Chapter 16.3, Problem 21PP

Interpretation Introduction

Interpretation:

The rate law for the reaction $a\text{A}+b\text{B}\to \text{Product}$ needs to be determined.

Concept introduction:

The relationship between rate of a chemical reaction and concentration of reactants is expressed by rate law. Rate law is written using the concentration of reactants, each raised to a power which is experimentally determined. and the rate constant k.

Answer to Problem 21PP

The rate law for the reaction is, $\text{Rate}=k[\text{B}]$

Explanation of Solution

From the given experimental data, first the order of the reactants can be identified. Examining trials 1 and 2 indicates that double the concentration of A, that is, [A] has no effect on rate. Therefore, the order of reactant A is zero. Examining trials 2 and 3, doubling concentration of B doubles the rate. So, the reaction is first order in case of reactant B. So, the rate law of the reaction is,

$\begin{array}{c}\text{Rate}\text{=}k{[}^{\text{A}}[\text{B}]\\ =k[\text{B}]\end{array}$

Conclusion

The coefficient of the reactant in a reaction indicates the order of the reactant.