Botany2 mole each of A and B are allowed to react to attain the following equilibrium in a 1L vessel 2Ag + Bg⇌A2Bg . At equilibrium 0.5 mole of A2B is formed. The value of Kc for the decomposition of A2B is

$2 mole each of A and B are allowed to react to attain the following equilibrium in a 1 L vessel 2 A_{(g)} + B_{(g)} ⇌ A_{2} B_{(g)} . At equilibrium 0.5 mole of A_{2} B is formed . The value of Kc for the decomposition of A_{2} B is$

A
$\frac{1}{3} \frac{{lit}^{2}}{{mole}^{2}}$
B
$1 \frac{mole}{lit}$
C
$3 \frac{{mole}^{2}}{{lit}^{2}}$
D
$2 \frac{mole}{lit}$

Solution:

$2 A + B ⇌ A_{2} B [Δn = 1 - 3 = - 2] 2 2 0 2 - 2 x 2 - x x [as x = 0.5] 1 1.5 0.5 K_{c} = \frac{0.5}{1^{2} \times 1.5} = \frac{1}{3} {lit}^{2} {mole}^{- 2} ∴ K_{c} (Re verse) = 3 {mole}^{2} / {lit}^{2}$