Question #44556

Consider the $\ce{Co^{3+}/Co^{2+}}$ redox couple with a standard reduction potential $E^\circ = +1.82 \text{ V}$ at $298 \text{ K}$. In the presence of $\ce{NO_2^-}$ ligands, $\ce{Co^{3+}}$ initially forms the kinetically favored O-bonded nitrito complex, $\ce{[Co(ONO)_6]^{3-}}$ ($\log \beta_O = 14$). Over time, it completely isomerizes to the thermodynamically stable N-bonded nitro complex, $\ce{[Co(NO_2)_6]^{3-}}$ ($\log \beta_N = 24$). The $\ce{Co^{2+}}$ ion forms a weaker complex $\ce{[Co(NO_2)_4]^{2-}}$ with $\log \beta_{II} = 4$.

A half-cell is prepared by adding $0.05 \text{ M}$ $\ce{Co(ClO_4)_3}$ and $0.05 \text{ M}$ $\ce{Co(ClO_4)_2}$ to a buffer solution that maintains a constant free ligand concentration of $[\ce{NO_2^-}] = 1.0 \text{ M}$ at $298 \text{ K}$.

Calculate the initial reduction potential ($E_{initial}$) of this half-cell (assuming only the O-bonded complex has formed for $\ce{Co^{3+}}$) and the standard Gibbs free energy of isomerization ($\Delta G^\circ_{iso}$) for the reaction $\ce{[Co(ONO)_6]^{3-} \rightleftharpoons [Co(NO_2)_6]^{3-}}$.

(Given: $\frac{2.303 RT}{F} = 0.06 \text{ V}$, $F = 96500 \text{ C mol}^{-1}$)