For the consecutive unimolecular-type first-order reaction $A\overset{\quad k_{1}\quad}{\rightarrow}

Question

For the consecutive unimolecular-type first-order reaction $A\overset{\quad k_{1}\quad}{\rightarrow}R\overset{\quad k_{2}\quad}{\rightarrow}S$, the concentration of component ‘R’, CR, at any time, ‘t’ is given by $C_{R} = C_{A}^{o}.K_{1}\left\lbrack \frac{e^{- k_{1}t}}{\left( k_{2} - k_{1} \right)} + \frac{e^{- k_{2}t}}{\left( k_{1} - k_{2} \right)} \right\rbrack$.

If $C_{A} = C_{A}^{o},C_{R} = C_{S} = 0$ at t = 0, the time at which the maximum concentration of ‘R’ occurs is

Accepted Answer

For CR max, $\frac{dC_{R}}{dt} = 0$$\Rightarrow {t\frac{\ln\left( K_{2}/K_{1} \right)}{K_{2} - K_{1}}}_{\max}$

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