For N2(g) + 3H2(g) 2NH3(g), K_c = 0.50 L^2 mol^-2 at 700 K. For 1/2 N2(g) + 3/2 H2(g) NH3(g) at the same temperature, K_p in atm^-1 is (use R = 0.0821 L atm mol^-1 K^-1)

JEE Main levelSingle correct optionDifficulty 2 of 3ce076

For $N X_{2} (g) + 3 H X_{2} (g) 2 NH X_{3} (g)$ , $K_{c} = 0.50 L^{2} mo l^{- 2}$ at 700 K. For $\frac{1}{2} N X_{2} (g) + \frac{3}{2} H X_{2} (g) NH X_{3} (g)$ at the same temperature, $K_{p}$ in $at m^{- 1}$ is (use $R = 0.0821 L atm mo l^{- 1} K^{- 1}$ )

Halving the equation takes the square root:

K_{c}^{'} = 0.50 = 0.7071

. For the new reaction

Δ n = 1 - 2 = - 1

, so

K_{p}^{'} = K_{c}^{'} / (RT) = 0.7071/57.47 = 1.23 \times 1 0^{- 2} at m^{- 1}