A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is _________ min. (Round

Initially : [ A_0 ] = [ B_0 ] = a After time 't' min : [ A ] = 16[ B ] [ A ] = [ A_0 ]e^ - k_At [ B ] = [ B_0 ]e^ - k_Bt &nb

A and B decompose via first order kinetics with halflives 54: (Chemistry)

Initially : $\left[ {{A_0}} \right] = \left[ {{B_0}} \right] = a$

After time 't' min : $\left[ A \right] = 16\left[ B \right]$

$\left[ A \right] = \left[ {{A_0}} \right]{e^{ - {k_A}t}}$

$\left[ B \right] = \left[ {{B_0}} \right]{e^{ - {k_B}t}}$

$\Rightarrow a\,.\,{e^{ - {k_A}t}} = 16a{e^{ - {k_B}t}}$

$\Rightarrow {e^{ - \left( {{k_A} - {k_B}} \right)t}} = 16$

$\Rightarrow \left( {{k_B} - {k_A}} \right)t = \ln 16$

$\Rightarrow \ln 2\left( {{1 \over {18}} - {1 \over {54}}} \right)t = 4\ln 2$

$\Rightarrow t = {{54 \times 18 \times 4} \over {36}} = 108$ min