Given the following two standard reduction potentials, M^3++3 e^- ⟶M ℰ^∘=-0.10 V M^2++2 e^- ⟶

step 1 For this problem, we have to find the potential for this reaction. Now, since the N values of th

Given the following two standard reduction potentials,...

Given the following two standard reduction potentials, $$\mathrm{M}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{M} \quad \mathscr{E}^{\circ}=-0.10 \mathrm{~V}$$ $$\mathrm{M}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{M} \quad \mathscr{E}^{\circ}=-0.50 \mathrm{~V}$$ solve for the standard reduction potential of the half-reaction$$\mathrm{M}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{M}^{2+}$$

Given the following two standard reduction potentials,
$$\mathrm{M}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{M} \quad \mathscr{E}^{\circ}=-0.10 \mathrm{~V}$$
$$\mathrm{M}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{M} \quad \mathscr{E}^{\circ}=-0.50 \mathrm{~V}$$
solve for the standard reduction potential of the half-reaction$$\mathrm{M}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{M}^{2+}$$

Key Concepts

Standard Reduction Potential

This is an intrinsic property of a half?reaction under standard conditions, indicating the tendency of a chemical species to gain electrons and be reduced. It provides a measure of the driving force behind the reduction process and is typically reported in volts.

Gibbs Free Energy Relation

The connection between the standard reduction potential and the Gibbs free energy change, given by ?G = –nFE (where n is the number of electrons transferred and F is Faraday's constant), is fundamental in electrochemistry. This relation allows us to convert potentials into energy changes, which are additive when combining reactions.

Combining Half-Reactions

When redox half-reactions are combined to yield an overall reaction, the standard free energy changes of the individual reactions add up, even though the standard reduction potentials themselves do not directly add. This approach is used to determine unknown potentials by equating the total free energy change of the overall reaction to the sum of the free energy changes of its constituent half-reactions.

Electron Transfer Stoichiometry

The number of electrons involved in each half-reaction is crucial in calculations because it serves as a scaling factor in the ?G = –nFE relation. Accounting for the electron stoichiometry ensures that free energy contributions are correctly weighted when combining half-reactions to determine the overall reaction conditions.

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