Question

Consider the following reactions in which all the reactants and the products are in gaseous state.
$2PQ\rightleftharpoons P_2+Q_2;$ $K_1=2.5\times {10}^5$
$PQ+\frac{1}{2}{R}_2\rightleftharpoons PQR;$ $K_2=5\times {10}^{-3}$
The value of $K_3$ for the equilibrium
$\frac{1}{2}{P}_2+\frac{1}{2}{Q}_2+\frac{1}{2}{R}_2\rightleftharpoons PQR,$ is

• A. $2.5\times {10}^{-3}$
• B. $2.5\times {10}^3$
• C. $1.0\times {10}^{-5}$
• D. $5\times {10}^3$
• E. $5\times {10}^{-3}$

Answer 1

Answer: (C)

Given, $2PQ{P}_2+Q_2;$
$K_1=\frac{[P_2][Q_2]}{{[PQ]}^2}=2.5\times {10}^5$
$PQ+\frac{1}{2}{R}_{2}PQR;$
$K_2=\frac{[PQR]}{[PQ]{[R_2]}^{1/2}}=5\times {10}^{-3}$
Required equilibrium is $\frac{1}{2}{P}_2+\frac{1}{2}{Q}_2+\frac{1}{2}{R}_{2}PQR$
$K_3=\frac{[PQR]}{{[P_2]}^{1/2}{[Q_2]}^{1/2}{[R_2]}^{1/2}}$
On multiplying and dividing by $[PQ],$
$K_3=\frac{[PQR]}{{[P_2]}^{1/2}{[Q_2]}^{1/2}{[R_2]}^{1/2}[PQ]}$
Or $K_3=K_2\times \sqrt{\frac{1}{K_1}}$
$=5\times {10}^{-3}\times \sqrt{\frac{1}{2.5\times {10}^5}}$
$=\frac{5\times {10}^{-3}}{0.5\times {10}^3}=1\times {10}^{-5}$