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(A) The relationship between $K_p$ and $K_c$ is given by $K_p = K_c(RT)^{\Delta n_g}$, where $\Delta n_g = y - x$ and $T = 400 \ K$. Here, $R = 0.0821

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$(i) \ x=1, y=2; (ii) \ x=2, y=1$

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(A) The relationship between $K_p$ and $K_c$ is given by $K_p = K_c(RT)^{\Delta n_g}$, where $\Delta n_g = y - x$ and $T = 400 \ K$. Here, $R = 0.0821 \ L \ atm \ K^{-1} \ mol^{-1}$.For $(i)$: $85.87 = 2.586 	imes (0.0821 	imes 400)^{\Delta n_g} \implies 33.2 = (32.84)^{\Delta n_g} \implies \Delta n_g \approx 1$. Thus, $y - x = 1$.For $(ii)$: $0.862 = 28.62 	imes (32.84)^{\Delta n_g} \implies 0.0301 = (32.84)^{\Delta n_g} \implies \Delta n_g \approx -1$. Thus, $y - x = -1$.Comparing with the options, for $(i)$, $x=1, y=2$ gives $\Delta n_g = 1$. For $(ii)$, $x=2, y=1$ gives $\Delta n_g = -1$.

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