In 1889, 25-year-old German physical chemist Walther Hermann Nernst (1864–1941) published his habilitation thesis in Zeitschrift für Physikalische Chemie (Vol. 4) titled “Die electromotorische Wirksamkeit der Jonen”.
Nernst derived the Nernst Equation, providing the fundamental quantitative relationship between electrochemical cell voltage ($E$), temperature ($T$), and ion concentration activities.
Derivation of the Nernst Equation¶
Nernst combined Josiah Willard Gibbs’s chemical free energy relation ($\Delta G = \Delta G^\circ + R T \ln Q$) with electrical work ($\Delta G = -n F E$):
$$E = E^\circ - \frac{R T}{n F} \ln Q$$
At $T = 298.15\,\text{K}$ ($25^\circ\text{C}$), substituting numerical values yields the practical base-10 equation:
$$E = E^\circ - \frac{0.05916\,\text{V}}{n} \log_{10} Q$$
Where:
- $E$ is reduction potential ($\text{Volts}$).
- $E^\circ$ is standard reduction potential.
- $n$ is number of moles of electrons transferred.
- $F = 96,485\,\text{C/mol}$ is Faraday’s constant.
- $Q$ is the reaction quotient of ion activities.
Nobel Prize in Chemistry (1920) & Biology¶
Nernst was awarded the 1920 Nobel Prize in Chemistry for his work in thermochemistry and the Third Law of Thermodynamics.
In biophysics and neuroscience, the Nernst equation calculates the resting membrane potential of biological neurons ($\text{Na}^+, \text{K}^+$ ion channels) and governs modern lithium-ion quantum energy storage batteries.
Key Takeaways¶
- Year: 1889
- Key Figure: Walther Nernst (German Physical Chemist)
- Core Discovery: Derived the Nernst Equation ($E = E^\circ - \frac{RT}{nF} \ln Q$).
- Nobel Laureate: Awarded the 1920 Nobel Prize in Chemistry.
- Quantum Relevance: Governs electrochemical energy storage, quantum battery cell potentials, and neuronal ion channel potentials.