For the reaction,N_{2(g)} + O_{2(g)} rightlef | vedclass

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(C) Given reactions:$1) N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)} ; K_1$$2) 2NO_{(g)} + O_{2(g)} \rightleftharpoons 2NO_{2(g)} ; K_2$Adding equ

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$\left[ \frac{1}{K_1K_2} \right]^{1/2}$

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(C) Given reactions:$1) N_{2(g)} + O_{2(g)} ightleftharpoons 2NO_{(g)} ; K_1$$2) 2NO_{(g)} + O_{2(g)} ightleftharpoons 2NO_{2(g)} ; K_2$Adding equations $(1)$ and $(2)$ gives:$N_{2(g)} + 2O_{2(g)} ightleftharpoons 2NO_{2(g)}$The equilibrium constant for this combined reaction is $K_{eq} = K_1 	imes K_2$.Now,to obtain the target reaction $NO_{2(g)} ightleftharpoons \frac{1}{2} N_{2(g)} + O_{2(g)}$,we reverse the combined reaction and multiply the coefficients by $\frac{1}{2}$.Reversing the reaction gives $K' = \frac{1}{K_1 K_2}$.Multiplying coefficients by $\frac{1}{2}$ gives $K = (K')^{1/2} = \left[ \frac{1}{K_1 K_2} ight]^{1/2}$.

For the reaction,$N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant is $K_1$. The equilibrium constant is $K_2$ for the reaction,$2NO_{(g)} + O_{2(g)} \rightleftharpoons 2NO_{2(g)}$. What is $K$ for the reaction,$NO_{2(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + O_{2(g)}$?

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