R3.2.14 Gibbs free energy and cell potential (Higher Level Only)

Gibbs Free Energy and Standard Cell Potentials

1. You’re designing a battery for a new electric vehicle.
2. You need to determine if the chemical reactions inside your battery will produce enough energy to power the car.
3. How can you predict whether the reaction in your battery will occur spontaneously and how much energy it will provide?

This is where the relationship between Gibbs free energy and standard cell potential becomes an essential tool.

The Equation: $\Delta G^{\circ }=-nF{E}_{\text{cell}}^{\circ }$

The equation $\Delta G^{\circ }=-nF{E}_{\text{cell}}^{\circ }$ links two fundamental concepts in chemistry:

Gibbs free energy change ($\Delta G^{\circ }$) and standard cell potential ($E_{\text{cell}}^{\circ }$).

Let’s break it down step by step to understand how it works.

1. $\Delta G^{\circ }$ (Standard Gibbs Free Energy Change):

• $\Delta G^{\circ }$ represents the maximum amount of energy available to do useful work from a chemical reaction under standard conditions (298 K, 1 atm, and 1 M concentrations for all solutions).
• The sign of $\Delta G^{\circ }$ determines spontaneity:
  • Negative $\Delta G^{\circ }$:The reaction is spontaneous under standard conditions.
  • Positive $\Delta G^{\circ }$:The reaction is non-spontaneous under standard conditions.
  • $\Delta G^{\circ }=0$: The system is at equilibrium.

2. $E_{\text{cell}}^{\circ }$ (Standard Cell Potential):

• $E_{\text{cell}}^{\circ }$ measures the voltage of an electrochemical cell under standard conditions.
• It is calculated as the difference between the standard electrode potentials of the cathode (reduction) and the anode (oxidation): $$E^{\ominus }\text{cell}=E_{\text{cathode}}^{\ominus }-E_{\text{anode}}^{\ominus }$$
  • A positive $E_{\text{cell}}^{\circ }$ corresponds to a negative $\Delta G^{\circ }$, indicating a spontaneous reaction.
  • Conversely, a negative $E_{\text{cell}}^{\circ }$ means $\Delta G^{\circ }$ is positive, and the reaction is non-spontaneous.

3.n (Number of Electrons Transferred):

• $n$ represents the number of moles of electrons transferred in the balanced redox reaction.

4. F (Faraday’s Constant):

• $F$ = 96500 C mol⁻¹, which is the charge of one mole of electrons.

By combining these terms, the equation $\Delta G^{\circ }=-nF{E}_{\text{cell}}^{\circ }$ allows you to calculate how much energy ( $\Delta G^{\circ }$) is available for a given electrochemical reaction based on its cell potential ($E_{\text{cell}}^{\circ }$).

Spontaneity and the Sign of $\Delta G^{\circ }$

The relationship between $\Delta G^{\circ }$ and $E_{\text{cell}}^{\circ }$ is straightforward:

• If $\Delta G^{\circ }<0$: The reaction is spontaneous under standard conditions.
• If $\Delta G^{\circ }>0$: The reaction is non-spontaneous and requires energy input.
• If $\Delta G^{\circ }=0$: The reaction is at equilibrium, meaning no net energy is available.

Common Mistakes to Avoid

Reflection and Practice