Independent Study
CHGN 353
Spring 2011
Most, though not all, of the material in this exam is drawn from Chapters 23, 24, 25, 28, and
29 and also assumes a working knowledge of the principles of statistical mechanics introduced
last semester. While you may study together, the problems should reflect only your effort.
If the solutions to these problems are shared, those involved will fail, as will anyone who has
knowledge that sharing is taking place and does not report it to me. The exam is due by
5:00 PM on May 5. I expect it to be neatly done. Clearly separate your answers from your
work. Partial credit will be given if you provide clear and concise comments that will allow
me to follow your calculations.
I reserve the right to add a few additional questions to the exam, but these will serve to get
you started.
GOOD LUCK!
1. Using no more than half a page, summarize the important scientific concepts in Chapter 23 of your text.
0
= 40.656 kJ/mol. Determine an equa2. At the normal boiling point of water, ∆vap Hm
tion for dT /dP of water at the boiling point, assuming the vapor is ideal.
3. What will be the boiling point of water at a pressure of exactly 1 bar?
4. The triple point of CO2 is 5 bar and -57 ◦ C , the critical point is 75 bar and 31 ◦ C ,
and the sublimation temperature at 1 bar is -78 ◦ C . What will be the physical state
of CO2 at (a) 0.5 bar and -70 ◦ C , (b) 25 bar and 25 ◦ C , and (c) 70 bar and 25 ◦ C ?
5. Using the following data prepare a phase diagram for O2 : triple point–54.4 K and
0.0015 bar, boiling point–90.02 K at 1.0133 bar, melting point–54.8 K at 1.0133 bar,
critical point–154.6 K and 50.43 bar, vapor pressure of solid at 54.1 K is 0.0013 bar.
6. Refine the phase diagram of the previous problem knowing that the vapor pressures
of the liquid at 60, 80, 100, 120, 140 K are 0.0071, 0.301, 2.542, 10.216 and 27.865 bar
respectively.
7. At the solid-liquid-vapor triple point, which curve will have the greater slope: (a)
solid-vapor line or liquid vapor line? (b) solid-vapor line or solid-liquid line?
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8. The vapor pressure of n-C5 H12 at 25 ◦ C is 0.674 bar, and that of n-C6 H14 is 0.198 bar.
Calculate the partial pressure of each substance and the total pressure over a solution
containing x(n-C5 H12 ) = 0.25. Assuming that these substances form an ideal solution.
9. You are Maxwell’s demon in a constant volume system of pure water. You are watching
a water molecule as it approaches an ice surface and transforms to the solid phase.
You record the molecule’s kinetic and potential energy. You also note any changes
to the system’s internal energy and entropy through the transformation of the water
molecule. Assuming the water has an initial velocity equal to that of the average
velocity of all the liquid water molecules, discuss how these variable change when the
system temperature is, (a) -10 ◦ C , (b) 0 ◦ C , and (c), 10 ◦ C .
10. Using the following temperature-composition data
T/(◦ C )
78.3
76.6
75.5
73.9
72.8
72.1
71.8
x(CH3 COOCH2 CH3 )liq
0.000
0.050
0.100
0.200
0.300
0.400
0.500
x(CH3 COOCH2 CH3 )vap
0.000
0.102
0.187
0.305
0.389
0.457
0.516
T/(◦ C )
71.8
71.9
72.2
73.0
74.7
76.0
77.1
x(CH3 COOCH2 CH3 )liq
0.540
0.600
0.700
0.800
0.900
0.950
1.000
x(CH3 COOCH2 CH3 )vap
0.540
0.576
0.644
0.726
0.837
0.914
1.000
prepare a liquid-vapor phase diagram for the ethanol-ethyl acetate system at 1 atm. Is
it possible to distill pure ethyl acetate from a mixture containing x(CH3 COOCH2 CH3 )
= 0.25?
11. Using no more than half a page, summarize the important scientific concepts in Chapter 24 of your text.
12. Determine the concentration of CO(g) in water at 25 ◦ C and 0.010 atm given that the
Henry’s law constant for this system is 5.80 x 104 atm.
13. Prepare a partial pressure-composition curve for the NH3 -H2 O system at 70 ◦ F using
the following data:
2
x(NH3 )
0.00
0.05
0.10
0.15
0.20
P (H2 O)/(torr)
18.6
17.6
16.5
15.5
14.5
P (NH3 )/(torr)
0.0
42.9
78.6
134.5
221.3
Given K(NH3 ) = 858 torr, include a plot of Henry’s law for NH3 . Also include a plot
of Raoult’s law for H2 O.
