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Chemistry 2000
Problem Set #5
Answers to Practice Problems
1.
Kinetic studies of the hypothetical reaction shown below are consistent with a one-step
mechanism.
A + B → AB
The activation energy for this hypothetical reaction is 32 kJ/mol. The activation energy for
the reverse reaction (AB→A+B) is 58 kJ/mol.
(a)
Draw a reaction co-ordinate for this reaction assuming that it has only one elementary step.
(b)
Is the forward reaction (A+B→AB) endothermic or exothermic?
Exothermic. (Activation energy for reverse reaction is higher than for forward
reaction.)
(c)
A catalyst is added that reduces the activation energy of the forward reaction to 20 kJ/mol.
What effect, if any, will this have on the activation energy of the reverse reaction?
It will reduce the activation energy for the reverse reaction by the same amount (i.e.
by 12 kJ/mol). The activation energy for the catalysed reverse reaction will
therefore be 46 kJ/mol.
(d)
The rate constant for the forward reaction is 3.61 × 10-3 L mol-1 s -1 at 20 ˚C. Calculate the
rate constant for the forward reaction at 37 ˚C.
Step 1: Gather information and convert to SI units
T1 = 20 ˚C = 293 K
k1 = 3.61 × 10-3 L mol-1 s -1
T2 = 37 ˚C = 310 K
k2 = ???
Ea = 32 kJ/mol = 3.2 × 104 J/mol
R = 8.3145 J mol-1 K-1
Step 2: Identify necessary formula(e)
ln
k1
E
= - a
R
k2
1
1
T1 T2
Step 3: Rearrange and solve for k2
k2
E
- a
=
R
e
k2
=
k1
1
1
T1 T2
k1
Ea
R
e
1
1
T1 T2
k1
=
e
- 0.7203
-3
-1 -1
= 3.61 x 10 L mol s
0.4866
k2
(e)
= 7.42 x 10-3 L mol-1 s-1
Write the rate equation for this hypothetical reaction at 20 ˚C.
rate = 3.61 × 10-3 L mol-1 s-1 [A][B]
(f)
***can do this because it is
an elementary step***
What is the overall order of this reaction?
second order
2.
Consider the following reaction mechanism:
Step 1
NO2Cl(g)
Æ
NO2(g) +
Cl(g)
Step 2
H2O(g) + Cl(g) Æ OH(g) + HCl(g)
Step 3
OH(g) +
NO2(g) + N2(g) Æ HNO3(g) + N2(g)
?
Overall
(a)
Æ
What is the molecularity of each step?
step 1 = unimolecular
step 2 = bimolecular
step 3 = termolecular
(b)
Write the overall equation for the reaction.
NO2Cl(g) + H2O(g) Æ HNO3(g) + HCl(g)
?
(c)
Identify the reaction intermediate(s).
NO2(g), Cl(g) and OH(g)
(d)
Identify catalytic steps, if any, and explain the role of the catalyst.
Step 3 is catalytic. N2 is both a reactant and a product in this step. It is likely that it
acts as a medium to improve the chances of the hydroxyl and nitrogen dioxide
radicals colliding in the correct orientation.
3.
Chlorine reacts with hydrogen sulfide in aqueous solution as follows:
Cl2(aq) +
H2S(aq) Æ
S(s) +
2 H+(aq)
+
2 Cl–(aq)
observed rate = k [Cl2][H2S]
Which, if any, of the mechanisms below are consistent with the observed rate equation?
The first mechanism (i)
Explain your reasoning.
i.
Step 1
Slow
Step 2
Fast
Cl2
HS–
+
H2S Æ
+ Cl+ Æ
HS–
+
H+ + Cl– + Cl+
H+ + Cl– + S
The rate equation for step 1 (slow therefore rate-determining) is:
rate = k1[Cl2][H2S]
This matches the observed kinetics.
ii.
Step 1
Fast equilibrium
Step 2
Slow
H2S '
HS–
+ Cl2 Æ
HS–
H+
+
H+
+ 2 Cl– + S
The rate equation for step 2 (slow therefore rate-determining) is:
rate = k2[Cl2][HS-]
To relate [HS-] to [H2S], use the equilibrium constant expression for step 1 (see
chapter 16).
K1 = [HS-][H+]
[H2S]
Therefore,
Therefore,
[HS-] = K1[H2S]
[H+]
rate = k2[Cl2]K1[H2S] = k[Cl2][H2S]
[H+]
[H+]
This reaction is -1 order with relation to [H+] so it does not match the observed
kinetics.
iii.
Step 1
Fast equilibrium
Step 2
Fast equilibrium
Step 3
Slow
H2S '
H+ + Cl2
Æ
Cl+ + HS–
Æ
HS–
+
H+
H+ + Cl– + Cl+
S
+
H+ + Cl–
The rate equation for step 3 (slow therefore rate-determining) is:
rate = k3[Cl+][HS-]
To relate [HS-] to [H2S], use the equilibrium constant expression for step 1.
K1 = [HS-][H+]
[H2S]
Therefore,
[HS-] = K1[H2S]
[H+]
To relate [Cl+] to [Cl2], use the equilibrium constant expression for step 2.
K2 = [H+][Cl-][Cl+] = [Cl-][Cl+]
[H+][Cl2]
[Cl2]
Therefore,
Therefore,
[Cl+] = K2[Cl2]
[Cl-]
rate = k3K1[H2S]K2[Cl2] = k[H2S][Cl2]
[H+][Cl-]
[H+][Cl-]
This reaction is -1 order with relation to [H+] and -1 order with relation to [Cl-] so it
does not match the observed kinetics.