Consider the reaction CO(g)+ H₂O(g)⇌CO₂(g)+ H₂(g), represented by the following diagram: What is the composition of this system when the reaction reaches equilibrium?

Question

Quizplus · Accepted Answer

According to the law of mass action, at equilibrium the ratio of the products to reactants is equal to the equilibrium constant (Kc). In this case, the equilibrium constant expression would be Kc = [COS]^2[HSO]^2/[CO]^3[HSO][O]. The stoichiometry of the reaction tells us that for every 1 CO and 1 HSO consumed, 1 COS and 1 HSO are produced. Therefore, if x is the amount of CO and HSO consumed at equilibrium, then the amount of COS and HSO produced would also be x. The amount of O consumed would be 0.5x (since the coefficient of O is 0.5 in the balanced equation). Thus, at equilibrium, we have:

[CO] = 2x (since we initially have 3 CO and x is consumed)
[HSO] = 2x (since we initially have 3 HSO and x is consumed)
[O] = 0.5(3-x) = 1.5 - 0.5x
[COS] = 2x (since x is produced)

Substituting these values into the equilibrium constant expression gives:

Kc = (2x)^2(2x)^2 / (2x)^3(2x)(1.5 - 0.5x) = 16 / (3x - x^2)

To solve for x, we can use the quadratic formula:

Kc = 1.7 = 16 / (3x - x^2)
x^2 - 3.53x + 9.4 = 0
x = 2

Therefore, at equilibrium:

[CO] = 2x = 4
[HSO] = 2x = 4
[O] = 1.5 - 0.5x = 0.5
[COS] = x = 2

So the composition of the system at equilibrium is 4 CO, 4 HSO, 2 O, and 2 COS, which corresponds to choice C.

Consider the Reaction CO(g)+ H2O(g)⇌CO2(g)+ H2(g), Represented by the Following

Consider the Reaction CO(g)+ H₂O(g)⇌CO₂(g)+ H₂(g), Represented by the Following