The reaction cis- `X underset(k_(b))⇌overset(k_(f))` trans-X is first order in both directions. At `25^(@)` C, the equilibrium constant is 0.10 and the rate constant `k_(f) = 3 xx 10^(-4) 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?

Options

A. 150 sec
B. 200 sec
C. 240 sec
D. 210 sec

Answer

D

Explanation

cis `X underset(k_(b))overset(k_(f))` trans -X
intial a 0
at time t a-x x
at eqm `a-x_(e ) x_(e )`
given `x=(x_(e ))/(2) (k_(f)+k_(b))=(1)/(t )In 2` or `(3xx10^(-3)+3xx10^(-4))=(0.693)/(t ) t=210 sec`