3.1 Gibbs Free Energy and Electrochemical Reactions

Gibbs free energy is a crucial concept in electrochemistry, predicting reaction spontaneity. It combines enthalpy and entropy changes, helping us understand the direction and extent of chemical reactions, including those in galvanic cells and electrolysis.

The relationship between Gibbs free energy and cell potential is key in electrochemistry. A negative Gibbs free energy change corresponds to a positive cell potential, indicating a spontaneous reaction. This connection helps us predict and control electrochemical processes in various applications.

Gibbs Free Energy and Spontaneity

Definition of Gibbs free energy

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• Thermodynamic quantity that predicts the spontaneity of a process at constant temperature and pressure
• Considers both enthalpy ($H$) and entropy ($S$) changes in a system
• Defined as $G = H - TS$, where $T$ is the absolute temperature (in Kelvin)
• Useful in determining the direction and extent of chemical reactions, including electrochemical reactions (galvanic cells, electrolysis)

Calculation of Gibbs free energy change

• Change in Gibbs free energy ($\Delta G$) for an electrochemical reaction calculated using the equation: $\Delta G = -nFE$
  • $n$ is the number of moles of electrons transferred per mole of reaction (stoichiometric coefficient)
  • $F$ is the Faraday constant (96,485 C/mol)
  • $E$ is the cell potential (in volts) under standard conditions (1 M concentrations, 1 atm pressure, 25°C)
• Standard Gibbs free energy change ($\Delta G^{\circ}$) calculated using standard cell potential ($E^{\circ}$): $\Delta G^{\circ} = -nFE^{\circ}$
• For non-standard conditions, the Nernst equation used to calculate the cell potential: $E = E^{\circ} - \frac{RT}{nF} \ln Q$
  • $R$ is the gas constant (8.314 J/mol·K)
  • $Q$ is the reaction quotient, which accounts for the actual concentrations of reactants and products (similar to equilibrium constant)

Spontaneity in electrochemical reactions

• Sign of $\Delta G$ determines the spontaneity of an electrochemical reaction
  1. Negative $\Delta G$ indicates a spontaneous reaction, which proceeds forward (galvanic cell)
  2. Positive $\Delta G$ indicates a non-spontaneous reaction, which proceeds backward (electrolytic cell)
  3. Zero $\Delta G$ indicates a reaction at equilibrium, with no net change
• Magnitude of $\Delta G$ indicates the driving force of the reaction
  • Larger negative value of $\Delta G$ implies a greater tendency for the reaction to proceed forward (more energetically favorable)
  • Larger positive value of $\Delta G$ implies a greater tendency for the reaction to proceed backward (less energetically favorable)

Relationship between Gibbs Free Energy and Cell Potential

Gibbs free energy vs cell potential

• Change in Gibbs free energy ($\Delta G$) directly related to the cell potential ($E$) through the equation: $\Delta G = -nFE$
  • Negative $\Delta G$ corresponds to a positive cell potential, indicating a spontaneous reaction (galvanic cell)
  • Positive $\Delta G$ corresponds to a negative cell potential, indicating a non-spontaneous reaction (electrolytic cell)
  • $\Delta G$ of zero corresponds to a cell potential of zero, indicating a reaction at equilibrium
• Standard cell potential ($E^{\circ}$) related to the standard Gibbs free energy change ($\Delta G^{\circ}$) by: $\Delta G^{\circ} = -nFE^{\circ}$
• Nernst equation relates the cell potential under non-standard conditions to the standard cell potential and the reaction quotient: $E = E^{\circ} - \frac{RT}{nF} \ln Q$
  • Allows for the calculation of $\Delta G$ under non-standard conditions using the actual cell potential (accounts for concentration effects)
  • Useful in determining the direction and extent of electrochemical reactions under various conditions (pH, temperature, pressure)