A flask is filled with equal moles of A and B . The half lives of A...

For first order reaction

$k = \dfrac{0 . 693}{{t}_{\dfrac{1}{2}}}$

\left[A\right] = 4\left[B\right]$</p><p>${\left[A\right]}_{0}{e}^{- {k}_{A}t} = 4{\left[B\right]}_{0}{e}^{- {k}_{B}t}$</p><p>$∵$as${\left[A\right]}_{0} = {\left[B\right]}_{0}; {e}^{- {k}_{A}t} = 4{e}^{- {k}_{B}t}$</p><p>$- {k}_{A}t = \ln 4 - {k}_{B}t$</p><p>$∴ t\left({k}_{B} - {k}_{A}\right) = 2\ln 2$</p><p>$t = \dfrac{2 \times 0 . 693}{\left(\dfrac{0 . 693}{50} - \dfrac{0 . 693}{100}\right)} = \dfrac{2 \times 100}{2 - 1} = 200sec$