For the reactions, `N_(2(g))+3H_(2(g))hArr2NH_(3(g))`. At `400 K`, `K_(p)=41 atm^(-2)`. Find the value of `K_(p)` for each of the following reactions at the same temperature:
(`i`) `2NH_(3(g))hArrN_(2(g))+3H_(2(g))`,
(`ii`) `(1)/(2)N_(2(g))+(3)/(2)H_(2(g))hArrNH_(3(g))`,
(`iii`) `2N_(2(g))+6H_(2(g))hArr4NH_(3(g))`

Explanation

To solve the problem, we will use the equilibrium constant \( K_p \) for the given reaction and apply the principles of equilibrium constants to find the values for the other reactions.

### Given Reaction:
1. \( N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \) with \( K_p = 41 \, \text{atm}^{-2} \) at \( 400 \, K \).

### (i) For the reaction:
\[ 2NH_3(g) \rightleftharpoons N_2(g) + 3H_2(g) \]

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