Question #44307

The Pauling electronegativity of a divalent metal $M$ is $1.6$ and that of a unidentate ligand $L^-$ is $3.1$. The formation of the square planar complex $[ML_4]^{2-}$ is driven by the ligand-metal electronegativity difference. The overall stability constant $\beta_4$ at $298\text{ K}$ is given by the empirical relation: $\log \beta_4 = \frac{100}{9} (\chi_L - \chi_M)^2 - 5$. Given the standard reduction potential $E^\circ_{M^{2+}/M} = +0.50\text{ V}$. A half-cell is constructed by immersing an electrode of metal $M$ into a solution containing $0.01\text{ M}$ of $[ML_4]^{2-}$ and $0.1\text{ M}$ of free $L^-$ at $298\text{ K}$. Calculate the reduction potential of this half-cell. (Assume $\frac{2.303 RT}{F} = 0.06\text{ V}$ at $298\text{ K}$).