Name:________________________________
PRINT family name first
Student Number:________________________
UNIVERSITY OF VICTORIA
EXAMINATIONS DECEMBER 2006
Chemistry 245 Introductory Physical Chemistry
Duration: 3 hours
Instructor: M. G. Moffitt
Print your name and student number in the spaces above. In addition, print and code in your name and
student number on the answer sheet provided.
This exam consists of a total of 16 pages (including cover sheet and one blank page). Students must
count the pages in this examination paper before beginning to write and report any discrepancy to the
invigilator. Part A (Multiple Choice) must be answered on the answer sheet provided, in pencil. Parts B
and C must be answered on the examination paper in the space provided. Indicate if you want the back
of any pages to be marked. Do NOT use your own scratch paper.
Calculators without continuous memories may be used. You may use a ruler.
Do not remove any pages from this exam. Hand back all pages of the exam plus the answer sheet.
Maximum score = 144 points.
Useful Constants:
R (gas constant) = 8.314 J K-1 mol-1 = 0.08314 L bar K-1 mol-1 = 0.08206 L atm K-1 mol-1
kB (Boltzmann constant) = 1.381 x 10-23 J K-1
NA (Avogadro constant) = 6.022 x 1023 mol-1
1 atm = 1.01325 bar = 760 Torr = 101.325 kPa
1 L atm = 101.325 J
1 L bar = 100 J
0°C = 273.15 K
N = 14.01 g mol-1
C = 12.01 g mol-1
O = 16.00 g mol-1
Atomic Masses:
Van der Waals Equation of State:
p=
nRT
⎛n⎞
− a⎜ ⎟
V − nb
⎝V ⎠
2
Clausius-Clapeyron:
⎛ p ⎞ Δvap H
ln⎜⎜ 2 ⎟⎟ =
R
⎝ p1 ⎠
⎡1 1 ⎤
⎢ − ⎥
⎣ T1 T2 ⎦
H = 1.008 g mol-1
He = 4.003 g mol-1
Ar = 39.95 g mol-1
Part A (Multiple Choice)
Mark
/ 48
Part B (Numerical Answer)
Mark
/ 24
Part C (Problems)
Question 19
Mark
/ 21
Question 20
Mark
/ 15
Question 21
Mark
/ 24
Question 22
Mark
/ 12
____________________________
TOTAL
/ 144
%=
Chemistry 245 page 2
Part A: Multiple Choice. For each question, fill in the correct answer on the answer sheet in
pencil, as instructed on the answer sheet.
1. (4 points)
The expression ΔG = ΔH-TΔS
a. can be used to prove that the isothermal expansion of an ideal gas is spontaneous.
b. can be used to determine the direction of a chemical reaction.
c. only applies to constant pressure processes, since q = ΔH only at constant pressure.
d. applies to the adiabatic compression of an ideal gas.
e. does not apply to a phase change since the absolute entropies of the two phases are different.
2. (4 points)
The combustion of propane in a constant-pressure calorimeter results in a measured increase in the
temperature of the calorimeter:
CH3CH2CH3(g) + 5O2(g) → 3CO2(g) + 4H2O(l)
Which of the following statements applies to the chemical reaction under these conditions?
I. The chemical reaction cannot be treated as an isothermal process since heat is released.
II. The heat is equal to the change in the internal energy of the system.
III. The enthalpy change is less than the internal energy change since work is positive.
IV. The entropy of the system decreases if the gases are assumed to be ideal.
V. The total entropy of the universe must remain constant since the calorimeter is adiabatic.
a. I, III & IV
b. II, IV & V
c. III & IV
d. I & V
e. V only
Chemistry 245 page 3
3. (4 points)
Which of the following hypothetical processes would NOT be in conflict with the First Law of
thermodynamics?
a. The internal energy of an isolated system increases as a result of a reversible process.
b. The internal energy of an isolated system decreases as a result of an irreversible process.
c. A cyclic adiabatic process does a net amount of work on the surroundings.
d. A cyclic isothermal process does a net amount of work on the surroundings while generating a
net amount of heat.
e. A cyclic process converts heat from the surroundings into work with 100% efficiency.
