What is the percent dissociation of COCl2, α if the total pressure of the equilibrium mixture is 30.7 atm?

Question

Phosgene gas, COCl2, dissociates to form carbon monoxide and chlorine.

COCl2(g) ↔ CO(g) + Cl2 (g)

A 0.80 mol sample of COCl2 (g) dissociates in a 1.0 dm3

flask at 420K. At equilibrium,

22.5% of COCl2 (g) has dissociated.

What is the percent dissociation of COCl2, α if the total pressure of the equilibrium

mixture is 30.7 atm?

Answer 1

First you can start off by putting up some important equations especially as it relates to equilibrium and the ideal gas laws. One important one is:

PV=nRT

Using this equation, you have to use the correct R constant related to the units in the problem.

We have

temperature in K, 420K

Pressure which was given in atm, 30.7 atm

volume in dm^3 but we will convert this to cm^3 and therefore mL because an mL is equivalent to a cm^3, and then we can take it from mL to L, for the purposes of the equation.

So the R constant will be 0.082057 L*atm/mol*K

you can take your volume given in the problem and use the equivalencies to get units to cancel until you have L or Liters:

1dm = 10cm

1dm^3= 10cm^3 = 10mL

Then take it to Liters

1 Liter = 1000mL

10mL x (1L/1000mL) mL cancels mL top to bottom and you are left with L, Liters. You can plug this into the equation.

0.01 L

PV=nRT

(30.7atmx0.01L)=n(0.082057L*atm/mol*K)420K

n= (30.7atmx0.01L)/

(0.082057L*atm/mol*K)420K

n= 0.008907861

So now that you have the moles that are related to the atmospheric pressure of phosgene gas, COCl2, at 30.7atm

and you know that in the problem you were given a sample of 0.80 mol of this gas

and that the percent disociation for this was 22.5% or 0.225 decimal,

You can set up a ratio to figure out what the new moles will yield: The properties of the gas did not change and we are at equilibrium.

0.80 mol = 0.225

0.008907861 mol= X

cross multipy divide and solve for X

X(0.80 mol) =0.225(0.008907861)

X= 0.002004268725/0.80

X= 0.0025053

this is the decimal form, multiply by 100 and you will have the percentage

0.0025053 X 100 = 0.251%