A voltaic cell is constructed that uses the following...

A voltaic cell is constructed that uses the following half-cell reactions: $$ \begin{array}{c}{\mathrm{Cu}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Cu}(s)} \\ {\mathrm{I}_{2}(s)+2 \mathrm{e}^{-} \quad \longrightarrow 2 \mathrm{I}^{-}(a q)}\end{array} $$ The cell is operated at 298 $\mathrm{K}$ with $\left[\mathrm{Cu}^{+}\right]=0.25 M$ and $\left[\mathrm{I}^{-}\right]=0.035 \mathrm{M}$ (a) Determine $E$ for the cell at these concentrations. (b) Which electrode is the anode of the cell? (c) Is the answer to part (b) the same as it would be if the cell were operated under standard conditions? (d) If $\left[\mathrm{Cu}^{+}\right]$ were equal to $0.15 \mathrm{M},$ at what concentration of I $\mathrm{I}^{-}$ would the cell have zero potential?

A voltaic cell is constructed that uses the following half-cell reactions:
$$
\begin{array}{c}{\mathrm{Cu}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Cu}(s)} \\ {\mathrm{I}_{2}(s)+2 \mathrm{e}^{-} \quad \longrightarrow 2 \mathrm{I}^{-}(a q)}\end{array}
$$
The cell is operated at 298 $\mathrm{K}$ with $\left[\mathrm{Cu}^{+}\right]=0.25 M$ and
$\left[\mathrm{I}^{-}\right]=0.035 \mathrm{M}$ (a) Determine $E$ for the cell at these concentrations. (b) Which electrode is the anode of the cell? (c) Is the answer to part (b) the same as it would be if the cell were operated under standard conditions? (d) If $\left[\mathrm{Cu}^{+}\right]$ were equal to $0.15 \mathrm{M},$ at what concentration of I $\mathrm{I}^{-}$ would the cell have zero potential?

Key Concepts

Voltaic (Galvanic) Cell

A voltaic cell is an electrochemical cell that converts chemical energy into electrical energy through a spontaneous redox reaction. It comprises two half-cells connected by a salt bridge or porous partition that maintains electrical neutrality, and its operation is based on the separation of oxidation and reduction processes at different electrodes, enabling the flow of electrons through an external circuit.

Half-Cell Reactions

Half-cell reactions describe the individual redox processes occurring at the electrodes within a voltaic (galvanic) cell. Each half-cell reaction involves either the gain of electrons (reduction) or the loss of electrons (oxidation) and is fundamental in analyzing and understanding the overall cell reaction, determining which process drives the flow of electrons through the external circuit.

Standard Electrode Potentials

Standard electrode potentials are measures of the intrinsic tendencies of chemical species to be reduced or oxidized under standard conditions (typically 1 M concentration, 1 atm pressure, and 25 °C). These values, found in electrochemical series tables, serve as reference points that allow for prediction of the direction of electron flow in a cell as well as calculations for non-standard conditions when combined with other concepts like the Nernst equation.

Nernst Equation

The Nernst equation quantitatively relates the cell potential to the concentrations (or activities) of the reactants and products involved in the redox reaction. It allows the calculation of cell voltage under non-standard conditions by accounting for the effect of concentration changes, making it a critical tool in determining how variations in ion concentrations can affect the overall cell potential.

Anode and Cathode

Within a voltaic cell, the anode is the electrode where oxidation (loss of electrons) occurs, whereas the cathode is the electrode where reduction (gain of electrons) takes place. The distinction between these electrodes is essential not only to the cell’s function but also to understanding how variations in conditions (such as ion concentrations) can alter electrode potentials and therefore the overall cell behavior.

Equilibrium and Zero Cell Potential

The condition of zero cell potential corresponds to equilibrium, where the forward and reverse reactions occur at equal rates, and there is no net driving force for electron flow. Understanding how changes in ion concentrations affect the cell potential via the Nernst equation allows one to predict the necessary conditions for achieving equilibrium, a concept that is central in both theoretical and practical aspects of electrochemistry.

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