Question

The half life period of 3rd order reaction is:

Answer 1

Answer:

The half life period ..................... is 3/2k[A]2

Explanation:

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Answer 2

Answer:

The half life time of $third$ order reaction is equal to  $\frac{3}{2k[A_{o}]^{2}}$.

Explanation:

We know $kinetic$ equation for $third$ order reaction is given by:

$\frac{1}{[A]^{2}} -\frac{1}{[A^{o}]^{2}} =2kt$                                      .................(1)

where $[A_{o}]$ is the initial concentration of reactants

          $[A]$ is the $concentration$ of reactants at $time$ $t$

          $k$ is rate constant of the reaction.

When $t=t_{\frac{1}{2} }$  the concentration of reactants decreased to half i.e. $[A]=\frac{[A_{o}]}{2}$, put in eq.(1);

We get,   $\frac{1}{(\frac{1}{2} [A_{o}])^{2}} -\frac{1}{[A_{o}]^{2}} =2kt_{\frac{1}{2} }$

               $\frac{4}{[A_{o}]^{2}} -\frac{1}{[A_{o}]^{2}} =2kt_{\frac{1}{2} }$

                $\frac{3}{2k[A_{o}]^{2}}=2kt_{\frac{1}{2} }$

                $t_{\frac{1}{2} }=\frac{3}{2k[A_{o}]^{2}}$