The equilibrium constants for the two reactions are known: $\begin{array}{ll}\mathrm{M}^{\mathrm{m}+}+4 \mathrm{~L}^{-} \leftrightarrows\left[\mathrm{ML}_{4}\right]^{\mathrm{m}-4}&&&K_{a}\\\mathrm{HL} \leftrightarrows \mathrm{H}^{+}+\mathrm{L}^{-}&&&K_{b}\\\end{array}$ What must be the value of the equilibrium constant, K_overall for the following overall reaction?
M^m+ + 4HL $\leftrightarrows$ [ML₄]^m^-⁴ + 4H⁺ K_overall

Question

The equilibrium constants for the two reactions are known:

\begin{array}{ll}\mathrm{M}^{\mathrm{m}+}+4 \mathrm{~L}^{-} \leftrightarrows\left[\mathrm{ML}_{4}\right]^{\mathrm{m}-4}&&&K_{a}\\\mathrm{HL} \leftrightarrows \mathrm{H}^{+}+\mathrm{L}^{-}&&&K_{b}\\\end{array}

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

\leftrightarrows

[ML₄]^m^-⁴ + 4H⁺ K_overall

Quizplus · Accepted Answer

The overall reaction is the sum of the two given reactions. The equilibrium constant for the overall reaction is the product of the equilibrium constants of the individual reactions, with the second reaction's constant raised to the power of 4 because it occurs four times. Thus, $K_{\text{overall}} = K_a K_b^4$.

The Equilibrium Constants for the Two Reactions Are Known What Must Be the Value of the Equilibrium Constant, Koverall

The Equilibrium Constants for the Two Reactions Are Known What Must Be the Value of the Equilibrium Constant, K_overall