Question

The system described by the reaction
CO(g)+Cl2(g)⇌COCl2(g)
is at equilibrium at a given temperature when PCO= 0.29 atm , PCl2= 0.12 atm , and PCOCl2= 0.62 atm . An additional pressure of Cl2(g)= 0.38 atm is added.

Find the pressure of CO when the system returns to equilibrium

Answer 1

CO(g)+Cl2(g)⇌COCl2(g)

To solve this problem you have to first determine the concentrations at time 0, before the system has a chance to attain equilibrium:

P(CO) = 0.29 atm
P(Cl2) = 0.12 + 0.38 atm = 0.50 atm
P(OCCl2) = 0.62 atm

Since you have more Cl2 than it is required at equilibrium, the reaction will proceed towards the product side diminishing the amounts of Cl2 and CO and increasing the amount of phosgene (OCCl2). Therefore, at equilibrium the concentrations should be:

P(CO) = 0.29 - x
P(Cl2) = 0.50 - x
P(OCCl2) = 0.62 + x

You can write the equilibrium expression for this system:

K = [P(COCl2)]/{[P(CO)][P(Cl2)]}

Since you know the concentrations at equilibrium (before adding more Cl2) you know what the K value is:

K = (0.62 atm)/{(0.29 atm)(0.12 atm)} = 17.82

Using this value and our expressions for the new pressures at equilibrium gives:

17.82 = (0.62 + x)/{(0.29 -x)(0.50 - x)}

Multiplying both sides by the denominator results in:

17.82 (0.29 - x) (0.50 - x) = 0.62 + x

17.82x² -15.08x +1.96 = 0

You can use the quadratic formula to solve this polynomial. The answer you get is:

x = 0.69 or 0.16

However, since you can't possibly have negative reagents, the only answer that physically and chemically makes sense is 0.16. Therefore, the pressures at equilibrium are:

P(CO) = 0.29 - x = 0.29 - 0.16 = 0.13 atm
P(Cl2) = 0.50 - x = 0.50 - 0.16 = 0.34 atm
P(COCl2) = 0.62 + x = 0.62 + 0.16 = 0.78 atm