Question #45018

Given the standard reduction potential of the aqueous cobalt couple $E^\circ(\ce{Co^{3+}}/\ce{Co^{2+}}) = +1.82\text{ V}$ at $298\text{ K}$. The overall formation constants ($\beta_3$) for the ethylenediamine (en) complexes $[\ce{Co(en)_3}]^{3+}$ and $[\ce{Co(en)_3}]^{2+}$ are $10^{33}$ and $10^5$, respectively. Consider the redox reaction where $[\ce{Co(en)_3}]^{2+}$ is oxidized by $\ce{Sn^{4+}}$ to form $[\ce{Co(en)_3}]^{3+}$ and $\ce{Sn^{2+}}$ under standard conditions. Given $E^\circ(\ce{Sn^{4+}}/\ce{Sn^{2+}}) = +0.15\text{ V}$ and $\frac{2.303 RT}{F} = 0.06\text{ V}$ at $298\text{ K}$. Assuming $[\ce{Co(en)_3}]^{2+}$ is a high-spin complex and $[\ce{Co(en)_3}]^{3+}$ is a low-spin complex, what is the standard cell potential ($E^\circ_{\text{cell}}$) for this reaction, and what is the change in the number of unpaired electrons ($\Delta n = n_{\text{product}} - n_{\text{reactant}}$) on the cobalt center?