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CHEM 341. Fall 2000. Problem Set #3.
Heat Capacities (Cv, Cp)
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: Cp,m =
35.46 J K-1 mol-1. Ethylene: Cp,m = 42.17 J K-1 mol-1. Hint: Think about H for the overall
process.
2. Considering H2O to be a rigid nonlinear molecule, what value of Cp,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. Cv is 28.3 J K molfor HI(g) at 2000 K; and 30.2 J K molfor I2(g) at the same
temperature. How do you explain this difference? Numerical calculations are not needed. Hint:
E
e V / T
 U vib 
 V 
CVvib  

R
where the vibration constant is V  vib



2

/
T
kB
 T V
 T  e V 1
2


1

k B is the Boltzmann constant, and the energy of vibration is E vib   n  h.
2

where n is the quantum number, n  0, 1, 2, ...
h is Planck' s constant
 is the frequency of vibration ,  
1 k
2 
where k is the force constant and  is the reduced mass :  
m1m2
m1  m2
4. The heat capacities of a gas may be represented by C p,m  a  bT  cT 2 , Cp,m is in J
K mol. How much heat is required to heat 1.00 mole N2 from 300 K to 1000 K at constant
pressure. [a = 26.984, b = 5.910 x 10, c = 3.377 x 10]
T V / T 2P
 P   V 
5. Starting from C p  C v  T 
.
 
 , show that C p  C v  
V/P T
 T  V  T  P
Then, evaluate Cp  Cv for a perfect gas.
Enthalpy
6. Predict the standard reaction enthalpy of 2NO2 ( g )  N 2 O 4 ( g ) 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 Cp,m(NO2, g) = 37.20 J K1 mol1 and Cp,m(N2O4, g) = 77.28 J K1
mol1.
7. Calculate the enthalpy change for heating 1.00 mole CO2 (gas) from 300 to 1500 K at
c
constant pressure. C p,m  a  bT  2 , where a = 44.22, b = 8.79 x 103, c = 8.62 x 105.
T
RT
 B , where the second virial coefficient B
8. A gas obeys the equation of state Vm 
P
 B 
 H 
is a function of T. Derive the formula 
  B  TB  , where B     .
 P T
 T  P
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CHEM 341. Fall 2000. Problem Set #3.
 Vm 
 H 
Hint: 
 .
  Vm  T 
 P  T
 T  P
9. Calculate the enthalpy of formation of PCl5 (s), given the heats of the following
reactions at 25C.
2P( s )  3Cl 2 ( g )  2PCl 3(l )
H  635.13 kJ
PCl 3(l )  Cl 2 ( g )  PCl 5( s )
H  137.28 kJ
Joule-Thomson Coefficient
10. For the following three questions, please choose one of the three italicized answers
for each case:
1. For an ideal gas, the Joule-Thomson coefficient (J-T) is negative, zero, positive; and
its temperature always decreases, remains constant, increases during a Joule-Thomson
expansion.
2. For a real gas, if J-T 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 Joule-Thomson inversion temperature
will show a cooling effect, no effect, heating effect below this inversion temperature.
11. A gas obeying the equation of state PV  b  RT undergoes a Joule-Thomson
expansion. Show that as the pressure drops during the Joule-Thomson expansion, the
 U 
 P 
temperature must increase. Hint: 
  T   P .
 V  T
 T V
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 Um and Hm.
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
RT
a
of state P 
.

Vm  b TVm2
Test for Exactness
15. If z is a state function (therefore, dz is an exact differential) and z  f x, y  , then
   z  
    
.
 y  x  y  x
Hint: This is Euler' s test for exactness.
?
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CHEM 341. Fall 2000. Problem Set #3.
PLEASE NOTE
 The work you hand in should be neat and well organized, and it should show the strategy and
steps you used in solving the problems, as well as the bottom-line answers (or solutions). In
grading the problems, both your work-up and your final answers/solutions will be examined
and evaluated.
 The work handed in for grading must carry a pledge that the work is entirely yours and was
done without any collaboration with other persons (except for the course instructor and
TA's). You are encouraged to work with others in doing the exercises and problems found in
the textbook, but all work handed in for grading should be done independently.
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