Question

Consider the following reversible first order reaction of $X$ at an initial concentration $[X{]}_0.$ The values of the rate constants are $K_f=2s^{-1}$ and $K_b=1s^{-1}$
$X\underset{\mathrm{K}{}_b}{\overset{\mathrm{K}{}_f}{\rightleftharpoons }}Y$
A plot of concentration of $X$ and $Y$ as function of time is

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

For first order reaction,
$X\rightleftharpoons Y$
Given, $K_f=2s^{-1}$
$K_b=1s^{-1}$
$\therefore K_{eq}=\frac{K_f}{K_b}=\frac{[Y]}{[X]}$
$K_{eq}=\frac{2}{1}=\frac{[Y]}{[X]}$
$\Rightarrow 2[X]=[Y]$
or $2[X{]}_{eq}=[Y{]}_{eq}$
$\therefore [Y]>[X]$
Thus, as the rate of reaction increases, there will be increased in the concentration $Y_{eq}$, but it will be less than initial concentration of $X\left(X_0\right)$, whereas the concentration of $X_{eq}$ decreases.