Chemistry 360
Fall 2014
Dr. Jean M. Standard
December 9, 2014
Name ______________________________________
Final Exam – 150 points
Note: You must show your work on problems in order to receive full credit for any answers. You must turn in
your equation sheet along with this exam in order to receive full credit for the exam. Please turn off cell phones
and store them during the exam.
1.) (13 points) Nitrogen tetroxide decomposes according to the reaction
N 2O 4 ( g)
2 NO 2 ( g) .
At 100˚C and 1atm, the average molecular weight of N2O4 and NO2 present at equilibrium is 71.5 g/mol.
Determine the equilibrium constant.
[Note: atomic
€
€ mass N = 14.007 g/mol; atomic mass O = 15.999 g/mol.]
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2.) (13 points) The standard molar enthalpy of formation of Fe2O3 (s) is
molar enthalpy of formation of SO2 (g) is
ΔH !f
ΔH !f
= −675.3 kJ/mol , and the standard
= −322.1 kJ/mol (both at 298 K). Use this information, along
with the standard molar enthalpy change of the following reaction at 298 K,
€
2 FeS 2 (s) +
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2
O 2€(g)
→
Fe 2O 3 (s) + 4 SO 2 (g)
ΔH r! = −1287 kJ/mol,
to determine the standard molar enthalpy of formation of FeS2 (s) at 298 K. [Note: The standard state of iron is
Fe(s) and the standard state of sulfur is S(s) at 298 K.]
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3.) (13 points) Determine the quantities q, w, and ΔU for the following processes involving one mole of an ideal
monatomic gas (argon). Express your results in Joules.
a.) One mole of argon gas at 300ºC and 3.0 bar is expanded reversibly and isothermally to a final pressure of
0.5 bar.
b.) One mole of argon gas at 300ºC and 3.0 bar is expanded isothermally against a constant external pressure
of 0.5 bar.
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4.) (12 points) Sketch a typical phase diagram for a one-component system. Make sure to carefully label all the
appropriate sections and points on the phase diagram. Explain the Gibbs phase rule and the role that it plays in
determining the degrees of freedom for each region or feature of the phase diagram.
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5.) (12 points) The entropy S is a state function that plays a key role in the Second and Third Laws of
Thermodynamics.
a.) A proposed differential form for the state function S in terms of pressure and temperature is given by
#
3&
dS = 2PT 2 dP + % 2P 2T −
( dT .
$
T'
Determine whether or not the differential is exact.
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b.) A researcher in thermodynamics proposed the following form for the temperature and volume dependence
of S for a real gas,
S(T ,V ) = nRT lnV + nRT 2 .
Construct an exact differential for S based on this function.
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6.) (12 points) True/false, short answer, multiple choice.
a.) True or False: The Helmholtz Energy is defined as U − TS .
b.) True or False: The Equipartition Theorem states that each degree of freedom of a gas contributes
3
2
nRT
to the internal energy U of the system.
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c.) Short answer
The ___________________________ is defined to be the pure form of an element at 1 bar and and a
specified temperature.
d.) Short answer
The ___________________________ provides a measure of the progress of a chemical reaction from
reactants to products.
e.) Multiple Choice: Which type of system allows energy but not matter to be exchanged between the system
and surroundings?
1) Open system.
2) Closed system.
3) Isolated system.
CH4 (g) + H2O (g), what is the
f.) Multiple Choice: For the reaction CO (g) + 3 H2 (g)
expected effect if carbon monoxide is removed from the system?
1) The system will shift to the left.
2) There will be no change in the proportion of reactants and products.
3) The system will shift to the right.
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7.) (13 points) The rate constant for the first-order decomposition of SO2 in the reaction
2SO 2
→
2SO + O 2
−3 −1
is 5.24 ×10 s at 25˚C. Determine the half-life of SO2.
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a.) Determine the half-life of SO2 in units of seconds.
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b.) Calculate the total pressure after 100 seconds if the pressure of SO2 is initially 300 torr.
