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'.

 

[Blueshift5]

I can understand your confusion and I would like to help clarify your understanding of pressure and concentration equilibria. First, it is important to note that the equilibrium constant, Kp, is a measure of the equilibrium concentrations of gases based on their partial pressures. This means that Kp is not directly related to the actual concentrations of the gases, but rather the ratio of their partial pressures at equilibrium.

Now, let's look at the given reaction: COCl2(g) ⇌ CO(g) + Cl2(g). The equilibrium constant, Kp, is given as 6.8 x 10^-9 at 100°C. This means that at equilibrium, the ratio of the partial pressures of CO and Cl2 to the partial pressure of COCl2 is 6.8 x 10^-9. In other words, the equilibrium concentration of CO and Cl2 will be very small compared to the concentration of COCl2.

Now, let's look at how to solve for the equilibrium concentrations of all three gases. We are given that 1.0 atm of phosgene (COCl2) is placed into a 5.0L reaction vessel. This means that the initial partial pressure of COCl2 is 1.0 atm. Using the ideal gas law, we can calculate the initial concentration of COCl2 as 1.0 atm / (0.0821 L atm/mol K * 373 K) = 0.033 M.

To solve for the equilibrium concentrations of CO and Cl2, we can use the equilibrium constant expression: Kp = (PCO * PCl2) / (PCOCl2). Since we know that the initial partial pressure of COCl2 is 1.0 atm and the equilibrium constant, Kp, is 6.8 x 10^-9, we can set up the following equation:

6.8 x 10^-9 = (PCO * PCl2) / 1.0

We also know that at equilibrium, the partial pressures of CO and Cl2 will be equal, so we can substitute P for both gases with the same variable, x. This gives us:

6.8 x 10^-9 = (x * x) / 1.0

Solving for x, we get x = 2.6 x 10^-5. Since the partial pressure is equal to the concentration in moles