For the decomposition of azomethane. CH 3   N 2 CH 3 g → CH 3 CH 3 g + N 2 a first order reaction…

For first order reaction

$$\begin{gathered} \mathrm{k}=\frac{1}{\mathrm{t}}\ln \left(\frac{{\mathrm{P}}_0}{\mathrm{P}}\right) \\ -\mathrm{kt}=\ln \left(\frac{\mathrm{P}}{{\mathrm{P}}_0}\right) \\ \ln \left(\frac{\mathrm{P}}{{\mathrm{P}}_0}\right)=\left(-\mathrm{k}\right)\mathrm{t} \end{gathered}$$

Slope=$-\mathrm{k}=$$$\begin{gathered} -3.465\times {10}^4 \\ \mathrm{k}=3.465\times {10}^4 \end{gathered}$$

For a first order reaction,Half-life is related to rate constant as given below

${\mathrm{t}}_{1/2}=\frac{\ln 2}{\mathrm{k}}=\frac{0.693}{3.465\times {10}^4}=2\times {10}^{-5}$seconds