Chapter 16.3, Problem 24SSC

Interpretation Introduction

Interpretation:

The rate law equations needs to be applied to show the difference between a first order reaction with a single reactant and second order reaction with a single reactant.

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 rate constant k.

Answer to Problem 24SSC

For a first order reaction, if the concentration of reactant increases two times rate will also increases to two times and for a second order reaction if concentration increases two times rate will increase four times.

Explanation of Solution

Consider the decomposition of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}$ is expressed by the following rate equation,

$\text{Rate=}k[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}]$

From the rate equation, it is known that the decomposition of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}$ is a first order reaction. In a first order reaction, the reaction rate changes in same proportion as the concentration of reactant changes. If concentration of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}$ increases by two times, rate will also increases two times.

For a second order reaction,

$\text{Rate}\text{=}k{[{\text{CH}}_{\text{3}}\text{CHO}]}^2$

If the concentration of ${\text{CH}}_{\text{3}}\text{CHO}$ increases two times, the rate increases to four times.

Conclusion

Rate depends upon the order of the reaction.