JEE Main 2020 — Chemical Equilibrium Question with Solution

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 $K_p$:

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

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:

$$\Delta n=1-1.5=-0.5$$

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