Explanation

For a gaseous equilibrium reaction,

$$ K_p = K_c (RT)^{\Delta n} $$

where

$$ \Delta n = y - x $$

At $T = 400\,\text{K}$ and $R = 0.082$,

$$ RT = 0.082 \times 400 = 32.8 $$

For case (i),

$$ \frac{K_p}{K_c} = \frac{85.87}{2.586} \approx 33.2 $$

$$ (RT)^{\Delta n} \approx 32.8 $$

This implies,

$$ \Delta n = +1 $$

Hence,

$$ y - x = 1 \Rightarrow (x,y) = (1,2) $$

For case (ii),

$$ \frac{K_p}{K_c} = \frac{0.862}{28.62} \approx 0.03 $$

$$ (RT)^{-1} \approx \frac{1}{32.8} $$

So,

$$ \Delta n = -1 $$

$$ y - x = -1 \Rightarrow (x,y) = (2,1) $$

Therefore, the correct values are

$$ \boxed{(i)\ 1,2 \quad (ii)\ 2,1} $$

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