Two consecutive irreversible first order reaction can be represented by $$A\xrightarrow[{}]{{{k}_{1}}}B\xrightarrow[{}]{{{k}_{2}}}C$$.The rate equation for A is integrated to obtain$${{[A]}_{t}}={{[A]}_{0}}{{e}^{-{{k}_{1}}t}}$$ and $${{[B]}_{t}}=\frac{{{k}_{1}}[{{A}_{0}}]}{{{k}_{2}}-{{k}_{1}}}[{{e}^{-{{k}_{1}}t}}-{{e}^{-{{k}_{2}}t}}]$$.At what time will B be present in the greatest concentration?

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TuteeHUB · Accepted Answer

$${{t}_{\max }}=\frac{1}{{{k}_{2}}+{{k}_{1}}}\ln \frac{{{k}_{1}}}{{{k}_{2}}}$$

TuteeHUB · Answer

$${{t}_{\max }}=\frac{1}{{{k}_{1}}+{{k}_{2}}}\ln \frac{{{k}_{2}}}{{{k}_{1}}}$$

TuteeHUB · Answer

$${{t}_{\max }}=\frac{1}{{{k}_{1}}+{{k}_{2}}}\ln \frac{{{k}_{2}}}{{{k}_{1}}}$$

TuteeHUB · Answer

None of these

1.	Two consecutive irreversible first order reaction can be represented by \[A\xrightarrow[{}]{{{k}_{1}}}B\xrightarrow[{}]{{{k}_{2}}}C\].The rate equation for A is integrated to obtain\[{{[A]}_{t}}={{[A]}_{0}}{{e}^{-{{k}_{1}}t}}\] and \[{{[B]}_{t}}=\frac{{{k}_{1}}[{{A}_{0}}]}{{{k}_{2}}-{{k}_{1}}}[{{e}^{-{{k}_{1}}t}}-{{e}^{-{{k}_{2}}t}}]\].At what time will B be present in the greatest concentration?
A.	\[{{t}_{\max }}=\frac{1}{{{k}_{1}}+{{k}_{2}}}\ln \frac{{{k}_{2}}}{{{k}_{1}}}\]
B.	\[{{t}_{\max }}=\frac{1}{{{k}_{1}}+{{k}_{2}}}\ln \frac{{{k}_{2}}}{{{k}_{1}}}\]
C.	\[{{t}_{\max }}=\frac{1}{{{k}_{2}}+{{k}_{1}}}\ln \frac{{{k}_{1}}}{{{k}_{2}}}\]
D.	None of these
Answer» C. \[{{t}_{\max }}=\frac{1}{{{k}_{2}}+{{k}_{1}}}\ln \frac{{{k}_{1}}}{{{k}_{2}}}\]

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