Question

Consider the following reactions in which all the reactants and the products are in gaseous state.

$2PQ \rightleftharpoons P_{2}+Q_{2};K_{1}=2.5\times 10^{5}$

$PQ+1/2R_{2} \rightleftharpoons PQR;K_{2}=5\times 10^{- 3}$

The value of $K_{3}$ for the equilibrium

$1/2P_{2}+1/2Q_{2}+1/2R_{2} \rightleftharpoons PQR$ is

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

Answer 1

Answer: (D)

Given , $2PQ\rightleftharpoons P_{2}+Q_{2};$

$K_{1}=\frac{\left[\right. P_{2} \left]\right. \left[\right. Q_{2} \left]\right.}{\left[\right. P Q \left]\right.^{2}}=2.5\times 10^{5}$

$PQ+1/2R_{2}\rightleftharpoons PQR;$

$K_{2}=\frac{\left[\right. P Q R \left]\right.}{\left[\right. P Q \left]\right. \left[\right. R_{2} \left]\right.^{1 / 2}}$

$=5\times 10^{- 3}$

For the required equilibrium

$1/2P_{2}+1/2Q_{2}+1/2R_{2} \rightleftharpoons PQR;$

$K_{3}=\frac{\left[\right. P Q R \left]\right.}{\left[\right. P_{2} \left]\right.^{1 / 2} \left[\right. Q_{2} \left]\right.^{1 / 2} \left[\right. R_{2} \left]\right.^{1 / 2}}$

$K_{3}=K_{2}\times \sqrt{\frac{1}{K_{1}}}$

$=5\times 10^{- 3}\times \sqrt{\frac{1}{2.5 \times 1 0^{5}}}=\frac{5 \times 1 0^{- 3}}{0.5 \times 1 0^{3}}$

$=1\times 10^{- 5}$