How Do You Calculate CO Concentration at Equilibrium in a Gaseous Reaction?

[zorro]

Homework Statement

At a certain temperature, the equilibrium constant for the gaseous reaction of CO with O2 to produce CO2 is 5000 lit/mole. Calculate [CO] at equilibrium, if 1 mol each of CO and O2 afre placed in a 2 L vessel and allowed to come to equilibrium.

Homework Equations

The Attempt at a Solution

Concentration at equilibrium
CO= 1-x
O2= 1-x/2
CO2=x where x is the no of moles dissociated

Kc=x^2/(1-x)^2(1-x/2)=5000

I don't understand what assumption I should make to solve this.
answer is [CO]= 0.014

 

[Borek]

I have not tried to solve, so it is possible there will be some more hurdles, but first step is more or less obvious - equilibrium is shifted far to the right, so amount of product is almost stoichiometric.

I have a gut feeling that it will be better to approach the question from the other end - assume you started with 1 mole of CO₂ and half mole of oxygen. x will be very small then and approximations will be much more obvious.

 

[zorro]

As you said I took 1 mole CO2 and half mole O2
and got x value as 0.058 (moles of CO)
But how do we relate this the problem (1 mole CO and 1 mole O2)

 

[Borek]

Through stoichiometry. If total amount of substances present is identical, it doesn't matter if you start with products or reactants, equilibrium is the same.