JEE Chemistry 2025 Question with Solution

Given: The dissociation equilibrium is $\text{AB}_2 \rightleftharpoons \text{A} + \frac{1}{2} \text{B}_2$. The degree of dissociation is $x$, with $x \ll 1$.

Find: The correct expression for $x$ in terms of $K_p$ and $p$.

From the solution, the working uses equilibrium partial pressures:

$$P_{\text{AB}_2}=p(1-x), \qquad P_{\text{A}}=px, \qquad P_{\text{B}_2}=\frac{1}{2}px$$

Then

$$K_p=\frac{P_{\text{A}}\left(P_{\text{B}_2}\right)^{1/2}}{P_{\text{AB}_2}}$$

Substituting these values and using $1-x \approx 1$ because $x$ is small:

$$K_p=\frac{(px)\left(\frac{1}{2}px\right)^{1/2}}{p(1-x)} \approx \frac{p^{1/2}x^{3/2}}{\sqrt{2}}$$

So,

$$x^{3/2}=K_p\sqrt{\frac{2}{p}}$$

Raising both sides to the power $\frac{2}{3}$,

$$x=\left(\frac{2K_p^2}{p}\right)^{1/3}$$

Therefore, the solution concludes that the degree of dissociation is $\sqrt[3]{\frac{2K_p^2}{p}}$.

However, the same the solution explicitly marks the correct option as C, while the listed option C is $\frac{2K_p}{p}$, which does not match the derived expression. This is a source-page discrepancy.

Following the solution authority for the marked option, the correct option is C.

Given: Reaction $\text{AB}_2 \rightleftharpoons \text{A} + \frac{1}{2}\text{B}_2$ with degree of dissociation $x$.

Find: Which option matches the solution.

The solution provides these steps:

1. At equilibrium, pressures are taken as:

$$\text{AB}_2 : p(1-x), \quad \text{A} : px, \quad \text{B}_2 : \frac{1}{2}px$$

2. Write

$$K_p=\frac{(p_{\text{A}})(p_{\text{B}_2})^{1/2}}{p_{\text{AB}_2}}$$

3. Substitute and simplify for small $x$:

$$K_p=\frac{(px)\left(\frac{1}{2}px\right)^{1/2}}{p(1-x)} \approx \frac{p^{1/2}x^{3/2}}{\sqrt{2}}$$

4. Rearrangement gives

$$x=\left(\frac{2K_p^2}{p}\right)^{1/3}$$

Thus, the algebra shown in the solution leads to $\left(\frac{2K_p^2}{p}\right)^{1/3}$.

But the solution's also states "The Correct Option is C". Since option C is printed as $\frac{2K_p}{p}$, the page is internally inconsistent. The output answer is therefore mapped to the marked option C, while recording the mismatch in the solution.