14. Assuming that C6 H6 and C6 H5 CH3 form ideal solutions, calculate ∆G, ∆H, and ∆S
at 25 ◦ C for the addition of 1.00 mol of the C6 H6 to an infinitely large sample of
solution with x(C6 H6 ) = 0.35. The vapor pressure of C6 H6 at 25 ◦ C is 0.153 bar.
15. Using the following data
x(CH3 OH)
0
0.1499
0.1785
0.2107
0.2731
0.3106
P (H2 O)/(torr)
54.7
39.2
38.5
37.2
35.8
34.9
P (CH3 OH)/(torr)
0.0
66.1
75.5
85.2
100.6
108.8
x(CH3 OH)
0.401
0.470
0.558
0.689
0.860
1.000
P (H2 O)/(torr)
32.8
31.5
27.3
20.7
10.1
0.0
P (CH3 OH)/(torr)
127.7
141.6
158.4
186.6
225.2
260.7
calculate the activity coefficient for both components at x(CH3 OH) = 0.2107. Prepare
a plot of the activity coefficients as a function of concentration. Does this system show
positive or negative deviations from ideality?
16. At x(CH3 OH) = 0.1499, a(H2 O) = 0.717, and a(CH3 OH) = 0.254 for the system
described below:
x(CH3 OH)
0
0.1499
0.1785
0.2107
0.2731
0.3106
P (H2 O)/(torr)
54.7
39.2
38.5
37.2
35.8
34.9
P (CH3 OH)/(torr)
0.0
66.1
75.5
85.2
100.6
108.8
x(CH3 OH)
0.401
0.470
0.558
0.689
0.860
1.000
P (H2 O)/(torr)
32.8
31.5
27.3
20.7
10.1
0.0
P (CH3 OH)/(torr)
127.7
141.6
158.4
186.6
225.2
260.7
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If a(H2 O) = 0.704 at x(CH3 OH) = 0.1785, calculate a(CH3 OH).
17. The volume of aqueous NaOH solutions containing 1000.00 g of H2 O for 0 ≤ m/(mol
· kg−1 ) ≤ 2 is given by:
V /(cm3 ) = 1001.56 − 4.35[m/(mol · kg−1 )] + 1.74[m/(mol · kg−1 )]2
Determine the partial molar volume of NaOH in a 1.000 m solution.
18. Using the following data:
The volume of aqueous NaOH solutions containing 1000.00 g of H2 O for 0 ≤ m/(mol
· kg−1 ) ≤ 2 is given by:
V /(cm3 ) = 1001.56 − 4.35[m/(mol · kg−1 )] + 1.74[m/(mol · kg−1 )]2
Determine the partial molar volume of H2 O for m = 1.000 mol · kg−1 .
19. Using no more than half a page, summarize the important scientific concepts in Chapter 26 of your text.
20. The rate law for the equation CH3 NC(g) → CH3 CN(g) is first-order in CH3 NC at high
pressures and is second-order in CH3 NC at low pressures. Write the rate law for each
case.
21. Consider the chemical equation A(g) → nB(g), which is first-order. Derive an equation
for the total pressure of the system as a function of time.
22. Determine the order of reaction for the dimerization equation
2CH3 OC6 H4 CNO(CCl4 ) → products
using the following data:
t/(s)
ξ
0
3600 7200 12900 19500 33900 56520 64800 72720 81480 91080
1.000 0.909 0.833 0.735 0.673 0.527 0.391 0.353 0.334 0.315 0.297
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23. Consider the following proposed mechanism:
k1
*
A−
)
−B
k2
k
3
B+A−
→
C
for the overall chemical equation 2A → C. Write the rate expressions for each species.
Assuming that [B] is essentially constant, rewrite the rate expressions for [A] and [C]
so they do not contain the [B] term. Under what conditions will the reaction appear
first-order to second-order?
24. Consider the following proposed mechanism:
A2 2A (K1 )
A + B C (K2 )
k
A2 + C →
− D+A
for the overall chemical equation A2 +C →
− D. Assuming that the equilibria are rapidly
established in the first two steps, write the rate expression for [D].