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8.) (12 points) A solution is prepared by dissolving 40.0 g of a solute in 300 g of water at 300 K. The vapor
pressure above the solution is 38.2 torr and the vapor pressure of pure water is 40.5 torr at this temperature.
Determine the molecular weight of the solute.
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9.) (12 points) Sketch a graph of a temperature-composition (T-x) diagram for a binary liquid-vapor system with
two components, A and B, that form an ideal solution. Assume that component A is the more volatile
component. Make sure to label the axes as well as the various phases present in each region. In addition, you
*
*
should label the boiling points of the pure compounds, T A and T B .
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€
a.) Define the bubble point and dew point lines and label them on the graph.
b.) For a certain temperature T between the two pure boiling points, the liquid phase mole fractions are found
to be x A = 0.3 and x B = 0.7 . Discuss whether or not the vapor phase mole fractions are larger or smaller
than the liquid phase mole fractions. That is, is the vapor phase enriched or depleted in component A?
And what about for component B? [Note that you will not be able to determine specific numerical values
for y A and y B in this case.]
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10.) (13 points) The proposed mechanism for a certain chemical reaction is given by
k
step 1 :
A
""1 →
←"
"
k
B +
X
2
step 2 :
X + C
k
""3 →
D.
a.) What is the overall balanced reaction?
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b.) Using the steady state approximation for any intermediates present, develop an expression for the rate
equation for species A. Make sure that the expression you obtain is simplified using common
denominators where appropriate.
c.) If step 1 in the proposed mechanism is the rate-determining step, determine how the rate equation from part
(b) simplifies. What is the order of the reaction with respect to A in this case?
11
–3
–1
11.) (13 points) The first-order rate constant for the decomposition of formaldehyde is 2.51×10 s at 25ºC and
6.55×10–3 s–1 at 50ºC. Determine the activation energy and pre-exponential factor.
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12.) (12 points) True/false, short answer, multiple choice.
a.) True or False: Benzene and toluene would be expected to form an ideal solution (or a nearly ideal
solution).
b.) True or False: One mole of NaCl is expected to be twice as effective in lowering the freezing point of
water as one mole of sugar.
c.) Short answer
The __________________________________ is the point at which both components freeze out
simultaneously from the liquid phase as the temperature is lowered in a binary system.
d.) Short answer
The _________________________________
chemical reaction.
gives the concentration dependence of the rate of a
e.) Multiple Choice: Starting from an initial concentration of 1.0 M for a certain zero-order reaction, it takes
5.0 minutes for the concentration to be reduced to 0.5 M. Based on this information, how much additional
time will it take for the concentration to be further reduced to 0.25 M?
1) 10 minutes
2) 5 minutes
3) 2.5 minutes
f.) Multiple Choice: For a second-order reaction, what is the correct graph that would yield a linear
relationship?
1) concentration (y-axis) versus time (x-axis)
2) inverse of concentration (y-axis) versus time (x-axis)
3) natural log of concentration (y-axis) versus time (x-axis)
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CHE 360 PHYSICAL CONSTANTS AND EQUATIONS
R = 0.08206 L atm mol–1 K–1 = 8.314 J mol–1 K–1 = 0.08314 L bar mol–1 K–1
1 atm = 101325 Pa = 1.013 bar = 760 torr
1 bar = 105 Pa = 0.98692 atm
1 L atm = 101.3 J; 1 L bar = 100 J
1 cal = 4.184 J
Fundamental Equations
dU = T dS − P dV
dH = T dS + V dP
dA = − S dT − P dV
dG = − S dT + V dP
Maxwell€Relations
#∂ T &
#∂ P &
%
( = −%
(
$ ∂ V 'S
$ ∂ S 'V
#∂ T &
#∂ V &
%
( = %
(
$ ∂ P 'S
$ ∂ S 'P
#∂ S &
#∂ P &
%
( = %
(
$ ∂ V 'T
$ ∂ T 'V
#∂ S &
#∂ V &
%
( = −%
(
$ ∂ P 'T
$ ∂ T 'P
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