A reaction A₂(g) + B₂(g) 2AB(g) is carried out in a 1 L flask. At equilibrium at temperature T , the number of moles of A₂(g) , B₂(g) , and AB(g) are found to be 2, 2, and 4 mol respectively. Under this condition, x mol of AB(g) is added to the flask and the temperature is maintained at T . When the new equilibrium is established, the number of moles of A₂(g) in the flask is found to be 3 mol. The value of x is ____.

Step-by-step solution

The equilibrium constant for the reaction A₂(g) + B₂(g) 2AB(g) is calculated from the initial equilibrium state: K_c = [AB]^2 [A₂][B₂] = 4^2 2 2 = 4 When x mol of AB(g) is added, the system shifts backward to reach a new equilibrium. The new equilibrium moles of A₂(g) is given as 3 mol, which is an increase of 1 mol from its initial equilibrium value of 2 mol. According to the stoichiometry of the reaction, if A₂(g) increases by 1 mol, B₂(g) also increases by 1 mol, and AB(g) must decrease by 2 mol. Therefore, at t