NORTH CAROLINA STATE UNIVERSITY

Department of Chemistry                                                Name________________________________

 

CH 431                                                                                                                 Practice Mid-term 1

Physical Chemistry I                                                                                                                            

 

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


                                    DH = DU + DPV          DS = q/T

                                    P = P0exp{-Mgh/RT}

 

                                     

Please answer all questions.

 

1.      Assuming that N2 gas is ideal calculate its density at:

a.       1 atm and 100oC: r(gL-1) = ___________________

 

 

 

 

 

b.       15 m below the surface of the ocean at 20oC, noting that sea water has a density

       of 1.03 x 103 gL-1:

                             r(gL-1) = ___________________

 

 

 

 

 

 

 

 

c.       On the top of mount Everest at 9000 m and at –40oC, 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 1.00 atm and 350 K.  Its volume is initially 7.5 L and the gas expands isothermally to 22.2 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.      The energy levels for a particle are shown below. 

 

A.     Write an expression for the molecular partition function assuming that the particle is fixed in space (i.e. it cannot translate).

 

 

 

 

 

 

B.     Assume that the particle can translate, calculate its molecular partition function q for both the energy levels shown above and for translation.

 

 

 

 

 

 

 

 

 

C.     Assuming that a system consists of N indistinguishable particles calculate the system partition function (including translation).

 

 

 

 

 

 

 

D.     Calculate the average energy of a system of N particles (including translation).

 

 

 

 

 

 

 

 

 

4.     

(a) Given the partition function below calculate the heat capacity of an ideal diatomic gas.

 


In the above expression m is the mass, h is Planck’s constant, V is the volume, and C is an arbitrary constant.

 

 

 

 

 

 

 

 

 

 

 

5.      Show how you can use the definition of PV work and the internal energy dU = CvdT together with

      the first law of thermodynamics to derive an expression relating the temperatures before and after a

      reversible adiabatic volume change of an ideal gas (i.e. the ratio of Vfinal/Vinitial).  Justify the crucial

      steps of the derivation by showing your reasoning.