2 mole each of A and B are heated in a 1L vessel to establish an equilibrium $\left[2{\mathrm{A}}_{\left(\mathrm{g}\right)}+{\mathrm{B}}_{\left(\mathrm{g}\right)}\stackrel{ }{\rightleftharpoons }{\mathrm{A}}_2{\mathrm{B}}_{\left(\mathrm{g}\right)}\right]$ at equilibrium 0.5 mole of A2B is formed, the value of k_c for the above equilibrium. [Only magnitude] 

Equilibrium Question

Reaction: 2A(g) + B(g) ⇌ A₂B(g)

Initial moles in 1 L vessel: [A] = 2 M, [B] = 2 M, [A₂B] = 0.

At equilibrium, 0.5 mol of A₂B is formed.

Consumption based on stoichiometry:

• A decreases by 1.0 M → [A] = 1.0 M
• B decreases by 0.5 M → [B] = 1.5 M
• A₂B formed = 0.5 M

Equilibrium expression: 
Kc = [A₂B] / ([A]² × [B])

Substitute values: 
Kc = 0.5 / (1.0² × 1.5) = 0.5 / 1.5 = 1/3

Final Answer: Kc = 1/3