Consider a concentration cell made of the following two compartments: \(\mathrm{Cl}_{2}(0.20 \mathrm{~atm}) \mathrm{ICl}^{-}(1.0 \mathrm{M})\) and \(\mathrm{Cl}_{2}(2.0 \mathrm{~atm}) \mid \mathrm{Cl}^{-}(1.0 \mathrm{M}) .\) Platinum is used as the in- ert electrodes. Draw a cell diagram for the cell and calculate the emf of the cell at \(25^{\circ} \mathrm{C}\).

The Nernst equation plays a pivotal role in understanding the behavior of electrochemical cells. It relates the electromotive force (emf) of a cell to the concentration of the species involved in the electrochemical reaction.
Simply put, it incorporates the effect of temperature and concentrations (or partial pressures for gases) into the calculation of cell potential. Used widely in concentration cell emf calculations, the equation is expressed mathematically as:
\[ E = E^{0} - \frac{RT}{nF} \ln Q \]
where:

• \(E\) is the cell potential,
• \(E^{0}\) is the standard cell potential,
• \(R\) is the universal gas constant,
• \(T\) is the temperature in Kelvin,
• \(n\) is the number of moles of electrons exchanged,
• \(F\) is the Faraday constant,
• \(Q\) is the reaction quotient, the ratio of product activities to reactant activities.

In a concentration cell like the one described in the exercise, because the standard cell potential \(E^{0}\) is zero, the emf can be calculated only based on the reaction quotient \(Q\), which accounts for the different concentrations or pressures of the chemicals involved in the half-cell reactions.

An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause a chemical change. This fascinating process is the basis for batteries, fuel cells, and electrolysis units.

In a concentration cell, both electrodes are made of the same material, and the same chemical reaction occurs at both the anode and cathode, but with different concentrations. As a result, there is a natural tendency for the reaction to move towards equilibrium, leading to the creation of an electromotive force (emf).

Understanding how these cells work provides insight into applications that include not only energy storage and retrieval but also sensors and various forms of corrosion monitoring.

In electrochemistry, the standard cell potential is a critical concept. It is defined as the potential difference between two half-cells in an electrochemical cell when all components are at their standard states, typically 1 M concentration for solutions, 1 atm pressure for gases, and 25°C or 298 K for temperature.

For any cell, it is calculated under standard conditions using a table of standard electrode potentials, which are established by measuring against a standard hydrogen electrode. However, in a concentration cell where the electrode reactions are identical and their concentrations or pressures differ, the standard cell potential \(E^{0}\) is zero. This zero value significantly simplifies the Nernst equation when calculating the cell's emf.

Chemical thermodynamics is the study of energy changes accompanying chemical reactions and physical processes. In the context of electrochemistry, it helps us understand the spontaneity, feasibility, and energy aspects of reactions within cells.

In terms of concentration cells, thermodynamics dictates that the cell will produce electricity until equilibrium is reached, at which point no net reaction occurs, and therefore, no emf is generated. The Nernst equation is essentially a thermodynamic equation; it incorporates entropy and enthalpy changes via the reaction quotient and allows us to predict the voltage of a cell under non-standard conditions.

One essential takeaway from chemical thermodynamics is the relationship between equilibrium, the Gibbs free energy change (\(\triangle G\)), and the emf of a cell. The emf is a direct measure of the driving force behind a chemical reaction and is closely related to the maximum useful work that the reaction can perform.