Question

The compounds $A$ and $B$ are mixed in equimolar proportion to form the products, $A+B\rightleftharpoons C+D$. At equilibrium, one-third of $A$ and $B$ are consumed. The equilibrium constant for the reaction is:

• A. $0.5$
• B. $4.0$
• C. $2.5$
• D. $0.25$

Answer 1

The correct option is D $0.25$

	$A$	$B$	$C$	$D$
Initial concentration (M)	1	1	0	0
Change in concentration (M)	$\frac{-1}{3}$	$\frac{-1}{3}$	$\frac{1}{3}$	$\frac{1}{3}$
Equilibrium concentration (M)	$\frac{2}{3}$	$\frac{2}{3}$	$\frac{1}{3}$	$\frac{1}{3}$

Assume initial concentrations of $A$ and $B$ be 1 M each.
The equilibrium constant expression is
$K=\frac{\left[C\right]\left[D\right]}{\left[A\right]\left[B\right]}$
$K=\frac{\frac{1}{3}\times \frac{1}{3}}{\frac{2}{3}\times \frac{2}{3}}=\frac{1}{4}=0.25$