NORTH CAROLINA STATE UNIVERSITY

Department of Chemistry                                                Name________________________________

 

CH 431                                                                                                                              Mid-term 2

Physical Chemistry I                                                                                                          29 Oct 1998

 

Given:  R = 8.314 J mol-1 K-1 = 0.08206 L atm mol-1 K-1

             1 atm = 1.0133 x 105 Nm-2 = 760 Torr


                                   


                                     

Please answer all questions.

 

1.      a. Assume that the work of isothermal expansion in the cylinder of an internal combustion engine is an irreversible expansion against an external pressure of 1.6 atm.  Assuming that the initial pressure is 16 atm and that the initial volume is 50 cm3 and final volume is 500 cm3, calculate the entropy change for the system, surroundings and the total entropy change for the expansion step.  The initial temperature is 385 K.

 

 

 

 

 

 

b.      An internal combustion engine produces 3.0 kJ of work for each 10.0 kJ of fuel combusted.  Assuming that the engine behaves as an ideal reversible cycle, calculate the thermodynamic efficiency and temperature of the isothermal expansion phase of an internal combustion engine if the exhaust temperature is 295 K.

 

 

 

 

 

 

 

c.       Calculate the residual entropy of NA molecules FClO3.  It is known that FClO3 has four orientations in the crystalline form that are frozen in at 0 K.

 

2.  Argon and Neon gas placed in an insulated vessel with volume of 10 L with a gas tight seal dividing the vessel in two equal volumes of 5 L each at 1 atm of pressure.  Initially the temperature of argon is 300 K and temperature of neon is 500 K.  The seal is removed (reversibly) and the two gases are allowed to come to equilibrium in the final volume of 10 L.

a.       Calculate the entropy of mixing.

 

 

 

 

 

 

b.      Calculate the entropy change associated with the volume change as argon is expanded from the initial to the final volume.

 

 

 

 

 

c.       Calculate the entropy change associated with the volume change as neon is expanded from the initial to the final volume.

 

 

 

 

 

 

 

 

d.      Calculate the total entropy change (system and surroundings) at the equilibrated final  

temperature.

 

3.      Find an expression for (U/V)T for (a) an ideal gas (b) a van der Waals gas in terms of only the pressure, temperature, and volume (P, V, and T).

 

Useful expressions:

H = U + PV

A = U - TS

G = H - TS

4.      The standard enthalpy of the reaction N2 (g) + 3H2 (g) ® 2NH3 (g) is – 92.38 kJ/mol of ammonia and the standard Gibb’s energy is –33.26 kJ/mol at 298 K.  Assuming that the entropy and enthalpy are independent of temperature calculate the Gibb’s free energy at 1000 K.  Given the heat capacity data below calculate the Gibb’s free energy at 1000 K based on the temperature dependence of the enthalpy and entropy.

 

Gas

Cp (J/mole-K)

NH3

29.75

H2

27.28

N2

28.58