Physical Chemistry Third Edition

526 12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms

whered 12 is the collision diameter for substance 1 and substance 2, and whereμ 12

is the reduced mass of molecules of massm 1 andm 2 , defined in Eq. (9.8-27) and in

Appendix B:

μ 12 

m 1 m 2

m 1 +m 2

or

1

μ 12



1

m 1

+

1

m 2

(12.1-7)

We can now summarize our results for both types of bimolecular processes in gaseous

reactions:A gaseous bimolecular elementary process is second order overall, and for

a two-substance reaction it is first order in each substance.

Exercise 12.2

Show that Eq. (12.1-6) is correct.

EXAMPLE12.1

For the gas-phase reaction

H 2 +I 2 −→2HI

at 373.15 K, the rate constant is equal to 8. 74 × 10 −^15 L mol−^1 s−^1. Assume that the reaction

is elementary and estimate the fraction of collisions that leads to reaction.

Solution

From Table A.15,

d 12 

1

2

(2. 72 × 10 −^10 m+ 6. 53 × 10 −^10 m) 4. 54 × 10 −^10 m

μ

(0.002016 kg mol−^1 )(0.2538 kg mol−^1 )

(0.002016 kg mol−^1 + 0 .2538 kg mol−^1 )(6. 022 × 1023 mol−^1 )

 3. 321 × 10 −^27 kg

f

k

πd 122

(

8 kBT

πμ 12

) 1 / 2

NAv

f

(8. 74 × 10 −^15 L mol−^1 s−^1 )(0.001 m^3 L−^1 )

π(4. 54 × 10 −^10 m)^2

(

8(1. 3807 × 10 −^23 JK−^1 )(373.15 K)

π(3. 321 × 10 −^27 kg)

) 1 / 2

(6. 022 × 1023 mol−^1 )

 1. 1 × 10 −^26

Exercise 12.3

At 473.15 K the rate constant for the reaction of the previous example is equal to

9. 53 × 10 −^10 L mol−^1 s−^1. Estimate the fraction of collisions that leads to reaction at this

temperature.