CHEM 107 MIDTERM TEST PAPERS
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CHEM 107 MIDTERM TEST PAPERS
Instructions:
• This is a CLOSED BOOK EXAM.
• DO NOT OPEN the exam until instructed to do so.
• Useful equations and constants are provided on the last page.
�
...
� All work must be shown and print clearly for credit.
• Place a box around your final answer.
This Exam has 6 questions and total of 8 pages. Make sure that you have all pages. See the last page for a list of equations.
Place a check in this box if you would like your exam kept confidential and do NOT want your exam returned during class.
1 10
2 10
3 20
4 20
5 20
6 20
Total 100
Problem 1
MARK the following statements, a – j as TRUE or FALSE. You might find it useful to consult the information on page 8 for some of the statements. Only ONE answer will be graded (1 point each).
a) For a sequential mechanism A
k1 10 min1
I k2 1 min1
P , the
time for I to reach its maximum value is 15.35 seconds.
b) For a pre-equilibrium mechanism (A k1
k1
B k2 C ), k1
is equal
to k-1.
c) For a reaction
A k P
with k = 1.00 s-1 and H‡ = 70.0 kJ/mol at
298 K, S‡ must be equal to -10.0 J K-1 mol-1.
d) S‡ of the solvent is negative when two reactants of the same charge in aqueous solution form a charged transition state.
e) The Michaelis constant (KM) for an enzyme is equal to the substrate dissociation constant when k2 >> k-1.
f) An enzyme with kcat/Km = 108 M-1 s-1 and Vmax = 0.10 M/s will catalyze the formation of 1.0 millimole of product per liter in 10-2 seconds when KM is much greater than the substrate concentration.
g) The mean free path of an ideal gas molecule increases when the pressure increases at constant temperature.
h) The integrated rate law for A
k1
1
can be written as
[P](t) [ A]0 [ A]eq 1 ek1 k1 t .
i) The reaction S O 2-(aq) + I-(aq) ½ I + 2SO 2- will occur at a slower
2 8 2 4
rate when the ionic strength is increased.
j) For the elementary reaction A B
1 1
C , if [A]0
= [B]0 =
0.10 M and [C]0 = 0, the concentration of C formed in 1.0 second is
0.023 M.
Problem 2 (1 point each = 10 points total)
Match each concept in the left column with the best statement of that concept in equation or symbol form, from the right column.
Note: You may need to use some equations more than once and others not at all. Write only one number of the equation in the provided blank space.
2 m
3
2
mc 2
2k B T
(a) Catalytic efficiency
1) f (c) 4c
2k
e
BT
(b) Half-life
2) d 2
1 / 2
Z1t
(c) Kinetic theory of gases
3) k Ae Ea / RT
(d) Maxwell distribution
(e) Eadie-Hofstee plot
4)
RT
2d 2 PN A
(f) Mean free path
5) k 8RT
3
(g) Root mean square displacement
6) kd
ka
Keq
(h) Arrhenius equation
(i) Kinetic salt effect
7) A d 2
8) t1 / 2 1
(j) Diffusion limited rate constant
[A] ]n 1
9) v0 Vmax v0 KM
[S ]
10)
11)
log
k2
k z AzB
k0
k1k2
KM k1 k2
12)
1 / 2
d
Z1t
13)
t1 / 2
1
k1 k1
Nm v 2
14) P
15)
3V
Z11
Problem 3
(a) Consider the reaction mechanism, A k1
k1
B k2 C
[A] = [A]0 at t = 0 and [B]0 = [C]0 = 0. 1 k1 k1
Show all work.
