The equilibrium constants for the two reactions are known:
M^m⁺+ 4L^- [ML₄]^m^-⁴ $~~~~~~~~$ K_a
HL H⁺+ L^- $~~~~~~~~$ $~~~~~~~~$ $~~ ~~~~$ K_b
What must be the value of the equilibrium constant, K_overall for the following overall reaction?
M^m⁺ + 4HL [ML₄]^m^-⁴ + 4H⁺ $~~~~~~~~$ K_overall

Question

The equilibrium constants for the two reactions are known:
M^m⁺+ 4L^-

The equilibrium constants for the two reactions are known: M<sup>m</sup><sup>+</sup>+ 4L<sup>-</sup> [ML<sub>4</sub>]<sup>m</sup><sup>-</sup><sup>4</sup> ~~~~~~~~ K<sub>a</sub> HL H<sup>+</sup>+ L<sup>-</sup> ~~~~~~~~~~~~~~~~~~ ~~~~ K<sub>b</sub> What must be the value of the equilibrium constant, K<sub>overall</sub> for the following overall reaction? M<sup>m</sup><sup>+</sup> + 4HL [ML<sub>4</sub>]<sup>m</sup><sup>-</sup><sup>4</sup> + 4H<sup>+</sup> ~~~~~~~~ K<sub>overall</sub> A) K<sub>a</sub>K<sub>b</sub> B) K<sub>a</sub> + 4K<sub>b</sub> C) K<sub>a</sub> +K<sub>b</sub><sup>4</sup> D) K<sub>a</sub>K<sub>b</sub><sup>4</sup> E) K<sub>a</sub>K<sub>b</sub><sup>1/4</sup>

[ML₄]^m^-⁴

~~~~~~~~

K_a
HL

H⁺+ L^-

~~~~~~~~

~~~~~~~~

~~ ~~~~

K_b
What must be the value of the equilibrium constant, K_overall for the following overall reaction?
M^m⁺ + 4HL

[ML₄]^m^-⁴ + 4H⁺

~~~~~~~~

K_overall

Quizplus · Accepted Answer

The overall reaction involves the combination of two sub-reactions. The equilibrium constant for the overall reaction can be written as the product of the equilibrium constants of the two sub-reactions because we can multiply the equilibrium constants of reactions to obtain the equilibrium constant of the overall reaction. Therefore, K_overall = K_a × K_b. Also, the species ^{m and} are present in both the sub-reactions and therefore, they cancel out in the overall reaction. Hence, we can ignore them in the calculation of the equilibrium constant of the overall reaction. Therefore, the correct answer is D.

The Equilibrium Constants for the Two Reactions Are Known ~~~~~~~~ Ka HL H++ L-

The Equilibrium Constants for the Two Reactions Are Known $~~~~~~~~$ K_a
HL H⁺+ L^-