We have seen that complex formation can stabilize oxidation states. An important illustration of this fact is the oxidation of water in acidic solutions by \(\mathrm{Co}^{3+}(\) aq) but not by \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+} .\) Use the following data. \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+\mathrm{e}^{-} \longrightarrow\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) $$ E^{\circ}=1.82 \mathrm{V} $$ \(\left[\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}+3 \mathrm{en} \longrightarrow\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{2+}+6 \mathrm{H}_{2} \mathrm{O}(1)\) $$ \log \beta_{3}=12.18 $$ \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+3 \mathrm{en} \longrightarrow\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}+6 \mathrm{H}_{2} \mathrm{O}(1)\) $$ \log \beta_{3}=47.30 $$ Calculate \(E^{\circ}\) for the reaction $$ \left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}+\mathrm{e}^{-} \longrightarrow\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{2+} $$ Show that \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) is stable in water but \(\mathrm{Co}^{3+}(\mathrm{aq})\) is not.

Step by step solution

01

Calculate \(E^{\circ}\) for the complex compound reduction reaction

Use the Nernst equation for calculating \(E^{\circ}\) values. This equation \(\Delta G = -nFE^{\circ}\) links the Gibbs free energy change \(\Delta G\) to the cell potential \(E^{\circ}\). Using \(\Delta G = -RT\ln(K)\) equation, where \(K\) is the equilibrium constant. In this case, the equilibrium constant is given by \(10^{\log \beta_3}\). Hence, \(E^{\circ} = -\frac{RT}{nF}\ln(K)\), substituting for \(R =8.314\ JK^{-1}mol^{-1}\), \(T = 298\ K\), \(F = 96485\ Cmol^{-1}\), \(n=1\) and \(\log \beta_3 = 47.30\), you can calculate the value of \(E^{\circ}\).

02

Compare the stability of cobalt III complexes in water

The difference in oxidation stability for the \(\mathrm{Co}^{3+}\) and \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) ions relies on the comparison of their \(E^{\circ}\) values. A more positive \(E^{\circ}\) indicates a greater tendency for reduction to occur, hence making the ion less stable in its oxidized state. Comparing the \(E^{\circ}\) values, it can be shown how \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) is more stable than \(\mathrm{Co}^{3+}\).

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