Determine the values of Δr G^∘ for the following reactions...

Determine the values of $\Delta_{\mathrm{r}} G^{\circ}$ for the following reactions carried out in voltaic cells. (a) $2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Cu}^{2+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{Cu}(\mathrm{s})$ (b) $\mathrm{O}_{2}(\mathrm{g})+4 \mathrm{I}^{-}(\mathrm{aq})+4 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(1)+2 \mathrm{I}_{2}(\mathrm{s})$ (c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+14 \mathrm{H}^{+}(\mathrm{aq})+6 \mathrm{Ag}(\mathrm{s}) \longrightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+6 \mathrm{Ag}^{+}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(1)$

Determine the values of $\Delta_{\mathrm{r}} G^{\circ}$ for the following reactions carried out in voltaic cells.
(a) $2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Cu}^{2+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{Cu}(\mathrm{s})$
(b) $\mathrm{O}_{2}(\mathrm{g})+4 \mathrm{I}^{-}(\mathrm{aq})+4 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(1)+2 \mathrm{I}_{2}(\mathrm{s})$
(c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+14 \mathrm{H}^{+}(\mathrm{aq})+6 \mathrm{Ag}(\mathrm{s}) \longrightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+6 \mathrm{Ag}^{+}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(1)$

Key Concepts

Gibbs Free Energy Change

Gibbs free energy change (?G°) is a thermodynamic quantity that indicates the spontaneity of a reaction at standard conditions. In the context of electrochemical cells, it quantifies the maximum amount of work obtainable from a redox process, excluding electrical energy losses, and is used to determine if a reaction will proceed on its own under standard conditions.

Standard Cell Potential

The standard cell potential is the voltage difference between the two electrodes of an electrochemical cell when all reactants and products are in their standard states. It reflects the driving force behind the redox reaction and is determined by the difference between the standard reduction potentials of the cathode and anode, serving as a critical measure of the cell's ability to perform electrical work.

Redox Reactions

Redox reactions, involving the transfer of electrons from one species to another, are the basis of electrochemical cells. In these reactions, one species is oxidized (loses electrons) and another is reduced (gains electrons). Understanding the direction of electron flow and the roles of oxidizing and reducing agents is essential when analyzing and predicting the outcome of electrochemical processes.

Electron Stoichiometry

Electron stoichiometry refers to the determination of the number of electrons transferred in a redox reaction based on its balanced chemical equation. This concept is vital because the number of electrons exchanged, multiplied by the Faraday constant, directly influences the relationship between the cell potential and the Gibbs free energy change via the equation ?G° = –nFE°.

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