Q. At 550 K, the $K_{c}$ for the following reaction is $10^{4}\ mol^{- 1}L$ $X(g) + Y(g) \rightleftharpoons Z(g)$ At equilibrium, it was observed that $\lbrack X\rbrack = \frac{1}{2}\lbrack Y\rbrack = \frac{1}{2}\lbrack Z\rbrack$ What is the value of $\lbrack Z\rbrack(in\ mol\ L^{- 1})$ at equilibrium?
A) $2 \times 10^{- 4}$
B) $10^{- 4}$
C) $2 \times 10^{4}$
D) $10^{4}$
Explanation
(a)
$X(g) + Y(g) \rightleftharpoons Z(g)$
$K_{c} = \frac{\lbrack Z\rbrack}{\lbrack X\rbrack\lbrack Y\rbrack}$ or $10^{4} = \frac{\lbrack Z\rbrack}{\lbrack X\rbrack\lbrack Y\rbrack}$
$\therefore$ $\lbrack Z\rbrack = 10^{4}\lbrack X\rbrack\lbrack Y\rbrack$
$= 10^{4} \times \frac{1}{2}\lbrack Z\rbrack\lbrack Z\rbrack$
(Given, $\lbrack X\rbrack = \frac{1}{2}\lbrack Y\rbrack = \frac{1}{2}\lbrack Z\rbrack)$
$\therefore$ $\lbrack Z\rbrack = 2 \times 10^{- 4}\ mol\ L^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.