For the following gas phase equilibrium reaction at constant temperature, NH 3 ( g ) rightleftharpoons 1/2 N 2 ( g )+3/2 H 2 ( g ) If the total pressure is √(3) atm and the pressure equilibrium constant ( K p ) is 9 atm , then the degree of dissociation is given as ( x × 10 -2 ) -1 / 2 . The value of x is \ \ \ \ (Nearest integer)

Chemistry · Chemical Equilibrium

JEE Main 2026 — 23 January, Morning Shift — Question 67

For the following gas phase equilibrium reaction at constant temperature, $\mathrm{NH}_{3}(\mathrm{~g}) \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{3}{2} \mathrm{H}_{2}(\mathrm{~g})$ If the total pressure is $\sqrt{3} \mathrm{~atm}$ and the pressure equilibrium constant $\left(\mathrm{K}_{\mathrm{p}}\right)$ is 9 atm , then the degree of dissociation is given as $\left(\mathrm{x} \times 10^{-2}\right)^{-1 / 2}$ . The value of $x$ is $\_\_\_\_$ (Nearest integer)

Answer: 125

Numerical answer — enter this value.

Step-by-step solution

\mathrm{NH_3(g)} \;\rightleftharpoons\; \frac{1}{2}\,\mathrm{N_2(g)} + \frac{3}{2}\,\mathrm{H_2(g)}

\begin{array}{c|ccc} & \mathrm{NH_3} & \mathrm{N_2} & \mathrm{H_2} \\ \hline t = 0 & 1\,\text{mole} & - & - \\ t = t_{\mathrm{eq}} & 1-\alpha & \dfrac{\alpha}{2} & \dfrac{3\alpha}{2} \end{array}

K_p = \frac{\left(\dfrac{\alpha}{2}\right)^{1/2} \left(\dfrac{3\alpha}{2}\right)^{3/2}} {(1-\alpha)} \left[\frac{P_T}{1+\alpha}\right]^{-1} \qquad \left[\therefore P_T = \sqrt{3}\,\text{atm}\right]

9 = \frac{\left(\dfrac{\alpha}{2}\right)^{1/2} \left(\dfrac{3\alpha}{2}\right)^{3/2}} {(1-\alpha)} \times \frac{(3)^{1/2}}{1+\alpha}

9 = \frac{9\left(\dfrac{\alpha}{2}\right)^2}{1-\alpha^2}

1 - \alpha^2 = \frac{\alpha^2}{4}

\frac{5\alpha^2}{4} = 1

\alpha^2 = 0.8

\alpha = (0.8)^{1/2}

\alpha = \left[\frac{1}{0.8}\right]^{-1/2}

\alpha = \left[125 \times 10^{-2}\right]^{1/2}

x = 125

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 23 January, Morning Shift
Subject: Chemistry
Chapter: Chemical Equilibrium
Topic: Factors affecting equilibrium &Le Chatelier's Principle

Consider the general reaction given below at 400 K xA( g) leftharpoons yB( g) The values of K p and K c are studied under the same…

Answer: 125

Step-by-step solution

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