For the reaction,
Kp = 0.200
initial,
PCl3 = Cl2 = 0.5 atm
PCl5 = 0.3 atm
ICE chart
          Â
PCl3(g) + Cl2(g) <==> PCl5(g)
IÂ Â Â Â Â Â Â Â Â Â Â Â
0.5Â Â Â Â Â Â Â Â Â
0.5Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.3
CÂ Â Â Â Â Â Â Â Â Â
-x          Â
-x                Â
+x
EÂ Â Â Â Â Â Â Â Â
0.5-x    Â
0.5-x           Â
0.3+x
So,
Kp = [PCl5]/[PCl3][Cl2]
0.200 = (0.3+x)/(0.5-x)(0.5-x)
0.05 - 0.2x + 0.2x^2 = 0.3 + x
0.2x^2 - 1.2x - 0.25 = 0
x = -0.2025 atm
at equilibrium,
partial pressure of PCl3 = 0.5 + 0.2025 = 0.702 atm
partial pressure of Cl2 = 0.5 + 0.2025 = 0.702 atm
partial pressure of PCl5 = 0.3 - 0.2025 = 0.097 atm