(i) Write an expression for
d[B]
dt
in terms of [A], [B], k1, k-1 and k2 (2 pts):
(ii) Assuming a fast pre-equilibrium ( k1[A] k1[B] k2[B]), write an expression for [B](t > ) in terms of [B]eq, k2 and t (hint: [B]()=[B]eq, [A]() = [A]eq and [C]() = 0; integrate d[B]/dt from to final t) (4 pts):
2 pts
(iii) Assuming a fast pre-equilibrium ( k1[A] k1[B] k2[B]), write an expression for the overall rate law ( d[C] ) in terms of [A], k1, k-1, and k2 (4 pts):
dt
2 pts
(b) Consider the following reversible elementary reaction:
A + B
k1
1
(i) If [A]0 = [B]0 and [P]0 = 0, write d[A]/dt in terms of k1, k-1, [A] and [A]0. (5 pts)
(ii) If [B]0 >> [A]0, write the relaxation time () in terms of [B]0, k1 and k-1. (hint: [P]0 = 0 and is also called pseudo-first order 1/e time) (5 pts)
Problem 4
Reactant A reacts with H2O according to the following kinetic scheme:
A H 2
k1
k1
Keq
[P]
[ A][H 2O]
k1 k1
10.0 M 1
When [A] << [H2O], a pseudo first order relaxation time (
1
(k1[H 2O] k1 )
) was
measured to be 20.0 s with an equilibrium constant (Keq = k1/k-1) equal to 10.0 M-1 at 298
K. The pseudo first order rate constant, k’1 = k1[H2O] and [H2O] = 55.5 M. The activation energy of the forward reaction is equal to 90.0 kJ/mol and Hº = -10.0 kJ/mol.
(a) Calculate the value of k1 and k-1 at 298 K and include proper units (8 pts).
4 pts each for k1 and k-1
.
(b) If [A]0 = 1.00 M and [P]0 = 0, first calculate [A]eq (at equilibrium) and then calculate the concentration of A ([A](t)) at time (t) equal to 10.0 seconds (4 pts).
(c) What is k1, k-1 and Keq at 310 K (8 pts)?
3pts each for k1 and Keq, and 2 pts for k-1
Problem 5
The following data were collected for the reaction below at 700 C:
2H (g) + 2NO(g) 2H O(g) + N (g)
2 2 2
Show all work, use proper significant figures and state any assumptions.
(a) What is the rate law for the reaction? (4 pts)
(b) Calculate the rate constant for the reaction. (4 pts)
k rate
[NO]2[H 2 ]
2.4 106 M / s
(0.025)2 (0.01)
1 pt each for setup, correct number, sig fig, and units
(c) Suggest a plausible mechanism that is consistent with this rate law. (hint: Assume that the oxygen atom is the intermediate) (6pts)
(d) More careful studies show that the rate law should be rate
What happens to the rate law at very high and very low H2 concentrations. (6 pts) 3pts each for rate law at high and low H2
At high H2 concentrations, k2[H2] >> 1 (1 pt). Therefore the rate law becomes:
2 pts for correct rate law
At low H2 concentrations, k2[H2] << 1 (1 pt). Therefore the rate law becomes:
rate
2 pts for correct rate law
Problem 6
Answer questions about the mechanism:
A k1 B k2 C
k1 = 0.10 s-1 and k2 = 1.0 x 102 s-1 at 298 K
[A]0 = 0.10 M and [B]0 = [C]0 = 0.0 M; [ A](t) [ A]0 ek1t
Show all work, use proper significant figures and include proper units.
a. Write a differential equation that calculates the change in concentration of B with respect to time ( d[B] ) (2 pts)
dt
1 pt for each term
b. Write an equation to calculate the concentration of B as a function of time ([B](t)) in terms of [A]0, k1, k2, and t, and assuming a steady-state ( d[B] 0 ). (4 pts)
dt
c. Write an equation to calculate the concentration of C as a function of time ([C](t))
in terms of [A]0, k1, k2, and t, and assuming a steady-state ( d[B] 0 ). (5 pts)
dt
2pts
d. Calculate the steady-state concentration of A, B and C at a time (t) equal to 5.0 seconds (9 pts)
3pts each for correct numbers for A, B and C
[ A](t) [ A]0 e k1t
(0.1 M )e(10 1 s 1 )(5 s)
1.5 pts setup and 0.5 pts each
for number, sig
fig , and units
[B](t)
k1 [ A]0
k2
e k1t
0.1 (0.1)e(10 1 s 1 )(5 s)
102
1.5 pts setup and 0.5 pts each
for number, sig
fig , and units
[C](t) [ A] (1 e k1t ) (0.1)(1 e(10 1 s 1 )(5 s) )
1.5 pts setup and 0.5 pts each
for number, sig
fig , and units
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