Q. 3 moles of $A$ and 4 moles of $B$ are mixed together and allowed to come into equilibrium according to the following reaction. $3A(g) + 4B(g) \rightleftharpoons 2C(g) + 3D(g)$ When equilibrium is reached, there is 1 mole of $C$. The equilibrium extent of the reaction is
A) $\frac{1}{4}$
B) $\frac{1}{3}$
C) $\frac{1}{2}$
D) $1$
Explanation
(c)
$3A + 4B \rightleftharpoons 2C + 3D$
$\Rightarrow$ $K_{1} = \frac{\lbrack C\rbrack^{2}\lbrack D\rbrack^{3}}{\lbrack A\rbrack^{3}\lbrack B\rbrack^{4}}$ …(i)
When moles of $C = 1$, the equation becomes
$\frac{3}{2}A + 2B \rightleftharpoons C + \frac{3}{2}D$
$\Rightarrow$ $K_{2} = \frac{\lbrack C\rbrack\lbrack D\rbrack^{\frac{3}{2}}}{\lbrack A\rbrack^{\frac{3}{2}}\lbrack B\rbrack^{2}}$ ...(ii)
On comparing Eq.(i) with Eq.(ii), we get
$K_{2}^{2} = K_{1}\ \ \ \ \ \ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ \ \ \ \ \ \ K_{2} = \left( K_{1} \right)^{\frac{1}{2}}$
Hence, equilibrium extent $= \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.