key term - $E_{cell}$

Definition

$E_{cell}$ is the cell potential or electromotive force (EMF) of an electrochemical cell, which is the potential difference between the two half-cells that make up the cell. It represents the ability of the cell to do electrical work and is a crucial parameter in understanding the spontaneity and feasibility of redox reactions. $E_{cell}$ is directly related to the Gibbs free energy change ($ ext{\Delta G}$) and the equilibrium constant ($K_{eq}$) of the overall cell reaction, providing a quantitative measure of the driving force behind the chemical process.

5 Must Know Facts For Your Next Test

1. $E_{cell}$ is measured in volts (V) and can be positive or negative, indicating whether the reaction is spontaneous or non-spontaneous, respectively.
2. The sign of $E_{cell}$ determines the direction of the reaction: a positive $E_{cell}$ indicates a spontaneous reaction, while a negative $E_{cell}$ indicates a non-spontaneous reaction.
3. The magnitude of $E_{cell}$ is a measure of the driving force of the reaction, with higher values indicating a greater tendency for the reaction to occur.
4. $E_{cell}$ is related to the Gibbs free energy change ($ ext{\Delta G}$) of the reaction by the equation: $ ext{\Delta G} = -nF E_{cell}$, where $n$ is the number of electrons transferred, and $F$ is the Faraday constant.
5. The equilibrium constant ($K_{eq}$) of a reaction is related to $E_{cell}$ through the equation: $ ext{ln} K_{eq} = \frac{nF E_{cell}}{RT}$, where $R$ is the universal gas constant and $T$ is the absolute temperature.

Review Questions

• Explain the relationship between $E_{cell}$ and the spontaneity of a redox reaction.
  • The cell potential, $E_{cell}$, is directly related to the Gibbs free energy change, $ ext{\Delta G}$, of the overall cell reaction. A positive $E_{cell}$ value indicates that the reaction is spontaneous, as the Gibbs free energy change is negative ($ ext{\Delta G} < 0$). Conversely, a negative $E_{cell}$ value indicates that the reaction is non-spontaneous, with a positive Gibbs free energy change ($ ext{\Delta G} > 0$). The magnitude of $E_{cell}$ also reflects the driving force of the reaction, with higher values corresponding to a greater tendency for the reaction to occur.
• Describe how $E_{cell}$ is used to determine the equilibrium constant ($K_{eq}$) of a redox reaction.
  • The cell potential, $E_{cell}$, is related to the equilibrium constant, $K_{eq}$, of a redox reaction through the Nernst equation: $ ext{ln} K_{eq} = \frac{nF E_{cell}}{RT}$, where $n$ is the number of electrons transferred, $F$ is the Faraday constant, $R$ is the universal gas constant, and $T$ is the absolute temperature. By measuring the cell potential, $E_{cell}$, and knowing the other parameters, one can calculate the equilibrium constant, $K_{eq}$, which provides a quantitative measure of the extent to which the reaction will proceed towards completion at equilibrium.
• Analyze how changes in the concentrations of reactants and products affect the value of $E_{cell}$ and the spontaneity of the overall cell reaction.
  • According to the Nernst equation, the cell potential, $E_{cell}$, is dependent on the concentrations of the reactants and products in the electrochemical cell. As the concentrations of the reactants and products change, the value of $E_{cell}$ will also change. This, in turn, affects the Gibbs free energy change, $ ext{\Delta G}$, of the overall cell reaction, as $ ext{\Delta G} = -nF E_{cell}$. If the change in concentrations results in a positive $ ext{\Delta G}$, the reaction becomes non-spontaneous. Conversely, if the change in concentrations results in a negative $ ext{\Delta G}$, the reaction becomes spontaneous. Therefore, by monitoring the $E_{cell}$ value, one can determine how changes in the system affect the spontaneity and feasibility of the redox reaction.

Related terms

Standard Cell Potential ($E_{cell}^{o}$): The cell potential measured under standard conditions, where the activities of all species are unity (1.0) and the temperature is 25°C (298 K).

Nernst Equation:

An equation that relates the cell potential ($E_{cell}$) to the standard cell potential ($E_{cell}^{o}$), the concentrations of reactants and products, and the temperature.

Spontaneity:

The natural tendency of a process to occur without the input of external energy, as determined by the sign of the Gibbs free energy change ($ ext{\Delta G}$).