25. Using no more than half a page, summarize the important scientific concepts in Chapter 28 of your text.
26. Consider the two following proposed mechanisms for the decomposition of ozone,
2 O3 (g) →
− 3 O2 (g).
Mechanism 1
k
1
O3 −
→
O2 + O·
k
2
O· + O3 −
→
2 O2
Mechanism 2
k
1
O3 −
→
O2 + O·
k
2
O· + O2 −
→
O3
k
3
O· + O3 −
→
2 O2
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Which mechanism predicts a first-order reaction during the early stages of the decomposition?
27. The Lindemann mechanism used to describe the overall chemical equation A →
− products consists of
k2
−
*
2A −
)
−
− A∗ + A
k−2
∗ k1
A −
→ products
where A∗ represents an excited molecule. Assuming the steady-state approximation
for [A∗ ], derive the rate expression for [products]. Under what conditions is this a
pseudo-first-order or a pseudo-second-order reaction?
28. The hydrolysis of fumarate ion to L-malate ion,
−
OOC−CH−CH−COO− (aq) + H2 O(l) →
− − OOC−CHOH−CH2 −COO− (aq)
is catalyzed by the enzyme fumarase. The proposed mechanism is
k1
k2
k−1
k−2
−−
*
−−
*
E+S)
−
−X)
−
−E+P
where E is the enzyme, S is the substrate, X is the enzyme-substrate complex, and P
is the product. The rate expression is
d[P]
dt
=
(VS /KS )[S]−(VP /KP )[P]
1+([S]/KS )+([P]/KP )
where
VS = k2 [E]0
VP = k−1 [E]0
KS = (k−1 + k2 )/k1
KP = (k−1 + k2 )/k−2
and k2 is known as the turnover constant. Describe the kinetics of the initial rate of
this reaction for [S] << KS and [S] >> KS .
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29. The following osmotic pressures were observed for solutions of polyisobutylene in cyclohexane at 25 ◦ C :
C 0 /(g· L−1 )
20.0 15.0 10.0 5.0
Π/(10−3 bar) 16.09 9.92 5.29 2.03
Determine M̄n and the second osmotic virial coefficient for this polymer.
30. Equation 28.57 of your book is known as the Arrhenius equation. Derive this equation
by considering a two state system in which state one is the energy of the reactants
and state two is the energy of the transition state with an energy Ea higher than the
reactants. Justify all of your assumptions. (Think partition function.)
31. Using no more than half a page, summarize the important scientific concepts in Chapter 29 of your text.
32. The vapor pressure of solid iodine is given by
− 2.013 ln(T /K) + 32.908
ln(P/atm) = − 8090.0K
T
Use this equation to calculate the normal sublimation temperature and the molar
enthalpy of sublimation of I2 (s) at 25◦ C . The experimental value of ∆sub H is 62.23
kJ · mol−1 .
33. Consider the ammonia-synthesis reaction, which can be described by
N2 (g) + 3H2 (g) 2NH3 (g)
Suppose initially there are n0 moles of N2 (g) and 3n0 moles of H2 (g) and no NH3 (g).
Derive an expression for KP (T ) in terms of the equilibrium value of the extent of
reaction, ξeq , and the pressure, P . Use this expression to discuss how ξeq /n0 varies
with P and relate your conclusion to Le Châtelier’s principle.
34. Use the statistical thermodynamic formulas of Section 26-8 of your book to calculate
KP (T ) at 900 K, 1000 K, 1100 K, and 1200 K for association of Na(g) to form dimers,
Na2 (g) according to the equation
2 Na(g) Na2 (g)
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Use your result at 1000 K to calculate the fraction of sodium atoms that form dimers
at a total pressure of one bar. The experimental values of KP (T ) are
T /K 900 1000 1100 1200
KP
1.32 0.47 0.21 0.10
Plot lnKP against 1/T to determine the value of ∆r H ◦ .
35. Apply what you know about statistical mechanics and the thermodynamics of phase
stability to explain why the vapor pressure of a gas above the corresponding liquid
or solid depends on the isotopic composition of the substance involved. For example,
given a 50-50 mixture of liquid H2 18 O and H2 16 O the vapor above the liquid will not
be a 50-50 mixture. Explain why this is the case and indicate which of the water
isotopes will be found in the higher composition. Repeat the argument for a mixture
of H2 O and D2 O.
36. Explain why Hg has a higher vapor pressure than Cd at the same temperature.
37. What grade do you believe you have earned in this class?
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