Physical Chemistry I
Homework Set #8
-
1. The rate law for the Br - catalyzed reaction
Br −
+
H + HNO2 + C6H5NH2 → C6H5N2+ + H2O
is observed to be R = k ⎡⎣ H + ⎤⎦ ⎡⎣ HNO 2 ⎤⎦ ⎡⎣ Br − ⎤⎦ .
A proposed mechanism is
(1)
k1
+
H + HNO2 ! H2NO2+
(fast equilibrium)
k−1
-
k2
(2)
H2NO2+ + Br → ONBr + H2O
(3)
ONBr + C6H5NH2 → C6H5N2+ + H2O + Br
k3
(slow)
-
(fast)
Apply steady-state approximation to the intermediates H2NO2+ and ONBr and determine the
rate law and compare with that observed experimentally. Under what conditions would
agreement with experiment be found?
2. The electrochemical reaction Hg 2 (g) + 2 Cl- (g) ! Hg 2Cl2 (s) + 2 e- has been observed to
follow the experimental rate law
d ⎡⎣ Hg 2Cl2 ⎤⎦
dt
2
= k ⎡⎣Cl− ⎤⎦ ⎡⎣ Hg 2 ⎤⎦
a. If the reactants are initially present in their stoichiometric amounts, i.e., ⎡⎣Cl− ⎤⎦ = 2 ⎡⎣ Hg 2 ⎤⎦0
0
derive the integrated rate expression.
b. If the reactants are present initially in equal concentrations derive the integrated form of
the rate expression.
*HINT: Reduce the differential form of the rate expression to a single variable by finding a
functional relationship between ⎡⎣Cl- ⎤⎦ and ⎡⎣ Hg 2 ⎤⎦t for all t.
t
3. The following data were reported for the proton transfer reaction
NO2C6H4CH2CN + C2H5O- → NO2C6H4CHCN- + C2H5OH
T (K)
k (liters mol-1 sec-1)
173
3.4 x 101
183
1.5 x 102
193
5.0 x 102
203
1.8 x 103
Calculate A and EA for this reaction. (*ref: W. C. Gardiner, Jr., Rates and Mechanisms of
Chemical Reactions, W. A. Benjamin, 1972.)
4. The decomposition of acetaldehyde into methane and carbon monoxide
CH3CHO(g) → CH4(g) + CO(g)
is a second order reaction: −
d [CH 3CHO]
2
= k [CH 3CHO]
dt
whose rate constant is 0.19 M-1 sec-1 at 791 K. Find t1/2 at constant volume, an initial
pressure of 1 atm and constant temperature of 791 K. (*ref: G. G. Hammes Principles of
Chemical Kinetics, Academic Press, 1966.)
*Hint: Express the rate equation in terms of total pressure and integrate.