Physical Chemistry Third Edition

11.3 Forward Reactions with More Than One Reactant 501

This is the same as

1

[A]t

−

1

[A] 0

kfbt (11.3-8)

where we drop the prime symbol (′)ont. Equation (11.3-8) is the same as Eq. (11.2-11)

except for the appearance of the factorbin the right-hand side.

EXAMPLE11.8

Some of the damage to the ozone layer of the upper atmosphere might involve the reaction

NO+O 3 −→NO 2 +O 2

The reaction is first order in each reactant and the rate constant is equal to 1. 3 × 106 L

mol−^1 s−^1 at 298 K. If the initial concentrations of NO and O 3 are both equal to 1. 00 ×

10 −^6 mol L−^1 , find the concentrations of NO and O 3 at timet 2 .00 s.

Solution

1

[NO]



1

NO 0

+kft

1

1. 00 × 10 −^6 mol L−^1

+(1. 3 × 106 L mol−^1 s−^1 )(2.00 s)

 3. 6 × 106 L mol−^1

[NO][O 3 ]

1

3. 6 × 106 L mol−^1

 2. 8 × 10 −^7 mol L−^1

Exercise 11.12

a.Find the half-life of the reaction in the previous example with the given initial concentrations.

b.Find the half-life of the reaction in the previous example with initial concentrations both

equal to 5. 00 × 10 −^5 mol L−^1.

In the case that the reactants are not mixed in the stoichiometric ratio we separate

the variables in Eq. (11.3-6a):

1

([A] 0 −ax)([B] 0 −bx)

dxkfdt (11.3-9)

This equation can be integrated by the method ofpartial fractions. If we write

1

([A] 0 −ax)([B] 0 −bx)



G

[A] 0 −ax

+

H

[B] 0 −bx

(11.3-10)

thenGandHare guaranteed by a theorem of algebra to be constants. These constants

are found to be

G

1

[B] 0 −b[A] 0 /a

and H

1

[A] 0 −a[B] 0 /b

Exercise 11.13

Verify the expressions forGandH.