The reaction cis- \( X \underset{k_{b}}{\stackrel{k_{f}}{\rightleftharpoons}} \) trans- \( X \) ...

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The reaction cis- \( X \underset{k_{b}}{\stackrel{k_{f}}{\rightleftharpoons}} \) trans- \( X \) is first order in both directions. At \( 25^{\circ} \mathrm{C} \), the equilibrium constant is \( 0.10 \) and the rate constant \( k_{f}=3 \times 10^{-4} \mathrm{~s}^{-1} \). In an experiment starting with the pure cis-form, how long would it take for half of the equilibrium amount of the trans-isomer to be formed?
(a) \( 150 \mathrm{sec} \)
(b) \( 200 \mathrm{sec} \)
(c) \( 240 \mathrm{sec} \)
(d) \( 210 \mathrm{sec} \)
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