Conversion of 'E' isomer of sorivudine to 'Z' isomer of sorivudine follows reversible first order kinetics with equilibrium constant equal to 10. Starting with 0.1 M of 'E' isomer only, calculate concentration of 'E' isomer 60 sec after the start if rate constant of forward reaction is 0.063 $\min^{- 1}$ .

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0.15 M

0.08 M

0.094 M

0.04 M

answer is D.

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Detailed Solution

$E ⇌ Z k_{eq} = 10$

$(\underset{0.1 - x x}{\frac{k_{f}}{k_{b}}} = 10 \Rightarrow k_{b} = 0 .0063 \min^{- 1})$

$\frac{x_{eq}}{0 .1 - x_{eq}} = 10$

$\Rightarrow x_{eq} = \frac{1}{11}$

$(k_{f} + k_{b}) t = \ln [\frac{x_{eq}}{x_{eq} - x}]$

$11 \times 0.0063 \times 1 = \ln [\frac{\frac{1}{11}}{\frac{1}{11} - x}]$

$\Rightarrow x = 0 .0061$

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