Given the equilibria:I: A + 2B rightleftharpo | vedclass

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(D) The given equilibria are:$I: A + 2B \rightleftharpoons C ; K_1 = \frac{[C]}{[A][B]^2}$$II: C + D \rightleftharpoons 3A ; K_2 = \frac{[A]^3}{[C][D]

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$K_1^3 	imes K_2 = K_3$

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(D) The given equilibria are:$I: A + 2B ightleftharpoons C ; K_1 = \frac{[C]}{[A][B]^2}$$II: C + D ightleftharpoons 3A ; K_2 = \frac{[A]^3}{[C][D]}$$III: 6B + D ightleftharpoons 2C ; K_3 = \frac{[C]^2}{[B]^6[D]}$To obtain equation $III$,we perform the operation: $(2 	imes I) + II$$(2 	imes (A + 2B ightleftharpoons C)) \implies 2A + 4B ightleftharpoons 2C$Adding this to $II: C + D ightleftharpoons 3A$$(2A + 4B) + (C + D) ightleftharpoons 2C + 3A$$4B + D ightleftharpoons C + A$ (This does not match $III$ directly. Let us re-evaluate.)Actually,$III = 2 	imes I + II$ is not correct. Let us check $2 	imes I + II$ again:$2A + 4B + C + D ightleftharpoons 2C + 3A \implies 4B + D ightleftharpoons C + A$. This is incorrect.Let us check $3 	imes I + II$:$3A + 6B + C + D ightleftharpoons 3C + 3A \implies 6B + D ightleftharpoons 2C + C = 3C$. Still not $III$.Wait,let us check $2 	imes I + II$ again. If we multiply $I$ by $2$,we get $2A + 4B ightleftharpoons 2C$. Adding $II$ gives $2A + 4B + C + D ightleftharpoons 2C + 3A$,which simplifies to $4B + D ightleftharpoons C + A$.Let us re-examine the target $III: 6B + D ightleftharpoons 2C$. If we take $2 	imes I$,we get $2A + 4B ightleftharpoons 2C$. If we add $II$ to this,we get $2A + 4B + C + D ightleftharpoons 2C + 3A$. Actually,the correct relation is $K_3 = K_1^2 	imes K_2$ is not matching. Let us check $K_1^2 	imes K_2 = (\frac{[C]^2}{[A]^2[B]^4}) 	imes (\frac{[A]^3}{[C][D]}) = \frac{[C][A]}{[B]^4[D]}$.Let us check $K_1^3 	imes K_2 = (\frac{[C]^3}{[A]^3[B]^6}) 	imes (\frac{[A]^3}{[C][D]}) = \frac{[C]^2}{[B]^6[D]} = K_3$.Thus,$K_3 = K_1^3 	imes K_2$.

Given the equilibria:
$I: A + 2B \rightleftharpoons C ; K_{eq} = K_1$
$II: C + D \rightleftharpoons 3A ; K_{eq} = K_2$
$III: 6B + D \rightleftharpoons 2C ; K_{eq} = K_3$
Which of the following relations is correct?

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Given the equilibria:$I: A + 2B \rightleftharpoons C ; K_{eq} = K_1$$II: C + D \rightleftharpoons 3A ; K_{eq} = K_2$$III: 6B + D \rightleftharpoons 2C ; K_{eq} = K_3$Which of the following relations is correct?