Physical Chemistry Third Edition

12.5 Chain Reactions 563

Two mechanisms are proposed.^27 The first is

(1) I+I
I 2 *

(2) I 2 *+M−→I 2 +M

where I 2 * represents a high-energy molecule. The second

mechanism is

(1) I+M+M
IM+M

(2) IM+I−→I 2 +M

where IM represents a loosely bound molecule that is not

necessarily capable of permanent existence.

a. Find the rate law for each mechanism, using the

rate-limiting step approximation and assuming that the

second step in each mechanism is rate-limiting.

b. It is found that the activation energy for the overall

reaction is negative. If M stands for an argon atom,

then the rate constantk 8. 3 × 10 −^33 cm^6 s−^1 at

300 K, andk 1. 3 × 1033 cm^6 s−^1 at 1300 K. Note

that the concentrations are expressed in atoms per

cubic centimeter for these values of the rate constants.

Find the value of the activation energy and the value

of the preexponential factor.

c.Explain the fact that the activation energy is negative.

12.42The gas-phase reaction

H 2 +I 2 
2HI

is second order in each direction (the orders are equal to

the stoichiometric coefficients). At 500 K, the value of

∆fG◦(HI) is− 10 .088 kJ mol−^1.

a.Find the value of the equilibrium constant for the

reaction at 500 K.

b.The forward rate constant is represented by the

Arrhenius formula withA 5. 47 × 109 L mol−^1 s−^1

andEa170 kJ mol−^1. Find the value of the forward

rate constant at 500 K.

(^27) H. S. Johnston,op. cit., p. 253ff. (note 26).
c.Find the value of the reverse rate constant at 500 K.
d.The value of∆U◦for the reaction is− 11 .244 kJ
mol−^1 at 500 K. Find the value of the activation
energy for the reverse reaction.
12.43Label each statement as either true or false. If a statement
is true only under special circumstances, label it as false.
a.A useful rule of thumb is that the rate of a chemical
reaction doubles for each increase in temperature of
10 ◦C.
b.Every chemical reaction proceeds by a multistep
mechanism.
c.Every reaction mechanism is a sequence of steps that
follows each other sequentially.
d.In a typical gas-phase chemical reaction, only a small
fraction of molecular collisions leads to reaction.
e.Termolecular steps are relatively rare in chemical
reaction mechanisms.
f.Diffusion-limited reactions are rapid because diffusion
is an inherently rapid process.
g.Only mechanisms with branching chains can lead to
explosions.
12.44For the reaction of CH 3 Br and I−in water, the Arrhenius
parameters areA 1. 68 × 1010 L mol−^1 s−^1 ,
Ea 76 .40 kJ mol−^1.
a.The activation energy has almost exactly the same
value if methanol is the solvent. Do you think that the
reaction is diffusion-controlled or
activation-controlled? Explain your answer.
b. Find the value of the rate constant at 50.0◦C.
c.If the initial concentrations are both equal to
0.500 mol L−^1 , find the half-life of the reaction.
Neglect any reverse reaction.
d.If the initial concentration of CH 3 Br is 0.500 mol L−^1
and that of I−is 0.350 mol L−^1 , find the time
required for 50.0% of the CH 3 Br to react.
Neglect any reverse reaction.