A galvanic cell is based on the following half-reactions at...

A galvanic cell is based on the following half-reactions at $25^{\circ} \mathrm{C}$ : $$\begin{aligned}\mathrm{Ag}^{+}+\mathrm{e}^{-} & \longrightarrow \mathrm{Ag} \\ \mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O} \end{aligned}$$ Predict whether $\mathscr{G}_{\text {cell }}$ is larger or smaller than $\mathscr{C}_{\text {cell }}^{\circ}$ for the following cases. a. $\left[\mathrm{Ag}^{+}\right]=1.0 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=2.0 \mathrm{M},\left[\mathrm{H}^{+}\right]=2.0 \mathrm{M}$ b. $\left[\mathrm{Ag}^{+}\right]=2.0 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=1.0 M,\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} M$

A galvanic cell is based on the following half-reactions at $25^{\circ} \mathrm{C}$ :
$$\begin{aligned}\mathrm{Ag}^{+}+\mathrm{e}^{-} & \longrightarrow \mathrm{Ag} \\
\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}
\end{aligned}$$
Predict whether $\mathscr{G}_{\text {cell }}$ is larger or smaller than $\mathscr{C}_{\text {cell }}^{\circ}$ for the following cases.
a. $\left[\mathrm{Ag}^{+}\right]=1.0 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=2.0 \mathrm{M},\left[\mathrm{H}^{+}\right]=2.0 \mathrm{M}$
b. $\left[\mathrm{Ag}^{+}\right]=2.0 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]=1.0 M,\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} M$

Key Concepts

Galvanic Cell

A galvanic cell is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two half-cells, each containing a redox couple, connected by a conductive electrolyte and an external circuit that allows electrons to flow from the oxidation half-cell to the reduction half-cell.

Standard Electrode Potential

The standard electrode potential (E°) is the potential difference measured under standard conditions (usually 1 M concentration, 1 atm pressure, and 25°C) for a given half-cell reaction. It serves as a reference point for predicting the direction of electron flow and comparing the driving forces of different redox reactions.

Reaction Quotient

The reaction quotient (Q) represents the ratio of the concentrations (or activities) of products to reactants at any point during a reaction. In electrochemistry, Q is used to assess how far a cell’s current conditions deviate from the standard conditions, thereby influencing the cell potential through the Nernst equation.

Nernst Equation

The Nernst equation relates the cell potential under non-standard conditions to the standard cell potential, temperature, number of electrons transferred, and the reaction quotient. This equation demonstrates how changes in ion concentrations and other reaction conditions affect the actual potential and, consequently, the cell’s spontaneity.

Gibbs Free Energy

Gibbs free energy (?G) indicates the spontaneity of a chemical reaction, with negative values corresponding to spontaneous processes. In the context of electrochemistry, ?G is directly related to the cell potential, linking the thermodynamic favorability of the redox reaction with its electrical output under both standard and non-standard conditions.

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