Cell EMF
The electromotive force (EMF) of an electrochemical cell is the maximum potential difference between the two electrodes when no current is flowing (open-circuit condition), representing the driving force for electron transfer in the external circuit. It is determined by the difference in the electrode potentials of the cathode and anode and is directly related to the Gibbs free energy change of the reaction by ΔG° = −nFE°. A positive cell EMF indicates a spontaneous reaction (ΔG < 0), while a negative cell EMF indicates a non-spontaneous reaction under the given conditions.
Key Formula
ΔG° = −n × F × E°_cell
LaTeX: \Delta G° = -nFE°_{cell}
| Symbol | Meaning | Unit |
|---|---|---|
| \Delta G° | Standard Gibbs free energy change | J mol⁻¹ |
| n | Moles of electrons transferred | mol |
| F | Faraday constant (96485) | C mol⁻¹ |
| E°_{cell} | Standard cell EMF | V |
Worked Example
Problem
The standard cell EMF of the Daniel cell (Zn|Zn²⁺||Cu²⁺|Cu) is 1.10 V and n = 2. Calculate ΔG° for the cell reaction at 25 °C.
Solution
Step 1: Identify values: E°_cell = 1.10 V, n = 2, F = 96485 C mol⁻¹ Step 2: Apply ΔG° = −nFE°: ΔG° = −2 × 96485 × 1.10 Step 3: ΔG° = −212267 J mol⁻¹ = −212.3 kJ mol⁻¹ Step 4: Since ΔG° < 0, the reaction is spontaneous.
Answer
ΔG° = −212.3 kJ mol⁻¹ (spontaneous)
Relationship Between E°_cell, ΔG°, and Equilibrium Constant K
| E°_cell | ΔG° | K (equilibrium) | Reaction |
|---|---|---|---|
| > 0 | < 0 (negative) | > 1 | Spontaneous in forward direction |
| = 0 | = 0 | = 1 | System at equilibrium |
| < 0 | > 0 (positive) | < 1 | Non-spontaneous; reverse is favoured |
Interactive Tools
Khan Academy – Cell EMF and Gibbs Energy
Detailed lessons connecting cell EMF to thermodynamic quantities ΔG and K
Open ToolWolfram Alpha – Cell EMF
Compute cell EMF, ΔG°, and equilibrium constants from electrode potential data
Open ToolBrilliant – Electrochemistry and Thermodynamics
Problems and explanations connecting EMF to Gibbs energy and spontaneity
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Galvanic Cell
A galvanic cell (also called a voltaic cell) is an electrochemical device that converts chemical energy into electrical energy through spontaneous redox reactions occurring at two electrodes separated by an electrolyte. The oxidation half-reaction occurs at the anode (negative terminal) and the reduction half-reaction occurs at the cathode (positive terminal), with electrons flowing through an external circuit. Galvanic cells are the basis of all batteries and are fundamental to understanding energy storage and conversion in chemistry.
Standard Electrode Potential
The standard electrode potential (E°) is the potential difference developed at an electrode when it is in contact with a 1 mol L⁻¹ solution of its ions at 25 °C (298 K) and 1 atm pressure, measured relative to the standard hydrogen electrode (SHE), which is assigned a potential of exactly 0.00 V. Positive values of E° indicate a greater tendency for reduction (the species is a stronger oxidising agent), while negative values indicate a tendency for oxidation. Standard electrode potentials are tabulated and used to predict the feasibility of redox reactions and to calculate cell EMFs.
Nernst Equation
The Nernst equation relates the electrode potential of a half-cell (or full cell) to the standard electrode potential and the reaction quotient Q, accounting for the actual concentrations or partial pressures of reactants and products at any temperature. It shows that the cell potential decreases as products accumulate and reactants are consumed, reaching zero at equilibrium when the cell is fully discharged. The equation is critical for predicting cell behaviour under non-standard conditions and forms the basis of pH measurement using electrochemical sensors.
EMF stands for "electromotive force," a term introduced by Alessandro Volta in the early 19th century. "Electromotive" combines Greek "elektron" with Latin "movere" (to move), describing the force that moves electrons through a circuit.