Consider the following gaseous equilibrium re | vedclass

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(A) The given reactions are:$I$) $\frac{1}{2} N_2 + \frac{3}{2} H_2 \rightleftharpoons NH_3$ $(K_1)$$II$) $2 NO \rightleftharpoons N_2 + O_2$ $(K_2)$$

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$\frac{K_3^3}{K_1^2 	imes K_2}$

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(A) The given reactions are:$I$) $\frac{1}{2} N_2 + \frac{3}{2} H_2 ightleftharpoons NH_3$ $(K_1)$$II$) $2 NO ightleftharpoons N_2 + O_2$ $(K_2)$$III$) $H_2 + \frac{1}{2} O_2 ightleftharpoons H_2 O$ $(K_3)$We want to find the equilibrium constant $K$ for the reaction:$2 NH_3 + \frac{5}{2} O_2 ightleftharpoons 2 NO + 3 H_2 O$To obtain this,we manipulate the given reactions:$1$. Reverse reaction $(I)$ and multiply by $2$: $2 NH_3 ightleftharpoons N_2 + 3 H_2$ $(K_{new1} = \frac{1}{K_1^2})$$2$. Reverse reaction $(II)$: $N_2 + O_2 ightleftharpoons 2 NO$ $(K_{new2} = \frac{1}{K_2})$$3$. Multiply reaction $(III)$ by $3$: $3 H_2 + \frac{3}{2} O_2 ightleftharpoons 3 H_2 O$ $(K_{new3} = K_3^3)$Adding these three reactions:$(2 NH_3) + (N_2 + O_2) + (3 H_2 + \frac{3}{2} O_2) ightleftharpoons (N_2 + 3 H_2) + (2 NO) + (3 H_2 O)$Canceling common species ($N_2$ and $3 H_2$): $2 NH_3 + \frac{5}{2} O_2 ightleftharpoons 2 NO + 3 H_2 O$The equilibrium constant $K$ is the product of the constants of the manipulated reactions:$K = K_{new1} 	imes K_{new2} 	imes K_{new3} = \frac{1}{K_1^2} 	imes \frac{1}{K_2} 	imes K_3^3 = \frac{K_3^3}{K_1^2 	imes K_2}$

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