4. (4 points)
2.00 moles of compound A (solid) undergo a chemical reaction to form 1.00 mole of compound B
(solid) and 1.00 mole of compound C (solid): 2A(s) → B(s) + C(s). The reaction is carried out at
constant pressure and at two different temperatures: T = 25°C and T = 120°C. The constant-pressure heat
capacities of the various chemical species (assumed to be independent of temperature) are as follows:
Cp(A) = 36.23 J K-1 mol-1, Cp(B) = 23.09 J K-1 mol-1, and Cp(C) = 39.13 J K-1 mol-1. Based only on this
information, which of the following conclusions can be made about the reaction carried out at the two
temperatures?
a. The reaction at both temperatures will be exothermic, and ΔrH(120°C) - ΔrH(25°C) = -973 J.
b. The reaction at both temperatures will be endothermic, and ΔrH(120°C) - ΔrH(25°C) = -973 J.
c. The reaction at both temperatures will be exothermic, but ΔrH(120°C) - ΔrH(25°C) cannot be
determined.
d. The reaction at both temperatures will be endothermic, but ΔrH(120°C) - ΔrH(25°C) cannot be
determined.
e. ΔrH(120°C) - ΔrH(25°C) = -973 J, but whether the reaction is endothermic or exothermic at the
two temperatures cannot be determined.
Chemistry 245 page 4
5. (4 points)
1 kg of liquid water at 100°C is confined under a moveable piston exerting a pressure of 5.00 atm in a
closed, temperature-variable container, such that no air space exists between the piston and the liquid. A
window in the container allows changes to be observed as the pressure and temperature are varied. From
the initial state, the pressure is first decreased at constant temperature until liquid water and vapour are
observed to coexist within the container. Then, the pressure and temperature are simultaneously lowered
to maintain coexistence between liquid and vapour, until a single definite pressure and temperature is
reached at which solid, liquid, and vapour are found to coexist. From this pressure and temperature, the
temperature inside the container is finally cooled by 0.01 K while maintaining constant pressure. What
is observed in the container at the end of this process?
a. solid only
b. liquid only
c. liquid and vapour
d. solid and vapour
e. solid, liquid, and vapour
6. (4 points)
For the derivation of boiling point elevation, which of the following statements does NOT apply?
a. The chemical potentials of solvent liquid and solvent vapour are equal at the solution boiling
point.
b. The chemical potentials of solvent liquid and solvent vapour are lowered by the addition of solute.
c. The solute is assumed to be non-volatile.
d. The enthalpy of vaporization of the solvent is assumed to be independent of temperature.
e. The change in the boiling point depends on the boiling point of the pure solvent.
Chemistry 245 page 5
7. (4 points)
For a solution of two volatile liquids (A and B) with composition xA = 0.40, the measured vapour
pressure is found to be significantly lower than that predicted by Raoult’s law. Based on this
information, which of the following conclusions about this A/B system is/are correct?
I. The partial pressure of A will be described by pA = xApA* at all compositions.
II. The chemical potential of A will be described by μA = μA* + RTlnxA at all compositions.
III. The partial pressure of A will be described by pA = xApA* as A becomes dilute.
IV. The partial pressure of B will be described by pB = KBpB* as B becomes dilute.
V. The activity coefficient of A will have a value greater than 1 at the composition xA = 0.40.
a. I & II
b. III & IV
c. III, IV, & V
d. IV only
e. II only
8. (4 points)
The Gibbs phase rule
a. holds only for systems with more than one component.
b. predicts that a maximum of three phases can coexist in a one-component system.
c. predicts that a two-component, three-phase system will have two degrees of freedom.
d. does not count phase compositions as intensive variables.
e. does not count pressure and temperature as intensive variables.
Chemistry 245 page 6
9. (4 points)
Considering the liquid-vapour phase diagram shown below, which of the following best describes the
distillation of a liquid mixture of acetone/chloroform with an initial liquid composition of
xchloroform = 0.40?
a. The initial liquid mixture boils to produce a vapour that is richer in acetone than the liquid. As
the vapour is continuously removed, the boiling point of the remaining liquid increases until it
forms an azeotrope.
b. The initial liquid mixture boils to produce a vapour that is richer in chloroform than the liquid.
