mole N_{2} 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 C_{p } C_{v} 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 C_{p,m}(NO_{2},_{ }g) = 37.20 J K^{1} mol^{1} and C_{p,m}(N_{2}O_{4},_{ }g) = 77.28 J K^{1} mol^{1}. 7. Calculate the enthalpy change for heating 1.00 mole CO_{2} (gas) from 300 to 1500 K at constant pressure. , where a = 44.22, b = 8.79 x 10^{3}, c = 8.62 x 10^{5}. 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 PCl_{5} _{(s)}, given the heats of the following reactions at 25° C. JouleThomson Coefficient 10. For the following three questions, please choose one of the three italicized answers for each case: 1. For an ideal gas, the JouleThomson coefficient (m_{JT}) is negative, zero, positive; and its temperature always decreases, remains constant, increases during a JouleThomson expansion. 2. For a real gas, if m_{JT} is positive, then dT is negative, zero, positive when dP is negative, and the temperature of the gas decreases, remains constant, increases during a JouleThomson expansion. 3. A real gas showing a heating effect above its JouleThomson 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 JouleThomson expansion. Show that as the pressure drops during the JouleThomson 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 DU_{m} and DH_{m}. 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

