Physical Chemistry Third Edition

11.5 A Simple Reaction Mechanism: Two Consecutive Steps 511

The solution of this equation is carried out in Appendix B for the case that no B or F

is present at timet0. The solution is

[B]t

k 1 [A] 0

k 2 −k 1

(e−k^1 t−e−k^2 t) (11.5-6)

Ifk 1 k 2 , the solution in Eq. (11.5-6) cannot be used. See Problem 11.34 for the

solution in this case.

Exercise 11.20

Substitute the function of Eq. (11.5-6) into the original differential equation of Eq. (11.5-5) and

show that it satisfies this equation.

The concentration of F is obtained from

[F][A] 0 −[A]−[B] (11.5-7)

Figure 11.6a shows the concentrations of all three substances for the case thatk 1 

0 .100 s−^1 andk 2  0 .500 s−^1 , and Figure 11.6b shows the concentrations for the case

Concentration

Concentration

Time

[A]

[B]

0 10 s

0

(a)

20 s

Time

(b)

[B]

[F]

[A]

[F]

10 s 20 s

Figure 11.6 The Concentrations of Substances A, B, and F for Consecutive Reac-

tions.(a) The case thatk 1 0.10 s−^1 and thatk 2 0.50 s−^1. (b) The case thatk 1 

0.50 s−^1 and thatk 2 0.10 s−^1.