Which of the following correctly relates the two equilibrium constants for the two reactions shown? A + B ⇄ 2 C, K₁; 2 A + 2 B ⇄ 4 C, K₂.
I don't see any choices but you note eqn 2 is twice eqn 1 so K2 = (K1)^2
The correct relation between the two equilibrium constants for the reactions A + B ⇄ 2 C (K₁) and 2 A + 2 B ⇄ 4 C (K₂) can be determined by applying the concept of equilibrium constant expression.
For the reaction A + B ⇄ 2 C, the equilibrium constant expression would be given as:
K₁ = [C]² / ([A] * [B])
For the reaction 2 A + 2 B ⇄ 4 C, the equilibrium constant expression would be:
K₂ = [C]⁴ / ([A]² * [B]²)
To relate these two equilibrium constants, we can take the ratio of the equilibrium constant expressions:
K₂ / K₁ = ([C]⁴ / ([A]² * [B]²)) / ([C]² / ([A] * [B]))
Simplifying the expression, we get:
K₂ / K₁ = ([C]⁴ * ([A] * [B])) / ([C]² * ([A]² * [B]²))
Further simplifying:
K₂ / K₁ = [C]² / ([A] * [B])
Therefore, the correct relation between the two equilibrium constants is:
K₂ / K₁ = [C]² / ([A] * [B])
To relate the two equilibrium constants for the reactions, we need to consider the stoichiometric coefficients of the reactants and products.
For the reaction A + B ⇄ 2 C with equilibrium constant K₁, the stoichiometric coefficients are:
- A: coefficient of 1
- B: coefficient of 1
- C: coefficient of 2
For the reaction 2 A + 2 B ⇄ 4 C with equilibrium constant K₂, the stoichiometric coefficients are:
- A: coefficient of 2
- B: coefficient of 2
- C: coefficient of 4
To relate the equilibrium constants, we need to consider the balanced equation that connects the two reactions. In this case, we notice that the second reaction is simply the double of the first reaction, suggesting that the equilibrium constant for the second reaction, K₂, will be the square of the equilibrium constant for the first reaction, K₁.
So, the correct relationship between the two equilibrium constants is:
K₂ = (K₁)²