The value of `K_(c)` for the reaction, `N_(2)(g) +2O _2(g) harr2NO_(2)(g)` at a certain temperature is `400`. Calculate the value of equilibrium constant for.
(i) `2NO_(2)(g)harrN_(2)(g)+2O_(2)(g)`, (ii) `1//2N_(2)(g)+O_(2)(g)harrNO_(2)(g)`

Explanation

To solve the problem, we need to calculate the equilibrium constants for two different reactions based on the provided equilibrium constant \( K_c \) for the reaction \( N_2(g) + 2O_2(g) \rightleftharpoons 2NO_2(g) \) with \( K_c = 400 \).

### Step 1: Determine the equilibrium constant for the reverse reaction

The first reaction we need to consider is the reverse of the original reaction:

\[
2NO_2(g) \rightleftharpoons N_2(g) + 2O_2(g)
...