Physical Chemistry Third Edition

13.1 Catalysis 571

with the mechanism

(1) A 2 +2 surface sites
2 A(adsorbed) (fast)

(2) A(adsorbed)−→further intermediates or products (slow)

Assume that the second step is rate-limiting.

Solution

From Eq. (13.1-15),

θ

K^1 /^2 [A 2 ]^1 /^2

1 +K^1 /^2 [A 2 ]^1 /^2

ratek 2 θ

k 2 K^1 /^2 [A 2 ]^1 /^2

1 +K^1 /^2 [A 2 ]^1 /^2

For the case of two substances that react with each other at a solid surface we consider

two possible mechanisms. If only one of the reactants is adsorbed the mechanism is

called theLangmuir–Rideal mechanism:

(1) A+surface site
A(adsorbed) (13.1-18a)

(2) A(adsorbed)+B−→

further intermediates

or products

(13.1-18b)

Since molecules must collide to react, this mechanism means that the B molecules

from the fluid phase must collide with the adsorbed A molecules without first being

adsorbed. If the second step is rate-limiting, the rate law is

rate

k 2 K[A][B]

1 +K[A]

(Langmuir–Rideal mechanism) (13.1-19)

This mechanism is thought to be quite unlikely.

Exercise 13.6

Derive Eq. (13.1-19).

If both of the reacting molecules are adsorbed and if at least one of them can

move around on the surface, a reaction between two adsorbed molecules can occur.

This mechanism is called theLangmuir–Hinshelwood mechanism. It is said to occur

more commonly than the Langmuir–Rideal mechanism. It can be represented by the

mechanism

(1) A+surface site 
A(adsorbed) (13.1-20a)

(2) B+surface site
B(adsorbed) (13.1-20b)

(3) A(adsorbed)+B(adsorbed)−→

further

intermediates

or products

(13.1-20c)

We assume that step 3 is rate-limiting. If both substances adsorb on the same set

of sites the fraction of free sites is equal to 1−θA−θB, whereθAis the fraction