Chemical Equilibrium Problem

[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.

 

[DeeNos]

3 mole/L

As a scientist, it is important to understand the concept of chemical equilibrium and how to solve problems related to it. In this problem, we are given the equilibrium constant (Kc) for a gaseous reaction and are asked to calculate the concentration of CO at equilibrium. To solve this problem, we need to make a few assumptions and use the given information.

Firstly, we can assume that the reaction is in a closed system and the volume remains constant. This means that the total number of moles of gas (CO and O2) remains constant throughout the reaction.

Next, we can use the given information to set up an equilibrium expression, which in this case is Kc=x^2/(1-x)^2(1-x/2)=5000. This expression is based on the stoichiometry of the reaction and the fact that the equilibrium constant is equal to the ratio of the products to the reactants at equilibrium.

To solve for x, we can use the quadratic formula or use an online calculator. The result will be x=0.0143 mole, which is the number of moles of CO2 produced at equilibrium.

Since the initial number of moles of CO and O2 were equal (1 mole each), we can assume that half of the CO molecules dissociated to form CO2 at equilibrium. This means that the concentration of CO at equilibrium is 0.0143 mole/L, as stated in the answer.

In conclusion, by making the appropriate assumptions and using the given information, we can calculate the concentration of CO at equilibrium in this chemical equilibrium problem.