Chapter 16.3, Problem 19PP

Interpretation Introduction

Interpretation:

The rate law for the reaction $a\text{A}\to b\text{B}$ 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.

Answer to Problem 19PP

Rate law for the reaction is, $\text{Rate}=k{[\text{A}]}^3$

Explanation of Solution

For an one step reaction such as $\text{A}\to \text{B}$, rate law is expressed by the product of concentration of reactant and the rate constant k.

$\text{Rate=}k[\text{A}]$

The given reaction is $a\text{A}\to b\text{B}$ and given that the order of the reaction is 3. Order 3 indicates that the coefficient of the reactant A ( a ) must be 3. So, the rate law for the reaction is,

$\text{Rate}=k{[\text{A}]}^3$

Conclusion

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