As the vapour is continuously removed, the boiling point of the remaining liquid decreases until
it forms an azeotrope.
c. The initial liquid boils to produce a vapour that is richer in acetone than the liquid. The vapour is
successively condensed and boiled in a fractionating column until an azeotropic vapour emerges
from the top of the column.
d. The initial liquid boils to produce a vapour that is richer in chloroform than the liquid. The
vapour is successively condensed and boiled in a fractionating column until an azeotropic vapour
emerges from the top of the column.
e. The initial mixture is a high-boiling azeotrope which forms a vapour that emerges as pure
chloroform from the top of a fractionating column and leaves behind a residue of pure acetone.
Chemistry 245 page 7
10. (4 points)
Which of the following best describes the cooling curve (T vs. time) for a two-component liquid solution
at the eutectic composition?
a. The liquid cools at a constant rate until the first appearance of solid is indicated by a change in
slope and continued cooling at a decreased rate.
b. The liquid cools at a constant rate until the first appearance of solid is indicated by a change in
slope and continued cooling at an increased rate.
c. The liquid cools at a constant rate until the first appearance of solid is indicated by a constanttemperature plateau.
d. The liquid cools at a constant rate until the first appearance of solid is indicated by a sudden drop
in temperature (i.e. the slope of the cooling curve becomes infinite).
e. The liquid cools at a constant rate with no detectable change in the slope when the solid first
appears.
11. (4 points)
The reaction A → Products is experimentally found to be zero-order in A. If the concentration, [A], is
monitored over time, t, for this reaction, which of the following plots is expected to be linear?
a.
b.
1
vs. t
[A]
1
[A]2
vs. t
⎛ [A ] ⎞
⎟⎟ vs. t
c. ln⎜⎜
⎝ [A 0 ] ⎠
⎛ 2 ⎞
d. ln⎜⎜
⎟⎟ vs. t
⎝ [A ] ⎠
e.
[A] vs. t
Chemistry 245 page 8
12. (4 points)
The Michaelis-Menten equation for the rate of enzyme-catalyzed product formation is v =
k b [E ]0 [S]
.
[S] + K M
Which of the following statements concerning the derivation of this equation is/are correct?
I. The free enzyme is an intermediate within the mechanism.
II. The mechanism contains a first-order step in which the enzyme-substrate complex decomposes.
III. The mechanism contains a second-order step in which the product binds to the free enzyme,
forming an enzyme-product complex.
IV. The enzyme concentration, [E]0, includes both free enzyme and enzyme-substrate complex.
V. The Michaelis constant, KM, is equal to the steady-state concentration of enzyme-substrate
complex, [ES].
a. II & IV
b. I & III
c. II, III, & IV
d. II, IV, & V
e. I only
Chemistry 245 page 9
Part B: Numerical Answer. Print your answers, with units indicated and the proper significant
figures, in the boxes provided. Only your answer will be marked.
13. (4 points)
Calculate the pressure (in bar) of 0.230 mole of Cl2 gas in a 4.00 L container at 10.0°C, using van der
Waals constants, a = 6.58 bar L2 mol-2 and b = 0.0562 L mol-1.
p =
bar (4 points)
14. (4 points)
A 2.00 kg iron block at 300.0ºC is placed in contact with a 1.00 kg iron block at 200.0ºC. The specific
heat capacity of iron is 0.450 J K-1 g-1 (independent of temperature). Assuming that no heat is lost to the
surroundings, calculate the equilibrium temperature (in ºC) of the blocks.
T =
ºC (4 points)
Chemistry 245 page 10
15. (4 points)
The partial molar volumes of ethanol and water in a solution with mole fraction xethanol = 0.20 are
Vethanol = 55.2 ml mol-1 and Vwater = 17.8 ml mol-1, respectively. Calculate the volume (in ml) of a
water/ethanol solution with composition xethanol = 0.20 containing 20.0 g water.
V =
ml (4 points)
16. (4 points)
Calculate ΔrG° (in kJ mol-1) at T = 298 K for the combustion of methane:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(l).
