key term - $E_{cell}^°$

Definition

$E_{cell}^°$ is the standard cell potential, which is a measure of the driving force for a redox reaction to occur under standard conditions. It represents the potential difference between the reduction potentials of the cathode and anode in an electrochemical cell, and is a fundamental concept in understanding the spontaneity and feasibility of chemical reactions.

5 Must Know Facts For Your Next Test

1. $E_{cell}^°$ is directly related to the Gibbs free energy change ($ ext{Δ} G^°$) of a reaction through the equation $ ext{Δ} G^° = -nF E_{cell}^°$, where $n$ is the number of electrons transferred and $F$ is the Faraday constant.
2. A positive $E_{cell}^°$ value indicates a spontaneous, favorable reaction, while a negative $E_{cell}^°$ value indicates a non-spontaneous, unfavorable reaction.
3. The magnitude of $E_{cell}^°$ reflects the strength of the oxidizing and reducing agents in the cell, with larger positive values indicating stronger oxidizing agents and larger negative values indicating stronger reducing agents.
4. The standard cell potential is measured under standard conditions, which include a temperature of 25°C, a pressure of 1 atm, and a concentration of 1 M for all dissolved species.
5. The Nernst equation relates the cell potential ($E_{cell}$) to the standard cell potential ($E_{cell}^°$), the number of electrons transferred ($n$), and the reaction quotient ($Q$) at non-standard conditions.

Review Questions

• Explain the relationship between $E_{cell}^°$ and the spontaneity of a redox reaction.
  • The standard cell potential, $E_{cell}^°$, is directly related to the Gibbs free energy change, $ ext{Δ} G^°$, of a reaction through the equation $ ext{Δ} G^° = -nF E_{cell}^°$, where $n$ is the number of electrons transferred and $F$ is the Faraday constant. A positive $E_{cell}^°$ value indicates a spontaneous, favorable reaction, as the negative $ ext{Δ} G^°$ value means the reaction will occur naturally. Conversely, a negative $E_{cell}^°$ value indicates a non-spontaneous, unfavorable reaction, with a positive $ ext{Δ} G^°$ value. The magnitude of $E_{cell}^°$ reflects the strength of the oxidizing and reducing agents in the cell, with larger positive values indicating stronger oxidizing agents and larger negative values indicating stronger reducing agents.
• Describe how $E_{cell}^°$ is used to determine the equilibrium constant ($K_{eq}$) of a redox reaction.
  • The standard cell potential, $E_{cell}^°$, is related to the equilibrium constant, $K_{eq}$, through the Nernst equation: $E_{cell} = E_{cell}^° - (RT/nF) ext{ln} Q$, where $R$ is the universal gas constant, $T$ is the absolute temperature, $n$ is the number of electrons transferred, and $F$ is the Faraday constant. At equilibrium, $E_{cell} = 0$, and the reaction quotient $Q = K_{eq}$. Rearranging the Nernst equation, we get $ ext{ln} K_{eq} = nF E_{cell}^°/RT$, which allows us to calculate the equilibrium constant from the standard cell potential. This relationship is crucial for understanding the extent of a redox reaction at equilibrium.
• Analyze how changes in temperature and pressure affect the value of $E_{cell}^°$, and explain the implications of these changes on the spontaneity and feasibility of the reaction.
  • The standard cell potential, $E_{cell}^°$, is measured under standard conditions of temperature (25°C) and pressure (1 atm). Changes in these conditions can affect the value of $E_{cell}^°$ and, consequently, the Gibbs free energy change ($ ext{Δ} G^°$) and the equilibrium constant ($K_{eq}$) of the reaction. According to the Nernst equation, an increase in temperature will decrease the value of $E_{cell}^°$, making the reaction less spontaneous (higher $ ext{Δ} G^°$) and shifting the equilibrium towards the reactants (lower $K_{eq}$). Conversely, a decrease in temperature will increase $E_{cell}^°$, making the reaction more spontaneous (lower $ ext{Δ} G^°$) and shifting the equilibrium towards the products (higher $K_{eq}$). Pressure changes have a smaller effect on $E_{cell}^°$, but can still impact the spontaneity and feasibility of the reaction. Understanding how environmental conditions affect $E_{cell}^°$ is crucial for predicting the behavior of redox reactions in various applications.

Related terms

Reduction Potential:

The reduction potential of a half-reaction is a measure of the tendency of a species to be reduced, with more positive values indicating a greater tendency to accept electrons.

Gibbs Free Energy ($ ext{Δ} G^°$): Gibbs free energy is a thermodynamic quantity that combines the concepts of enthalpy and entropy to determine the spontaneity and feasibility of a chemical process under standard conditions.

Equilibrium Constant ($K_{eq}$): The equilibrium constant is a quantitative measure of the extent of a reaction at equilibrium, and is related to the standard cell potential through the Nernst equation.