Chemical and Ionic Equilibrium - Result Question 10
10. Consider the following reversible chemical reactions,
$\begin{aligned} & A_2(g)+B_2(g) \stackrel{K_1}{\rightleftharpoons} 2 A B(g)\hspace {15mm} …(i)\\ & 6 A B(g) \stackrel{K_2}{\rightleftharpoons} 3 A_2(g)+3 B_2(g)\hspace {15mm}…(ii) \end{aligned}$
The relation between $K_1$ and $K_2$ is
(2019 Main, 9 Jan II)
(a) $K_2=K_1^3$
(b) $K_1 K_2=3$
(c) $K_2=K_1^{-3}$
(d) $K_1 K_2=\dfrac{1}{3}$
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Answer:
Correct Answer: 10. (c)
Solution:
- (i) $A_2(g)+B_2(g) \rightleftharpoons 2 A B(g) ; \qquad K_1=\dfrac{[A B]^2}{\left[A_2\right]\left[B_2\right]}$
$\begin{aligned} & \text { (ii) } 6 A B(g) \rightleftharpoons 3 A_2(g)+3 B_2(g) \\ & \qquad K_2=\dfrac{\left[A_2\right]^3\left[B_2\right]^3}{[A B]^6}=\dfrac{1}{\left(\dfrac{[A B]^2}{\left[A_2\right]\left[B_2\right]}\right)^3}=\dfrac{1}{K_1^3} \\ & \Rightarrow \quad K_2=K_1^{-3}\end{aligned}$
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