Explanation:
To solve this problem, we can use the ICE table method.
Given:
- Initial moles of CO2 = 2.0 moles
- Initial volume of the vessel = 5.0 L
- Initial concentrations: [CO2] = 2.0 moles / 5.0 L = 0.4 M
- Initial concentrations of CO and O2 are both 0 M
Now, let's define the change in concentration as x (since 2 moles of CO2 produce 2 moles of CO and 1 mole of O2):
The reaction is: 2CO2(g) -> 2CO(g) + O2(g)
Using the stoichiometry, the change in concentration for CO and O2 is 2x, and for CO2, it's -2x.
So, at equilibrium:
[CO2] = 0.4 - 2x
[CO] = 2x
[O2] = x
Now, we can set up the equilibrium expression using the given equilibrium constant:
K = [CO]^2 * [O2] / [CO2]^2
= (2x)^2 * (x) / (0.4 - 2x)^2
Substitute the value of K (2.0 x 10^-6) and solve for x. This will give us the equilibrium concentrations of all species.
Once you find the value of x, you can substitute it back into the equilibrium expressions to find the equilibrium concentrations of CO2, CO, and O2.
