At a certain temperature, K_c = 1.6 x 10^-3 for N2(g) + O2(g) 2NO(g) and K_c = 2.5 x 10^2 for 2NO(g) + O2(g) 2NO2(g). What is K_c at this temperature for NO2(g) 1/2N2(g) + O2(g)?

JEE Advanced levelSingle correct optionDifficulty 3 of 3ce036

At a certain temperature, $K_{c} = 1.6 \times 1 0^{- 3}$ for $N X_{2} (g) + O X_{2} (g) 2 NO (g)$ and $K_{c} = 2.5 \times 1 0^{2}$ for $2 NO (g) + O X_{2} (g) 2 NO X_{2} (g)$ . What is $K_{c}$ at this temperature for $NO X_{2} (g) \frac{1}{2} N X_{2} (g) + O X_{2} (g)$ ?

Adding the two given reactions gives

N X_{2} + 2 O X_{2} 2 NO X_{2}

with

K = K_{1} K_{2} = 0.40

. For

NO X_{2} \frac{1}{2} N X_{2} + O X_{2}

, reverse the reaction and halve the coefficients:

K_{c} = (K_{1} K_{2})^{- 1/2} = (0.40)^{- 1/2} = 1.58