Subjects and lessons to explore.

Law

General Chemistry II · Electrochemistry

Electrochemistry and Equilibrium

5 min read
SourcesReport an error
Want it in plain words first? Jump to Eli explains — the same idea, no jargon.
On this page 8 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Study tools
  8. Sources & references

In 30 seconds

Equilibrium and cell potential are two faces of the same thermodynamic reality. Combining ΔG° = −nFE°cell with ΔG° = −RT ln K gives ln K = nFE°cell / (RT) (equivalently E°cell = (RT/nF) ln K). Because the relationship is exponential, a positive cell potential of only a few tenths of a volt corresponds to an enormous K; conversely, measuring a cell voltage is a precise way to determine an equilibrium constant. This is the final link in the chain E°cell ⇄ ΔG° ⇄ K.

Why this matters

This equation makes electrochemistry a precision tool for thermochemistry: a voltmeter can measure equilibrium constants that are too large or too small to measure by ordinary concentration methods. It also explains battery design — the bigger the gap between the two electrodes' potentials, the more completely the reaction runs and the more energy per electron is available.

The college version

Core Concept

Equilibrium and cell potential are two faces of the same thermodynamic reality. Combining ΔG° = −nFE°cell with ΔG° = −RT ln K gives ln K = nFE°cell / (RT) (equivalently E°cell = (RT/nF) ln K). Because the relationship is exponential, a positive cell potential of only a few tenths of a volt corresponds to an enormous K; conversely, measuring a cell voltage is a precise way to determine an equilibrium constant. This is the final link in the chain E°cell ⇄ ΔG° ⇄ K.

Key Ideas

  • One chain, three quantities. E°cell (volts), ΔG° (joules), and K (dimensionless) all encode the same spontaneity information.
  • Logarithmic bridge. ln K = nFE°cell/(RT) follows directly from setting the two ΔG° expressions equal.
  • Exponential amplification. K = e^(nFE°cell/RT) — small voltage differences mean huge K differences.
  • At 25 °C, a convenient constant. (RT/nF) = 0.0257 V/n (using ln) or 0.0592 V/n (using log₁₀).
  • Positive E°cell ⇒ K > 1 (products favored); negative E°cell ⇒ K < 1 (reactants favored).

Equations and Variables

SymbolMeaningCommon units
E°cellStandard cell potentialV
KEquilibrium constantdimensionless
nMoles of electrons transferredmol e⁻
FFaraday constant = 96,485 C/mol e⁻C/mol
RGas constant = 8.314 J/(mol·K)J/(mol·K)
TAbsolute temperatureK

ln K = nFE°cell / (RT)

How It Works

  1. Balance the reaction and find n and E°cell.
  2. Use the ln form (or the 25 °C shortcut: log K = nE°cell / 0.0592 V).
  3. Solve for K = e^(ln K).
  4. Interpret: K ≫ 1 (product-favored), K ≈ 1 (balanced), K ≪ 1 (reactant-favored).

Worked Example

Calculate K at 25 °C for Zn(s) + Cu²⁺(aq) ⇌ Zn²⁺(aq) + Cu(s).

  • n = 2, E°cell = +1.10 V.
  • ln K = nFE°cell/(RT) = (2)(96,485 C/mol)(1.10 V) / (8.314 J/(mol·K) × 298 K)
  • Numerator = 212,267 J/mol; denominator = 2477.6 J/mol.
  • ln K = 212,267 / 2477.6 = 85.7
  • K = e^85.7 = 1.6 × 10³⁷

An essentially infinite equilibrium constant — the Zn/Cu reaction runs essentially to completion. (Using the shortcut: log K = (2 × 1.10)/0.0592 = 37.2, so K = 10^37.2 ≈ 1.6 × 10³⁷, matching.)

