Question

How do you calculate the half life for this reaction?

The first-order reaction of decomposition of azomethane is given below: At a certain temperature, the rate constant for this reaction equals 3.05 X 10^-3 s^-1. Calculate the half-life of this reaction (in seconds) at the same temperature.

Answer 1

Concepts and reason

This problem is based on calculating half life of a first order reaction. Half-life of a reaction is the time needed for the decrease in concentration of a reactant to half its initial value.

Fundamentals

The formula to calculate half-life period for a first order reaction is as follows:

${t_{1/2}} = \frac{{0.693}}{k}$

Here, ${t_{1/2}}$ is half-life of the reaction and k is rate constant.

The reaction is as follows:

${\rm{C}}{{\rm{H}}_3} - {\rm{N}} = {\rm{N}} - {\rm{C}}{{\rm{H}}_3}\left( g \right) \to {{\rm{N}}_2}\left( g \right) + {{\rm{C}}_{\rm{2}}}{{\rm{H}}_6}\left( g \right)$

The formula for calculating half life period of a reaction is as follows:

${t_{1/2}} = \frac{{0.693}}{k}$

Substitute ${\rm{3}}{\rm{.05}} \times {\rm{1}}{{\rm{0}}^{ - 1}}{\rm{ }}{{\rm{s}}^{ - 1}}$ for k.

$\begin{array}{c}\\{t_{1/2}} = \frac{{0.693}}{{{\rm{3}}{\rm{.05}} \times {\rm{1}}{{\rm{0}}^{ - 3}}{\rm{ }}{{\rm{s}}^{ - 1}}}}\\\\ = 227.213{\rm{ s}}\\\end{array}$

Ans:

The half-life for the reaction is $227.213{\rm{ s}}$ .