Question #44114

A half-cell consists of a Pt electrode immersed in an aqueous solution containing $0.01\text{ M } \ce{Co^{2+}}$ and $0.01\text{ M } \ce{Co^{3+}}$ at $298\text{ K}$. The initial reduction potential of this half-cell is $E_1$. Ammonia and ammonium chloride are then added to the half-cell such that the final equilibrium concentration of free $\ce{NH3}$ is $0.1\text{ M}$. The new reduction potential of the half-cell is $E_2$. Given: $E^\circ_{\ce{Co^{3+}/Co^{2+}}} = +1.82\text{ V}$, $\log \beta_6 \text{ for } \ce{[Co(NH3)6]^{2+}} = 4.0$, $\log \beta_6 \text{ for } \ce{[Co(NH3)6]^{3+}} = 34.0$, and $\frac{2.303 RT}{F} = 0.06\text{ V}$. Calculate the magnitude of the shift in the reduction potential, $|E_2 - E_1|$.