Chapter 13, Problem 13.133QP

Interpretation Introduction

Interpretation:

The rate constant of the reaction has to be calculated.

Concept introduction:

Integrated rate law for second order reactions:

Taking in the example of following reaction,

$\text{aA}\to \text{products}$

And the reaction follows second order rate law,

Then the relationship between the concentration of $\text{A}$ and time can be mathematically expressed as,

$\frac{\text{1}}{{\left[\text{A}\right]}_{\text{t}}}\text{=kt+}\frac{\text{1}}{{\left[\text{A}\right]}_{\text{0}}}$

The above expression is called as integrated rate for second order reactions.

Half life for second order reactions:

In second order reaction, the half-life is inversely proportional to the initial concentration of the reactant (A).

The half-life of second order reaction can be calculated using the equation,

${\text{t}}_{\text{1/2}}\text{=}\frac{\text{1}}{\text{(k}{\left[\text{A}\right]}_{\text{0}}\text{)}}$

Since the reactant will be consumed in lesser amount of time, these reactions will have shorter half-life.

To calculate the rate constant of the reaction