An equilibrium mixture of PCl5(g), PCl3(g), and Cl2(g) has partial pressures of 217.0 Torr, 13.2 Torr, and 13.2 Torr, respectively. A quantity of Cl2(g) is injected into the mixture, and the total pressure jumps to 263.0 Torr at the moment of mixing. The system then re-equilibrates. The chemical equation for this reaction is

p'PCl3 =  6.8 torr

p'Cl2 =26.4 torr

p'PCl5 =223.4 torr

Explanation:

An equilibrium mixture of PCl5(g), PCl3(g), and Cl2(g) has partial pressures of 217.0 Torr, 13.2 Torr, and 13.2 Torr, respectively. A quantity of Cl2(g) is injected into the mixture, and the total pressure jumps to 263.0 Torr at the moment of mixing. The system then re-equilibrates. The chemical equation for this reaction is

PCl3(g) + Cl2(g) ---> PCl5(g)

Calculate the new partial pressures after equilibrium is reestablished. [in torr]

pPCl3

pCl2

pPCl5

Step 1: Data given

Partial pressure before adding chlorine gas:

Partial pressure of PCl5 = 217.0 torr

Partial pressureof PCl3 = 13.2 torr

Partial pressureof Cl2 = 13.2 torr

A quantity of Cl2(g) is injected into the mixture, and the total pressure jumps to 263.0 Torr at the moment of mixing

Step 2: The equation

PCl3(g)+Cl2(g) ⇔ PCl5(g)

Step 3: The expression of an equilibrium constant before adding chlorine gas

Kp = pPCl5 / (pPCl3 * pCl2)

Kp = 217.0 / (13.2 * 13.2)

Kp =  1.245

Step 4:  The expression of an equilibrium constant after adding chlorine gas

Partial pressure of PCl5 = 217.0 torr

Partial pressure of PCl3 = 13.2

Partial pressure of Cl2 = TO BE DETERMINED

Step 5: The total pressure of the system

Ptotal = pPCl5 + pPCl3 + pCl2

263.0 torr = 217.0 torr + 13.2 torr + pCl2

pCl2 = 263.0 - 217.0 -13.2 = 32.8 torr

Step 6: The initial pressure

The equation: PCl3(g)+Cl2(g) ⇔ PCl5(g)

pPCl3 = 13.2 torr

pCl2 = 32.8 torr

pPCl5 = 217.0 torr

Step 7: The pressure at the equilibrium

p'PCl3 = (13.2 -x) torr

p'Cl2 = (32.8 - x) torr

p'PCl5 = (217.0 + x) torr

Step 8: The equilibrium constant

'Kp =  p'PCl5 / (p'PCl3 * p'Cl2)

1.245 = (217.0+x) / ((13.2-x)(32.8-x)

x = 6.40 torr

p'PCl3 = 13.2 -6.40 = 6.8 torr

p'Cl2 = 32.8 - 6.40 =26.4 torr

p'PCl5 = 217.0 + x) 6.4 = 223.4 torr