For the decomposition of azomethane. CH _ 3 N _ 2 CH _ 3 (g) → CH _...

For first order reaction

$k = \dfrac{1}{t}\ln \left(\dfrac{{P}_{0}}{P}\right) - kt = \ln \left(\dfrac{P}{{P}_{0}}\right)\ln \left(\dfrac{P}{{P}_{0}}\right) = \left(- k\right)t$

Slope=$- k =$$- 3 . 465 \times {10}^{4}k = 3 . 465 \times {10}^{4}$

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

${t}_{1/2} = \dfrac{\ln 2}{k} = \dfrac{0 . 693}{3 . 465 \times {10}^{4}} = 2 \times {10}^{- 5}$seconds