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(A) Given reactions:$(i) 2 A \rightleftharpoons B + C, K_{1} = 1$$(ii) 2 B \rightleftharpoons C + D, K_{2} = 16$$(iii) 2 C + D \rightleftharpoons 2 P,

Vedclass · Accepted Answer

$\frac{1}{20}$

Vedclass · Answer

(A) Given reactions:$(i) 2 A ightleftharpoons B + C, K_{1} = 1$$(ii) 2 B ightleftharpoons C + D, K_{2} = 16$$(iii) 2 C + D ightleftharpoons 2 P, K_{3} = 25$We need the equilibrium constant for $P ightleftharpoons A + \frac{1}{2} B$.Reverse reaction $(iii)$ and divide by $2$: $P ightleftharpoons C + \frac{1}{2} D, K' = \sqrt{\frac{1}{K_{3}}} = \frac{1}{5}$.Reverse reaction $(ii)$ and divide by $2$: $\frac{1}{2} C + \frac{1}{2} D ightleftharpoons B, K'' = \sqrt{\frac{1}{K_{2}}} = \frac{1}{4}$.Reverse reaction $(i)$ and divide by $2$: $\frac{1}{2} B + \frac{1}{2} C ightleftharpoons A, K''' = \sqrt{\frac{1}{K_{1}}} = 1$.Adding these reactions: $P + \frac{1}{2} C + \frac{1}{2} D + \frac{1}{2} B + \frac{1}{2} C ightleftharpoons C + \frac{1}{2} D + B + A$.Simplifying: $P ightleftharpoons A + \frac{1}{2} B$.The equilibrium constant $K_{final} = K' 	imes K'' 	imes K''' = \frac{1}{5} 	imes \frac{1}{4} 	imes 1 = \frac{1}{20}$.

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