Use the following thermodynamic data at this temperature: ΔfH°[CH4(g)] = -74.81 kJ mol-1,
ΔfH°[O2(g)] = 0 kJ mol-1, ΔfH°[CO2(g)] = -393.51 kJ mol-1, ΔfH°[H2O(l)] = -285.83 kJ mol-1, and
ΔrS° = -242.98 J K-1 mol-1.
ΔrG° =
kJ mol-1 (4 points)
Chemistry 245 page 11
17. (4 points)
When 0.978 g of glucose (C6H12O6) is dissolved in 10.0 g ethanol, the solution boils at 79.07°C. Given
that the boiling point of pure ethanol is 78.40°C, calculate the ebullioscopic constant, Kb, of ethanol.
Kb =
K kg mol-1 (4 points)
18. (4 points)
For the second-order reaction A → Products, an initial concentration of reactant [A]0 = 2.00 mol L-1 is
found to decay to one-half its value, [A] = 1.00 mol L-1, in 42.5 min. Calculate the rate constant of the
reaction.
k =
L mol-1 min-1 (4 points)
Chemistry 245 page 12
Part C: Problems. Show all your work.
19. (21 points)
0.320 mole of a linear ideal gas (CV = 5/2 R) is expanded adiabatically and irreversibly from
p1 = 2.00 atm and T1 = 298.0 K by a sudden decrease in pressure to p2 = 1.00 atm, such that cooling to
T2 = 255.4 K occurs upon expansion. Calculate ΔV, ΔU, ΔH, ΔS and w. Print your answers in the boxes
provided.
ΔV =
L (3 points)
ΔU =
J
(3 points)
ΔH =
J
(3 points)
w=
J
(3 points)
ΔS =
J K-1
(9 points)
Chemistry 245 page 13
20. (15 points)
The van’t Hoff equation for the osmotic pressure of a dilute solution of solute B in solvent A is:
π = RT [B] .
Sketch a diagram indicating the conditions on both sides of a semipermeable membrane used to measure
osmotic pressure. Then, starting with a description of the equilibrium condition across the membrane,
derive this equation, stating all of your assumptions. Print your derivation in a step-wise and organized
manner, using the back of this page if necessary.
Chemistry 245 page 14
21. (24 points)
The solid-liquid phase diagram for
the water (H2O)-sulfuric acid
(H2SO4) system is shown, where
xB indicates mole fraction of
H2SO4. Considering this phase
diagram, answer the following
questions in the space provided.
(a)
How
many
hydrated
compounds of sulfuric acid, with
general formula H2SO4⋅nH2O,
form in the solid state? Identify
the mole fraction composition and
write the molecular formula (i.e.
specify n) for each compound
(3 points):
(b) What is the melting point (in
°C) of each of the compounds
identified in (a)? Describe quantitatively what happens as each of these compounds melts (6 points):
(c) Consider the vertical line a-e, which describes the cooling of a liquid mixture of overall composition
xB = 0.60. At each of the specified points (a, b, c, d & e), state the composition and nature all phases
present, the relative amounts of each phase, and the number of degrees of freedom (use the back of this
page if necessary) (15 points):
Chemistry 245 page 15
22. (12 points)
Consider the reaction of methane with chlorine gas:
CH4(g) + Cl2(g) → CH3Cl(g) + HCl(g)
Experimental studies indicate the following rate law for HCl(g) formation: d[HCl]/dt = k[CH4][Cl2]1/2.
The following mechanism has been proposed to explain the observed rate law:
i) Cl2 → Cl⋅ + Cl⋅
ii) Cl⋅ + Cl⋅ → Cl2
rate constant = ka
rate constant = ka´
iii) Cl⋅ + CH4 → HCl + CH3⋅
rate constant = kb
iv) CH3⋅ + Cl2 → CH3Cl + Cl⋅
rate constant = kc
Applying the steady-state approximation to any intermediates, show that this mechanism is consistent
with the experimental rate law, and write an expression for the observed rate constant k based on the
mechanism.
END OF EXAM.
Chemistry 245 page 16