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For the parallel reactions depicted below, which of the following options are correct?

$\begin{array}{1 1}(a)\;\large\frac{[B]}{[c]}=\frac{k_2}{k_1}\;\normalsize at\; any\;time\;t\\(b)\;[B]=\large\frac{k_2[A_o]}{k_1+k_2}\normalsize(1-e^{-k_1t})\;at \;any\;time\;t\\(c)\;t_{1/2}=\large\frac{ln 2}{k_1+k_2}\\(d)\;k=\large\frac{k_1k_2}{k_1+k_2}\end{array}$

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Answer: (C) is correct.
$[A]=[A_o]e^{-kt}$, where $k=k_1+k_2 \rightarrow$ Hence (D) is incorrect
$[B]=\large\frac{k_1[A_o]}{k_1+k_2}$$(1-e^{-kt}) \rightarrow$ Hence (B) is incorrect
$[C]=\large\frac{k_2[A_o]}{k_1+k_2}$$(1-e^{-kt}) \rightarrow \large\frac{[B]}{[C]}=\frac{k_1}{k_2} \rightarrow $ Hence (A) is incorrect.
$t_{1/2}=\large\frac{ln\; 2}{k}=\frac{ln\; 2}{k_1+k_2} \rightarrow$ Hence (C) is correct.
answered Dec 16, 2013 by sreemathi.v
edited Jul 26, 2014 by balaji.thirumalai

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