Department
of Chemistry Name________________________________
CH 431 Mid-term
I
Given: R = 8.314 J mol-1
K-1 = 0.08206 L atm mol-1 K-1
a.m.u. = 1.672 x 10-27
kg
1 atm = 1.0133 x 105
Nm-2 = 760 Torr
P = P0exp{-Mgh/RT}
Please answer all
questions. Please sign each page. The honor pledge states:
“This
is my work. I have not used information
from other students or any notes during theis exam period”. Please sign the bottom of each page of the
exam.
1. A.
The Haber process 3H2 + N2 à 2NH3 occurs with an iron
catalyst at 500 K and 1000 atm of pressure.
Assuming the reaction proceeds entirely to form NH3 what is
the density of ammonia under these conditions.
r(gL-1)
= ___________________ (10 points).
B. Assuming
that NH3 is a hard sphere gas at P = 1000 atm and T = 500 K,
calculate the density using a hard sphere gas model. A hard sphere gas is a van
der Waal’s gas with a = 0. The excluded
volume parameter is b = 0.037 L/mole.
r(gL-1)
= ___________________ (10 points).
Honor
Pledge__________________
C. Calculate
the maximum possible density according to a hard sphere gas model. This is the density at infinite pressure or
at the minimum possible value of the molar volume.
Maximum density = _____________________ (10 points).
2. A.
Determine the average velocity of N2 gas molecules at 300 K in a
closed container with a volume of 15 L.
Assume that you can treat N2 as an ideal gas.
Average
velocity = ____________________ (15 points).
B.
If we assume that the molar volume is 30 L/mole calculate the average pressure
of N2 molecules.
Average
pressure = ______________________ (10 points).
C.
What is the total kinetic energy of the system of N2 molecules in
the 15 L volume?
Total
kinetic energy = _____________________ (5 points).
Honor
Pledge__________________
3. A.
The diameter of Mars is 6800 km. The
total mass of the Martian atmosphere is 3.97 x 1017 kg. The acceleration of gravity on Mars is gM
» 3.7 m/s2. The Martian atmosphere is mostly CO2. Using the available data calculate the
pressure of the Martian atmosphere at the surface of the planet Mars.
Pressure
at the surface of Mars = ________________________ (15 points).
B.
Calculate the pressure of the Martian atmosphere at an elevation of 1000 m
above the surface of the planet. Assume
a temperature of 50 K.
Pressure
1000 m above the surface of Mars = ____________________(15 points).
Honor
Pledge ______________________
4. Treating
NH3 as an ideal gas that is initially at 1000 atm and 500 K
following the Haber process calculate the work done for its expansion under the
following conditions. Its volume is
initially 500 L and the gas expands to 10,000 L under the following conditions:
(1.)Pexternal
= 0
(2.)Pexternal
= 1 atm
(3.)Pexternal
= Pgas (reversible expansion)
For each of the above conditions calculate DU
and w for the gas (30 points).
DU(J) w(J)
(1.)
__________
____________
(2.) __________
____________
(3.) __________ ____________
Honor
Pledge__________________
5. A
molecule has the two level energy diagram shown below.
A. Based
on the energy levels shown in the Figure, write an expression for the molecular
partition function assuming that the particle is fixed in space (i.e. it cannot
translate, rotate etc.). (5 points)
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). (5 points)
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).
(5 points)
Honor
Pledge__________________
D. Calculate
the average energy of a system of N particles (include both translation and the
energy levels shown in the Figure). Express your answer in terms of e
and b or kT. (15 points)
E. Calculate
the heat capacity for the system as a function of temperature. (15 points)
F. Derive
an equation for the pressure of the system consistent with above assumptions.
(10
points)
Honor
Pledge__________________
6. The
work done by an isothermal expansion is said to be reversible. To see what this means we will compare a
reversible and an irreversible process.
Two 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 and are then recompressed along two different paths.
The first is one isothermal and the second one constant pressure. For each expansion the final volume is 10
L.
A. Calculate
the work of isothermal expansion and the work of compression from 1 L to 10 L
and back.
Isothermal
expansion w = _____________________ (5 points)
Isothermal
compression w = _____________________ (5 points)
B. Calculate
the work of a constant pressure expansion from 1 L to 10 L. Then calculate the
work for compression back to 1 L at constant pressure.
Constant
pressure expansion w = _____________________ (5 points)
Constant
pressure compression w = _____________________ (5 points)
C. How
does the work along a reversible and irreversible path compare? Is work a state function? (5 points)
Honor
Pledge__________________