Chapter 12, Problem 121CP

Consider the hypothetical reaction

$\text{A}\text{+}\text{B}\text{+2C}\to 2\text{D}\text{+}\text{3E}$

In a study of this reaction three experiments were run at the same temperature. The rate is defined as −∆[B]/∆t.

Experiment 1:

[A]₀ = 2.0 M      [B]₀ = 1.0 × 10⁻³ M     [C]₀ = 1.0 M

[B] (mol/L)	Time(s)
2.7 × 10−4	1.0 × 105
1.6 × 10−4	2.0 × 105
1.1 × 10−4	3.0 × 105
8.5 × 10−5	4.0 × 105
6.9 × 10−5	5.0 × 105
5.8 × 10−5	6.0 × 105

Experiment 2:

[A]₀ = 1.0 × 10⁻²M     [B]₀ = 3.0 M     [C]₀ = 1.0 M

[A] (mol/L)	Time(s)
8.9 × 10−3	1.0
7.1 × 10−3	3.0
5.5 × 10−3	5.0
3.8 × 10−3	8.0
2.9 × 10−3	10.0
2.0 × 10−3	13.0

Experiment 3:

[A]₀ = 10.0 M     [B]₀ = 5.0 M     [C]₀ = 5.0 × 10⁻¹M

[C] (mol/L)	Time(s)
0.43	1.0 × 10−2
0.36	2.0 × 10−2
0.29	3.0 × 10−2
0.22	4.0 × 10−2
0.15	5.0 × 10−2
0.08	6.0 × 10−2

Write the rate law for this reaction, and calculate the value of the rate constant.