How it works

  1. Balance the reaction and find n and E°cell.
  2. Use the ln form (or the 25 °C shortcut: log K = nE°cell / 0.0592 V).
  3. Solve for K = e^(ln K).
  4. Interpret: K ≫ 1 (product-favored), K ≈ 1 (balanced), K ≪ 1 (reactant-favored).

Common confusions

  • "Use log K = nE°/0.0592 with E° in millivolts." — Wrong. E° must be in volts for the 0.0592 shortcut.
  • "Big E°cell means small K." — Wrong. Larger E°cell means larger K (positive E°cell ⇒ K > 1).
  • "K = nFE°/(RT) directly." — Wrong. It is ln K = nFE°/(RT); you must exponentiate to get K.
  • "The 0.0592 factor works at any temperature." — Wrong. 0.0592 V assumes 25 °C (298 K).
  • "n is the same as the cell's coefficient of the cathode." — Wrong. n is the total electrons transferred in the balanced net reaction.

Quick review

  • ln K = nFE°cell/(RT).
  • At 25 °C, log K = nE°cell/0.0592 V.
  • Positive E°cell ⇒ K > 1 (product-favored).
  • K depends exponentially on E°cell.
  • Chain: ΔG° = −nFE°cell = −RT ln K.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a see-saw where the two seats are "reactants" and "products." The cell voltage is how hard the see-saw tilts. You'd think a tiny tilt means the products barely win — but no: the tilt-to-K conversion is exponential, like a lever with a giant mechanical advantage. A modest 1-volt tilt slams the see-saw almost flat to the products side — K becomes astronomically large. That's why a humble 1.1-volt battery can drive its reaction essentially to completion. (The limit: K describes the equilibrium position, not how fast it gets there — a huge K can still be kinetically slow.)

Worked example

Worked Example

Calculate K at 25 °C for Zn(s) + Cu²⁺(aq) ⇌ Zn²⁺(aq) + Cu(s).

  • n = 2, E°cell = +1.10 V.
  • ln K = nFE°cell/(RT) = (2)(96,485 C/mol)(1.10 V) / (8.314 J/(mol·K) × 298 K)
  • Numerator = 212,267 J/mol; denominator = 2477.6 J/mol.
  • ln K = 212,267 / 2477.6 = 85.7
  • K = e^85.7 = 1.6 × 10³⁷

An essentially infinite equilibrium constant — the Zn/Cu reaction runs essentially to completion. (Using the shortcut: log K = (2 × 1.10)/0.0592 = 37.2, so K = 10^37.2 ≈ 1.6 × 10³⁷, matching.)

Key takeaways

  • ### High-Yield Facts
  • ln K = nFE°cell/(RT); K = e^(nFE°cell/RT).
  • At 25 °C: E°cell = (0.0257 V/n) ln K, or log K = nE°cell / 0.0592 V.
  • E°cell > 0 ⇒ K > 1; E°cell < 0 ⇒ K < 1; E°cell = 0 ⇒ K = 1.
  • Small voltage changes ⇒ huge K changes (exponential).
  • Full chain: ΔG° = −nFE°cell = −RT ln K.
  • Use T in Kelvin and consistent units for F, R, and E°cell.

Keep learning

Ready to build on this? Continue to the next lesson.

Practice General Chemistry II

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • Derive and use ln K = nFE°cell / (RT).
  • Calculate K from E°cell and E°cell from K.
  • Explain why even a modest cell voltage can imply an enormous equilibrium constant.
  • Connect E°cell, ΔG°, and K in a single logical chain.

Sources & references

  1. OpenStax, *Chemistry 2e*, Ch. 17.4 "Potential, Free Energy, and Equilibrium." https://openstax.org/books/chemistry-2e/pages/17-4-potential-free-energy-and-equilibrium
  2. NIST CODATA (Faraday constant). https://physics.nist.gov/cuu/Constants/
  3. NIST Chemistry WebBook. https://webbook.nist.gov/chemistry/

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

Educational content only. It is not medical, legal or professional advice. Found an error? Tell us.