1. Tardigrade
  2. Question
  3. Chemistry
  4. Consider the following reversible first order reaction of X at an initial concentration [X]0 . The values of the rate constants are Kf=2 s -1 and Kb=1 s -1 X <=>[Kf][Kb] Y A plot of concentration of X and Y as function of time is

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Q. Consider the following reversible first order reaction of $X$ at an initial concentration $[X]_{0} .$ The values of the rate constants are $K_{f}=2 s ^{-1}$ and $K_{b}=1 s ^{-1}$
$X \ce{<=>[K_f][K_b]} Y$
A plot of concentration of $X$ and $Y$ as function of time is

KVPYKVPY 2018

Solution:

For first order reaction,
$ X \rightleftharpoons Y $
Given, $K_{f}= 2 s ^{-1} $
$K_{b}= 1 s ^{-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.