Physical Chemistry Third Edition

582 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics

Find the rate law for the oxidation of CO. Use the

steady-state approximation, assuming that the rates of

change ofθCO,θO 2 , andθOare negligible. Assume that

1 −θCO−θO 2 −θO≈ 1 −θCO

and neglectk′ 2 compared withk 3 (1−θCO)θO 2.

13.8 The gas-phase thermal decomposition of acetaldehyde is

catalyzed by I 2. The proposed mechanism is^17

(1) CH 3 CHO+I 2 
CH 3 I+HI+CO

(2) CH 3 I+HI−→CH 4 +I 2

a. Find the rate law, using the steady-state

approximation.

b. Find the rate law, assuming that the back reaction in

step 1 is negligible.

c.Find the rate law, assuming that the second step is

rate-limiting.

d.How would you decide which assumption is

preferable?

13.9 For a homogeneously catalyzed reaction

A+B+C→F+C

where C is the catalyst, assume that the forward rate law is

d[F]

dt

k[A][B][C]

Integrate this rate law, assuming that [C] remains

constant.

13.10Obtain the rate law for the Michaelis–Menten mechanism

of Eq. (13.1-40), assuming the second step to be

rate-limiting instead of assuming the steady-state

approximation.

13.11 a.Add the reverse reaction to the second step of the
Michaelis–Menten mechanism of Eq. (13.1-40) and
obtain the rate law.
b.Take the limit of the rate expression as the
concentration of product approaches zero.
c.Take the limit of the rate expression as the
concentration of reactant approaches zero.
d.Write an expression for the equilibrium constant of the
reaction.

(^17) J. L. Latham,Elementary Reaction Kinetics, 2nd ed., Butterworths,
London, 1969, p. 108.
13.12For the enzymatically catalyzed hydrolysis of ATP at
25 ◦C and pH 7.0, the Michaelis–Menten constant,Km,
was found to equal 16.8μmol L−^1 , and the value of
k 2 [E]totalwas found to be 0. 220 μmol L−^1 s−^1.
a.Sketch a graph of the initial rate as a function of the
initial concentration of ATP for the given data,
including scales on the axes.
b.Find the initial rate at an initial ATP concentration of
30.0μmol L−^1.
13.13A certain enzymatically catalyzed reaction with negligible
back reaction and a single reactant has a maximum rate of
2.34 mmol L−^1 s−^1 at a temperature of 37◦C.
a.If the rate is 1.58 mmol L−^1 s−^1 at a reactant
concentration of 12.3 mmol L−^1 and at the same
temperature and the same total enzyme concentration,
find the value ofKmat this temperature.
b.What is the rate at a reactant concentration of
0 .400 mmol L−^1 and at the same temperature and the
same total enzyme concentration?
13.14Derive the rate law for the forward rate of the
enzyme-catalyzed reaction with the mechanism
(1) E+R
ER
(2) ER−→ER′+P 1
(3) ER′−→E+P 2
where P 1 and P 2 are two different products. Comment on
the relationship of your answer to the Michaelis–Menten
formula.
13.15For a fixed concentration of the enzyme succinoxidase,
the following initial rates were observed. The rates are
expressed as the rate of change of the absorbance at a
wavelength of 250 nm.
[succinate]/mol L−^1 0.0100 0.00100
initial rate/s−^11. 67 × 10 −^41. 13 × 10 −^4
Find the value of the Michaelis–Menten constantKm.
13.16For the fumarase-catalyzed reaction
fumarate+H 2 O−→L-malate
the forward-rate Michaelis–Menten equation for
a single reactant is found to apply. Assume that