Given the following electrode potentials at 25^∘ C Fe^3++e^- =Fe^2+ E1^∘=0.771 V

step 1 Here we need two equations that relate to our redox reactions. So we need delta G0, 0, reaction

Given the following electrode potentials at 25^∘ C ...

Given the following electrode potentials at $25^{\circ} \mathrm{C}$ \[ \begin{aligned} \mathrm{Fe}^{3+}+\mathrm{e}^{-} &=\mathrm{Fe}^{2+} & & E_{1}^{\circ}=0.771 \mathrm{V} \\ \frac{1}{2} \mathrm{Fe}^{2+}+\mathrm{e}^{-} &=\frac{1}{2} \mathrm{Fe}(\mathrm{s}) & E_{2}^{\circ} &=-0.440 \mathrm{V} \end{aligned} \] calculate the electrode potential for \[ \frac{1}{3} \mathrm{Fe}^{3+}+\mathrm{e}^{-}=\frac{1}{3} \mathrm{Fe} \quad E_{3}^{\circ}=? \]

Given the following electrode potentials at $25^{\circ} \mathrm{C}$
\[
\begin{aligned}
\mathrm{Fe}^{3+}+\mathrm{e}^{-} &=\mathrm{Fe}^{2+} & & E_{1}^{\circ}=0.771 \mathrm{V} \\
\frac{1}{2} \mathrm{Fe}^{2+}+\mathrm{e}^{-} &=\frac{1}{2} \mathrm{Fe}(\mathrm{s}) & E_{2}^{\circ} &=-0.440 \mathrm{V}
\end{aligned}
\]
calculate the electrode potential for
\[
\frac{1}{3} \mathrm{Fe}^{3+}+\mathrm{e}^{-}=\frac{1}{3} \mathrm{Fe} \quad E_{3}^{\circ}=?
\]

Key Concepts

Gibbs Free Energy and Its Relation to Electrode Potentials

There is a direct relationship between the Gibbs free energy change (?G) and the electrode potential (E) given by the equation ?G = –nFE, where n is the number of electrons transferred and F is the Faraday constant. This relation allows one to convert electrode potentials into free energy changes, which are additive even when the half-reactions are combined. It is crucial when calculating the overall potential for a reaction assembled from several steps.

Combination of Half-Reactions

When multiple half-reactions are involved in a redox process, their individual free energy changes (derived from their standard potentials and number of electrons involved) can be summed to yield the overall free energy change for the overall reaction. The total electrode potential is then determined by dividing this overall free energy change by the total number of electrons transferred in the combined reaction. This process is fundamental in determining the net potential for a complex redox reaction.

Standard Electrode Potential

Standard electrode potentials are a measure of the tendency of a chemical species to be reduced, measured under standard conditions. They are intensive properties and do not depend on the amount of material, meaning that even if a reaction is scaled, its standard potential remains the same. These values are obtained experimentally and are used as benchmarks to predict the direction of redox reactions.

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