Physical Chemistry Third Edition

13.1 Catalysis 581

b.The same reaction on nickel appears to follow the

Langmuir–Rideal mechanism. Write the rate law that

you would expect to find for this case.

13.2Apply the steady-state approximation to obtain a rate law

for the reaction A 2 −→products with the assumed

mechanism

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

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

What condition would make this rate law coincide with

that obtained with the quasi-equilibrium approximation?

13.3 a.Derive the rate law for the reaction of a substance A

that undergoes a unimolecular reaction on a catalytic

surface in the case that a nonreacting substance C also

adsorbs on the surface. Assume that each substance

obeys the Langmuir isotherm.

b.In the case that C adsorbs more strongly than A, the

catalyst can bepoisonedby C. Poisoning can occur if

lead is adsorbed on the surface of the catalyst in an

automobile’s catalytic converter. Find the rate law if C

is much more strongly adsorbed than A.

13.4Assume that a diatomic reactant dissociates when it is

absorbed on a solid catalyst from the gas phase:

A 2 (g)+2 surface sites
2 A(ads)

a.Find an expression forθ, the equilibrium fraction of

surface sites occupied as a function of [A 2 ], the

concentration of A 2 in the gas phase.

b.For the reaction A 2 +2B−→products assume the

Langmuir–Rideal mechanism, which means that a

B molecule in the gas phase collides with an adsorbed

A atom and reacts without being adsorbed itself:

(1) A 2 (g)+2 surface sites
 2 A(ads)

(2) A(ads)+B(g)−→products

Write the rate law, assuming the second step to be the

rate-limiting step.

13.5 The following reaction is catalyzed by the bromide ion:

H++HNO 2 +φNH 2

Br−

−→φN+ 2 +2H 2 O

whereφrepresents the phenyl group. A proposed

mechanism is

(1) H++HNO 2 
HNO+ 2

(2) H 2 NO+ 2 +Br−−→ONBr+H 2 O

(3) ONBr+φNH 2 −→φN+ 2 +H 2 O+Br−

a.Find the rate law, assuming the second step to be

rate-limiting.

b.Find the rate law, assuming the quasi-steady-state

approximation. What is the effect of assuming that the

third step is much faster than the second step?

13.6The decomposition of nitrous oxide, N 2 O, on a platinum

surface is apparently inhibited by the adsorption of the O 2

produced. For the case of zero initial partial pressure of

O 2 , the observed rate law is

−

dP(N 2 O)

dt



aP(N 2 O)

1 +(b/ 2 )[P 0 (N 2 O)−P(N 2 O)]



aP(N 2 O)

1 +bP(O 2 )

whereaandbare temperature-dependent parameters and

whereP 0 (N 2 O) is the initial pressure of N 2 O.

a.Assuming that both substances obey the Langmuir

isotherm, derive this rate law, stating any necessary

assumptions. Identify the parametersaandb.

b.Integrate the rate law to obtain

1 +bP 0

t

ln

(

P 0

P 0 −x

)

a+b

(x

t

)

whereP 0 P 0 (N 2 O)/2 and wherexP(O 2 ).

c.Following are data of Hinshelwood and Pritchard for

this reaction at 741◦C and forP 0 190 torr:

t/s 315 750 1400 2250 3450 5150

x/torr 10 20 30 40 50 60

Using a least-squares method, fit these data to the

integrated rate law and determine the values ofa

andb.

13.7The platinum-catalyzed oxidation of methanol apparently

proceeds through formation of formaldehyde and then

carbon monoxide.^16 The following mechanism is

proposed for the oxidation of the carbon monoxide:

(1) CO(g)+surface site
CO(adsorbed)

(2) O 2 +surface site
O 2 (adsorbed)

(3) O 2 (adsorbed)+surface site−→2O(adsorbed)

(4) CO(adsorbed)+O(adsorbed)−→CO 2 (g)

(^16) R. W. McCabe and D. F. McCready,J. Phys. Chem., 90 , 1428
(1986).