CHEM 4010                                                                              Name ___________

Dr. Perona                                                                                 May 28, 2004

                                                            FINAL EXAM

                                                             

 

1 atm = 1.01325x105 Pa = 760 Torr

1bar = 105 Pa

R = 8.3145 J K-1 mol-1 = 0.083145 L bar K-1 mol-1 = 0.0820578 L atm K-1 mol-1

1m3 = 103 L = 106 cm3

 

 

Maxwell Relations:

 

           

Do problems 1 through 8, and any two chosen from 9 through 12.  You must show all of your work clearly to obtain full credit.

 

 

Part 1.  Do problems 1 through 8.

 

1. ()  Assuming that naphthalene (M = 128.1 g/mol) and toluene (M = 92.1 g/mol) form ideal solutions, calculate the solubility of naphthalene in toluene at 30oC.  The enthalpy of fusion of naphthalene is 19.29 kJ/mol, and its melting point is 80.0oC.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. ()The boiling point–composition diagram for the ethanol–benzene system at a pressure of 1.013 bar is shown below. A mixture initially containing 0.20 mole fraction benzene is distilled.

 

 

a)       What is its boiling point?

 

 

 

b)       What is the composition of the first vapor to come off?

 

 

 

 

 

 

 

 

c)       Can pure benzene be obtained by the fractional distillation of this mixture?  Please explain.

 

 

 

 

 

 

 

 

 

 3.()  Benzene and toluene form ideal solutions.  At 100oC, pure benzene and pure toluene have vapor pressures of 180.9 kPa and 74.4 kPa, respectively.

 

a)       What is the mole fraction of benzene in a solution which boils at 100oC and at 1.013 bar pressure?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b)   What is the mole fraction of benzene in the vapor in equilibrium with the solution in part a)?       

 

 

 

4. (22) The synthesis of methanol, CH3OH, occurs according to the reaction

CO(g) + 2H2(g) = CH3OH(l)

Given the thermodynamic data below:

substance

DfHo, kJ mol-1, at 298 K

DfGo, kJ mol-1, at 298 K

CO(g)

-110.53

-137.17

CH3OH(l)

-238.66

-166.27

 

 

 

a)       Calculate the equilibrium constant, K, at 25oC.

 

 

 

 

 

 

 

 

 

 

 

 

b)       Calculate K at 100oC, assuming that DHo is independent of temperature.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.(35)  One mole of ideal gas, with  ,  initially at a temperature of 298 K and volume of 20 L,  expands to a final volume of 35 L.  The expansion occurs adiabatically against a constant external pressure of 0.50 atm, and the temperature of the surroundings is maintained at 298 K.

 

a)  What are w, q, DU, and DH for the gas?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

            b)  What is the entropy change of the surroundings?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. () Gaseous oxygen, O2, is condensed reversibly to the liquid at the normal boiling point of -183 oC.  The heat of vaporization of liquid oxygen at -183 oC and 1.01325 bar is 6820 J/mol.  Calculate w per mole, q per mole, and each of the thermodynamic quantities: , , , and

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7. () It can be shown that the dependence of the molar enthalpy, , on pressure is given by

 

Use the appropriate Maxwell relation (see page 1), and the ideal gas law to show that for an ideal gas

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 8. () For the heterogeneous reaction

 

CH4(g) ⇆ C(s) + 2 H2(g)

 

Derive an expression for the equilibrium constant in term of the extent of reaction and the total pressure.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Part 3.  Do two problems chosen from 9, 10, and 11.

 

9. (23)  In the laboratory, carbon dioxide, CO2, is stored in heavy-walled steel cylinders which contain both liquid and gaseous CO2.  Calculate the pressure inside a CO2 storage cylinder at 298.15 K.  The vapor pressure of liquid CO2, is 5.11 atm, at 216.8 K,  and its enthalpy of vaporization is 16.9 kJ mol-1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10. () One mole of  ideal gas with , initially at 300 K,  occupies a volume of 20 L.  It is subjected to a process in which  it simultaneously cools and expands.  The final temperature and volume are 230 K and and 31 L, respectively.  What is the entropy change for the process?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11. () How much heat is evolved when one mole of liquid water at –5.0 oC, and 1.01325 bar freezes to form ice at the same temperature and pressure?  The enthalpy of fusion of water, DfusH, is 6004 J mol-1 at 0 oC, and the heat capacities at constant pressure for liquid water and ice are, 75.3 J K-1 mol-1 and 36.8 J K-1 mol-1, respectively.