In: Chemistry
For the exothermic reaction
PCl3(g)+Cl2(g)?PCl5(g)
Kp = 0.200 at a certain temperature.
A flask is charged with 0.500 atm PCl3 , 0.500 atm Cl2, and 0.300 atm PCl5 at this temperature.
What are the equilibrium partial pressures of PCl3 , Cl2, and PCl5, respectively?
Express your answers numerically in atmospheres with three digits after the decimal point, separated by commas.
For the reaction,
Kp = 0.200
initial,
PCl3 = Cl2 = 0.5 atm
PCl5 = 0.3 atm
ICE chart
PCl3(g) + Cl2(g) <==> PCl5(g)
I 0.5 0.5 0.3
C -x -x +x
E 0.5-x 0.5-x 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