Equilibrium involving SO2(g), O2(g) & SO3(g) is important in sulfuric acid production. When a 0.0200 mol sample of SO3 is introduced into an evacuated 1.52 L vessel at 900 K, 0.0142 mol, SO3 is found to be present at equilibrium. What is the value of Kp for the dissociation of SO3(g) at 900 K?

Answer 1

Use PV = nRT and solve for pSO3 at the beginning and at equilibrium. I obtained about 1 for pSO3 initially but you need to get a more accurate answer.
Then
..........2SO3 ==> 2SO2 + O2
I.........1.0.......0......0
C.........-2x.......2x.....x
E........1.0-2x.....2x.....s

The problem tells you that 1.0-2x (or whatever more accurate answer you get for that 1.0 number) = pSO3 at equilibrium. You get that number from the 0.142 mol and PV = nRT.
Evaluate each equilibrium value from above and substitute into the Kp expression. Solve for Kp.

Answer 2

0.236