Near-equilibrium voltage curves are voltage measurements taken when an electrochemical system, such as a battery or an electrochemical cell, is very close to its thermodynamic equilibrium. This means that the net current flowing through the system is very small, ideally zero. Here's a breakdown of what that implies and why they are important:

Thermodynamic Equilibrium: In an electrochemical cell, equilibrium is reached when the rates of the forward and reverse electrochemical reactions at the electrodes are equal, resulting in no net change in the system. At this point, there is a specific potential difference between the electrodes, known as the equilibrium potential or Nernst potential. This potential is determined by the activities (or concentrations) of the electroactive species involved in the redox reactions and the temperature, as described by the Nernst equation:

$$ E=E^0-\frac{R T}{n F} \ln Q $$

Where:

• $E$ is the equilibrium potential.
• $E^0$ is the standard electrode potential.
• $R$ is the ideal gas constant.
• $T$ is the absolute temperature.
• $n$ is the number of electrons transferred in the cell reaction.
• $F$ is Faraday's constant.
• $Q$ is the reaction quotient.

🧠Example

The Daniell cell consists of a zinc electrode immersed in a zinc sulfate ($ZnSO_4$) solution and a copper electrode immersed in a copper(II) sulfate ($CuSO_4$) solution, connected by a salt bridge. The overall cell reaction is:

$$ Z n(s)+C u^{2+}(a q) \rightleftharpoons Z n^{2+}(a q)+C u(s) $$

Let's say we have the following non-standard conditions at 298 K :

• Concentration of ($Cu^{2+}(aq)), ([Cu^{2+}] = 0.10 \text{ M}$)
• Concentration of ($Zn^{2+}(aq)), ([Zn^{2+}] = 1.0 \text{ M}$)

We want to calculate the cell potential ($E$) under these conditions.

Step 1: Determine the Standard Cell Potential ($E^0$)

We need the standard reduction potentials for the two half-reactions: