NORTH CAROLINA STATE UNIVERSITY

Department of Chemistry                 Name________________________________

 

CH 431                                                                                      Practice Mid-term

Physical Chemistry

 

Given:                   g = 9.81 m/s2

                             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

                             P = P0exp{-Mgh/RT}


 


                              

Please answer all questions.

 

1.     A. It is thought that CH4 gas is found on the surface of Jupiter.  Calculate its density under the following conditions:

a.      assuming the gas is ideal at P = 1000 atm and T = 15 K:                     r(gL-1) = ___________________ .

 

 

 

 

 

 

 

b.     assuming that it is a hard sphere gas at P = 1000 atm and T = 15 K. A hard sphere gas is a van der Waal’s gas with a = 0.  The excluded volume parameter is b = 0.043 L/mole.             r(gL-1) = ___________________ .

 

 

 

 

 

 

c.     calculate the maximum possible density according to a hard sphere gas and comment on the validity of the ideal gas law for this problem.

 

 

 

 

 

 

 

B. In 1890 a scientist descends in a diving bell.  The volume of the gas inside the bell is 2000 L.  What is the volume at a depth of 15 m below the surface of the ocean at 20oC, noting that sea water has a density of 1.03 x 103 gL-1:   V(L) = _________________

 

 

 

 

 

 

 

 

 

C. Calculate the density of the nitrogen in the air on Kibo crater on the rim of Kilimanjaro at –20oC ( a lovely afternoon temperature in Africa!) assuming that the partial pressure of N2 is 0.8 atm at sea level.                   r(gL-1) of N2(g) = ___________________

 

                       

 

 

 

 

 

2.     An ideal gas is initially at 20.00 atm and 500 K.  Its volume is initially 0.5 L and the gas expands isothermally to 120.0 L under the following conditions:

 

(1.)Pexternal = 0

(2.)Pexternal = 0.333 atm

(3.)Pexternal = Pgas (reversible expansion)

 

     For each of the above conditions calculate DU, q, and w, for the gas.

                      DU(J)                      q(J)                         w(J)                        

 

     (1.)        __________          ___________          ____________ 

 

      (2.)        __________          ___________          ____________  

 

      (3.)        __________          ___________          ____________   

 

 

 

 

 

3.     Three energy  levels for a molecule are shown below. 

 

A.   Based on the energy levels shown in the Figure to left, write an expression for the molecular partition function assuming that the particle is fixed in space (i.e. it cannot translate, rotate etc.).

 

 

 

 

 

B.    Assume that the particle can translate, calculate its molecular partition function q for both the energy levels shown above in terms of e and for translation (you may assume that the particle cannot rotate or vibrate and that translation is the only possible motion you need consider).

 

 

 

 

 

C.   Assuming that a system consists of N indistinguishable particles calculate the system partition function (include both translation and the energy levels shown in the Figure).

 

 

 

 

 

D.   Calculate the average energy of a system of N particles (include both translation and the energy levels shown in the Figure).

 

 

 

 

4.     One can show that the heat capacity of a monatomic ideal gas is Cv = 3/2nR and that of an ideal diatomic gas is Cv = 5/2nR. 

A.   Give a plausible reason for the difference in the values of the heat capacity for a monatomic and a diatomic gas.

 

 

 

 

 

 

 

 

B.    Calculate the amount of energy required to heat the earth’s atmosphere to a median temperature of 285 K from 0 K at constant volume.  The radius of the earth is R = 6.37 x 106 m and the area of the earth’s surface is 4pR2.  Assume that the atmosphere is an ideal diatomic gas with a molar mass of M = 29 g/mole.

 

 

 

 

 

 

5.  The work done by an isothermal expansion is said to be a maximum.  Three systems containing an ideal gas have the same initial volume of 1 L, pressure of 10 atm, and temperature of 300 K.  The systems expand along two different paths, the first one isothermal, the second one adiabatic, and the third one constant pressure.  For each expansion the final volume is 10 L.  Calculate (a) the work of isothermal expansion, (b) the work of adiabatic expansion, and (c) the work of a constant pressure expansion from 1 L to 10 L.  How do these compare?