For a reaction A → 2B + C the half lives are 100s and 50s when the...

The relation between half-life and initial concentration of ${n}^{th}$ order reaction can be written as follows,

$t\dfrac{1}{2} ∝ \dfrac{1}{{\left[{A}_{0}\right]}^{n - 1}}$

\left[100\right] ∝ \dfrac{1}{{\left(0 . 5\right)}^{n - 1}}$</p><p>\left(50\right) ∝ \dfrac{1}{{\left(1\right)}^{n - 1}}$

${\left[2\right]}^{1} = {\left[\dfrac{1}{0 . 5}\right]}^{n - 1}$

${\left[2\right]}^{1} = {\left[2\right]}^{n - 1}$

$n - 1 = 1$

$n = 2$

order $= 2$

For the second order reactions half-life is inversely proportional to initial concentration.