Question #45019

Consider a transition metal $M$ that forms coordination complexes with a tetradentate Schiff-base ligand $H_2L$. The standard reduction potentials and formation constants ($K_f$) at 298 K are given below:

$E^\circ(M^{3+}/M^{2+}) = +0.40$ V $E^\circ(M^{2+}/M) = -0.20$ V $M^{3+} + L^{2-} \rightleftharpoons ML^+$ $\log K_{f,III} = 30$ $M^{2+} + L^{2-} \rightleftharpoons ML$ $\log K_{f,II} = 16$

The ligand $H_2L$ has acid dissociation constants $pK_{a1} = 4.0$ and $pK_{a2} = 6.0$. An electrochemical cell is set up where the activities of the complexes $ML^+$ and $ML$ are maintained at $1.0$ M, and the total concentration of the uncomplexed ligand species ($[H_2L] + [HL^-] + [L^{2-}]$) is $1.0$ M. At what pH does the disproportionation of $ML$ into $ML^+$ and $M(s)$ just become thermodynamically favorable? (Given: $\frac{2.303 RT}{F} = 0.06$ V. Assume no other side reactions occur.)