Pressure and concentration equilibria

[vipertongn]

1. COCl2(g) D CO(g) + Cl2(g) Kp = 6.8 x 10-9 at 100oC

What will be the equilibrium concentrations of all 3 gases if 1.0 atm of phosgene (COCl2) is placed into 5.0L reaction vessel?

The answer is

[COCl2]eq = 0.033M
[CO]eq = [Cl2]eq = 2.69 x 10-10M


I don't get how the second one is solved. I used this method

I found out it's going towards the products because the reactant is decomposing and there is no products yet to be in equilibrium

Finding initial 1 -> 0 + 0
Finding the amount taken out -x +x +x

I can use the assumption method to assume that since Kp is sooo small x can be ignored for 1-x so...

Kp= x^2/1

Also since it can be ignored i assumed that the equilibrium pressure for phosgene is 1 and then i used C=P/RT to get 0.033.

However! for the concentrations of the products I can't seem to get them at all!

I tried converting Kp to Kc --> Kc=Kp(RT)^-delta (n)

delta(n)=2-1=1 so its Kc= Kp/RT which equals 2.27e-10.

So I tried doing products/reactants=Kc

but (2.69 x 10-10)^2/0.033 does NOT equal 2.27e-10 so I'm lost to where I went wrong with this equation...

 

[chemisttree]

So, in the denominator you think that the 'x' (1-x in your analysis) is small enough to be ignored but you want to assume it is there in the numerator. I'm afraid you are going to have to do a complete solution. 'Complete' means that 1-x is not equal to 1.

You can make that assumption (x=0) when you are only using two significant figures to denote the phoshene concentration but you can't if you ever want to actually calculate 'x'.