For the reaction: CO(g) + H2O(g) ⇌ CO2(g) + H2(g) the value of Kc is 1.845 at a specific temperature. We place 0.500mol CO and 0.500mol H2O in a 1.00L container at this temperature and allow the reaction to reach equilibrium. Determine the equilibrium concentration of all species present in the container.

Explanation:

In the equilibrium:

CO(g) + H₂O(g) ⇄ CO₂(g) + H₂(g)

Kc is:

Kc = 1.845 = [CO₂] [H₂] / [CO] [H₂O]

Where [] are equilibrium concentrations of each species

Initial concentrations:

[CO] = 0.500mol / 1.00L = 0.500M

[H₂O] = 0.500mol / 1.00L = 0.500M

In equilibrium, concentrations will be:

[CO] = 0.500M - X

[H₂O] = 0.500M - X

[CO₂] = X

[H₂] = X

Where X is reaction coordinate. The amount of reactant that reacts producing products.

Replacing in Kc expression:

1.845 = [CO₂] [H₂] / [CO] [H₂O]

1.845 = [X] [X] / [0.500M - X] [0.500M - X]

1.845 = X² / X² - X + 0.25

1.845X² - 1.845X + 0.46125 = X²

0.845X² - 1.845X + 0.46125 = 0

Solving for X:

X = 0.288M; Right solution

X = 1.9M; False solution: Produce negative concentrations.

Replacing, equilibrium concentrations are:

[CO] = 0.500M - X = 0.212M

[H₂O] = 0.500M - X = 0.212M

[CO₂] = X = 0.288M

[H₂] = X = 0.288M

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