Calculate the value of Kp for this system.?

Question

At 25°C, gaseous SO2Cl2 decomposes to SO2(g) and Cl2(g) to the extent that 12.5% of the original SO2Cl2 (by moles) has decomposed to reach equilibrium. The total pressure (at equilibrium) is 0.900 atm. Calculate the value of Kp for this system.

Answer 1

SO2Cl2 =SO2(g) + Cl2(g)

Initially

mol SO2Cl2 = x

mol SO2 and mol Cl2 = 0

12.5%x mol SO2Cl2 decomposes to form 12.5%x mol SO2 and 12.5%x mol Cl2

At equilibrium

mol SO2Cl2 = x - 12.5%x = 87.5%x

mol Cl2 = 12.5%x

mol SO2 = 12.5%x

Kp = P(SO2) . P(Cl2) / P(SO2Cl2)

total mol gases at equil. = (87.5%x)+(12.5%x)+(12.5%x)=112.5%x

P(SO2) = 12.5%x / 112.5%x * 0.9 = 0.1

P(Cl2) = 12.5%x / 112.5%x * 0.9 = 0.1

P(SO2Cl2) = 87.5%x / 112.5%x * 0.9 = 0.864

Therefore Kp = 0.1^2 / 0.864 = 0.01157 atm