QJEEM20Ch909e: JEE Main 2020 Chemistry - Class 11 JEEM20Ch909e Solution: For the reaction Fe 2 N(s) + 3 2 H 2 (g) ⇌ 2Fe(s) + NH 3 (g)

To determine the correct relationship between the equilibrium constants $K_C$ and $K_p$ for the reaction:

$${\text{Fe}}_2\text{N(s)}+\frac{3}{2}{\text{H}}_2\text{(g)}\rightleftharpoons 2\text{Fe(s)}+{\text{NH}}_3\text{(g)}$$

First, consider the general relationship between $K_C$ and $K_p$ :

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

where $\Delta n$ is the change in the number of moles of gas between the products and the reactants, $R$ is the ideal gas constant, and $T$ is the temperature in Kelvin.

For the given reaction, calculate $\Delta n$ :

Moles of gas in products: NH_3(g) = 1 mole

Moles of gas in reactants: $$\frac{3}{2}$$ H_2(g) = 1.5 moles

Therefore:

$$\mathrm{\Delta }n=1-1.5=-0.5$$

Substitute this value into the equation relating $K_C$ and $K_p$ :

$$K_p=K_C(RT{)}^{-0.5}$$

Rearrange to express $K_C$ :

$$K_C=K_p(RT{)}^{0.5}$$

Thus, the correct option is:

Option A: $$K_C=K_p(RT{)}^{1/2}$$