In the reaction 2SO_2(g) + O_2(g)$\rightleftharpoons$2SO_3(g), 2 moles of SO₂ ,1 mole of O₂ and 2 moles of SO₃ are present in equilibrium. what is the number of moles of O₂ be introduced into the vessel to increase the equilibrium moles of SO₃ to 3 moles

Following is the given equilibrium,

The volume of the container is not given let us assume it to be 1 lit

Let the moles of O₂ to be introduced so that the moles of SO₃ becomes 3 at equilibrium be x.

Again,

	2SO2	+O2		2SO3(g)
t = teq	2-2y			2 +2 y

Now, 2 +2 y = 3 ⇒ y = $\frac{1}{2}$   and at same temperature K_C remains constant, equating both K_c  values