Question

Predict the equilibrium constant for the first reaction shown here given the equilibrium constants for the second and third reactions:

CO2(g) + 3H2(g) ⇌ CH3OH(g) + H2O(g), K1=?
CO(g) + H2O(g) ⇌ CO2(g) + H2(g), K2=8.0×10^4
CO(g) + 2H2(g) ⇌ CH3OH(g), K3=1.8×107^"
a) 1.25 × 10^3
b) 2.50 × 10^3
c) 5.00 × 10^3
d) 1.00 × 10^4
e) none of these

Answer 1

By using the relationship between equilibrium constants for individual reactions and their sum, we find that K1 is 2.25×10², which does not match any of the provided options exactly, so the correct answer is 'none of these'. so, option e is the correct answer.

Step-by-step explanation:

To predict the equilibrium constant for the first reaction given the equilibrium constants for the other two reactions, we can use the fact that the equilibrium constant for a reaction that is the sum of two or more reactions is equal to the product of the equilibrium constants for the individual reactions. By arranging the given reactions, we recognize that:

CO(g) + 3H2(g) → CO2(g) + H2O(g), K2 = 8.0×104

CO(g) + 2H2(g) → CH3OH(g), K3 = 1.8×107

Summing these reactions gives:

CO2(g) + 3H2(g) → CH3OH(g) + H2O(g)

Therefore, K1 for the overall reaction is:

K1 = K3 / K2 = (1.8×107) / (8.0×104) = 2.25×102

The closest answer from the given options is 2.50 × 103, so none of the provided options is exactly correct, making option 'e' the best answer.