Chapter 19, Problem 139A

Interpretation Introduction

Interpretation : The order of the reaction with respect to A, B, and C and the overall order of the reaction is to be determined.

Concept Introduction : The link between a chemical reaction's rate and the concentration of the species involved is referred to as the order of the reaction.

Answer to Problem 139A

The order of the reaction with respect to A, B, and C are one, two, and zero respectively.

The overall order of the reaction is three.

Explanation of Solution

The power dependency of the rate on the concentrations of all reactants can be used to define the order of the reaction.

From the given table, the four experiments of initial concentrations of A, B and C with rate can be determined.

Compare the experiment 1 and 2 values.

The concentrations of B and C are the same and only the concentration of A differs.

The concentration of A is given as

  $\left[{\text{A}}_{\text{2}}\right]\text{=}\text{2}\left[{\text{A}}_{\text{1}}\right]$

The rate of two reactions is given as

  $\begin{array}{c}{\text{Rate}}_2=2{\text{Rate}}_1\\ \text{k}{\left[{\text{A}}_2\right]}^{\text{a}}{\left[{\text{B}}_2\right]}^{\text{b}}{\left[{\text{C}}_2\right]}^{\text{c}}=2\left(\text{k}{\left[{\text{A}}_1\right]}^{\text{a}}{\left[{\text{B}}_1\right]}^{\text{b}}{\left[{\text{C}}_1\right]}^{\text{c}}\right)\\ \frac{\text{k}{\left[{\text{A}}_2\right]}^{\text{a}}{\left[{\text{B}}_2\right]}^{\text{b}}{\left[{\text{C}}_2\right]}^{\text{c}}}{\text{k}{\left[{\text{A}}_1\right]}^{\text{a}}{\left[{\text{B}}_1\right]}^{\text{b}}{\left[{\text{C}}_1\right]}^{\text{c}}}=2\\ \text{a}\text{=}1\end{array}$

The order of A is 1.

Compare the experiment 2 and 3 values.

The concentrations of A and C are the same and only the concentration of B differs.

The concentration of B is given as

  $\left[{\text{B}}_3\right]\text{=}\text{2}\left[{\text{B}}_2\right]$

The rate of two reactions is given as

  $\begin{array}{c}{\text{Rate}}_3=4{\text{Rate}}_2\\ \text{k}{\left[{\text{A}}_3\right]}^{\text{a}}{\left[{\text{B}}_3\right]}^{\text{b}}{\left[{\text{C}}_3\right]}^{\text{c}}=4\left(\text{k}{\left[{\text{A}}_2\right]}^{\text{a}}{\left[{\text{B}}_2\right]}^{\text{b}}{\left[{\text{C}}_2\right]}^{\text{c}}\right)\\ \frac{\text{k}{\left[{\text{A}}_3\right]}^{\text{a}}{\left[{\text{B}}_3\right]}^{\text{b}}{\left[{\text{C}}_3\right]}^{\text{c}}}{\text{k}{\left[{\text{A}}_2\right]}^{\text{a}}{\left[{\text{B}}_2\right]}^{\text{b}}{\left[{\text{C}}_2\right]}^{\text{c}}}=4\\ \text{b}\text{=}\text{2}\end{array}$

The order of B is 2.

Compare the experiment 1 and 4 values.

The concentrations of B and A are the same and only the concentration of C differs.

The concentration of C is given as

  $\left[{\text{C}}_4\right]\text{=}\text{2}\left[{\text{C}}_{\text{1}}\right]$

The rate of two reactions is given as

  $\begin{array}{c}{\text{Rate}}_4={\text{Rate}}_1\\ \text{k}{\left[{\text{A}}_4\right]}^{\text{a}}{\left[{\text{B}}_4\right]}^{\text{b}}{\left[{\text{C}}_4\right]}^{\text{c}}=\text{k}{\left[{\text{A}}_1\right]}^{\text{a}}{\left[{\text{B}}_1\right]}^{\text{b}}{\left[{\text{C}}_1\right]}^{\text{c}}\\ \frac{\text{k}{\left[{\text{A}}_4\right]}^{\text{a}}{\left[{\text{B}}_4\right]}^{\text{b}}{\left[{\text{C}}_4\right]}^{\text{c}}}{\text{k}{\left[{\text{A}}_1\right]}^{\text{a}}{\left[{\text{B}}_1\right]}^{\text{b}}{\left[{\text{C}}_1\right]}^{\text{c}}}=1\\ \text{c}\text{=}0\end{array}$

The order of C is 0.

The rate of the reaction is given as

  $\text{rate}\text{=}\text{k}{\left[\text{A}\right]}^{\text{1}}{\left[\text{B}\right]}^{\text{2}}{\left[\text{C}\right]}^{\text{0}}$

The overall order of the reaction is the sum of the order of the individual concentrations.

So, the overall order is 3.