Answer:
1) p(PCl3) = 0.66 atm
2) p(Cl2) = 0.66 atm
3) p(PCl5) = 0.038 atm
Step-by-step explanation:
Step 1: Data given
Kp = 0.0870
Temperature = 300 °C
Pressure of PCl3 = 0.50 atm
Pressure of Cl2 = 0.50 atm
Pressure of PCl5 = 0.20 atm
Step 2: The balanced equation
PCl3(g) + Cl2(g) ⇆ PCl5(g)
Step 3: The pressure at equilibrium
p = [PCl5] / [PCl3] [Cl2]
Q = [0.20] / [0.50] [0.50] = 0.8
Q >> Kp
The reaction will shift to the left to decrease the numerator PCl5
p(PCl3) = (0.50 + x) atm
p(Cl2) = (0.50 + x) atm
p(PCl5) = (0.20 - x) atm
Kp = (pPCl5) / (pPCl3) (pCl2)
0.0870 = (0.20-x) / (0.50+x) (0.50+x)
0.0870 (0.50+x)(0.50+x) = (0.20-x)
0.0870 (0.25 + 1.0x + x²)= (0.20-x)
0.02175 + 0.087x + 0.087x² = 0.2 -x
0.087x² + 1.087x -0.17825 = 0
x= 0.1619
Step 4: The equilibrium partial pressures
p(PCl3) = (0.50 + x) atm = 0.50 + 0.1619 = 0.6619 atm
p(Cl2) = (0.50 + x) atm = 0.50 + 0.1619 = 0.6619 atm
p(PCl5) = (0.20 - x) atm = 0.20 - 0.1619 = 0.0381 atm