04 // Interactive Formula Compendium // CHEMISTRY-THERMOE = E° − (R · T / (n · F)) · ln(Q)
Nernst Electrochemical Cell Potential Equation
The Nernst equation E = E° − (RT/nF)ln(Q) computes galvanic cell voltage E from standard potential E°, electrons transferred n, Faraday constant F = 96,485.3 C/mol, and reaction quotient Q.
Formula Reference
Main Formula
E = E° − (R · T / (n · F)) · ln(Q)
Rearranged Forms
E_298K = E° − (0.05916 V / n) · log₁₀(Q)
ΔG = −n · F · E
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| E | Cell Potential E | V |
| E0 | Standard Potential E° | V |
| T | Absolute Temperature | K |
| n | Electrons Transferred n | mol e⁻ |
| Q | Reaction Quotient Q | dimensionless |
Inputs & Parameters
[V]
[K]
[mol e⁻]
[dimensionless]
Calculated Result (Cell Potential E)
E =1.159159V
Formula Notes & Background
- Substituting ΔG = −nFE and ΔG° = −nFE° into thermodynamic identity ΔG = ΔG° + RT ln(Q) and dividing by −nF yields E = E° − (RT/nF)ln(Q).
- At chemical equilibrium ΔG = 0 and E = 0, giving E° = (RT/nF)ln(K_eq).
Step-by-Step Examples
#1: Daniell Zn/Cu cell (E° = 1.10 V, n = 2) at 298.15 K with [Zn²⁺] = 0.01 M and [Cu²⁺] = 1.0 M (Q = 0.01).
E° = 1.10 Vn = 2Q = 0.01T = 298.15 K
E = 1.10 − (0.025693 / 2) × ln(0.01) = 1.10 − 0.012846 × (−4.6052)
→ E = 1.159 V
#2: Potassium neuronal resting potential at 310 K (n = 1, E° = 0, [K⁺]_out = 5 mM, [K⁺]_in = 140 mM ⇒ Q = 28).
E° = 0 VT = 310 Kn = 1Q = 140/5 = 28
E_K = −(8.31446 × 310 / 96,485.3) × ln(28) = −0.02671 × 3.3322
→ E_K = −0.0890 V (−89.0 mV)
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Frequently Asked Questions
Where does the 0.05916 V factor come from?+
At T = 298.15 K (25 °C), (R·T / F) × ln(10) = 0.025693 V × 2.302585 = 0.05916 V.
What does E = 0 V signify in a battery?+
Q has grown equal to equilibrium constant K_eq, meaning ΔG = 0 and the battery is completely discharged.
Are pure solids and pure liquids included in reaction quotient Q?+
No — pure crystalline solids (like Zn(s) or Cu(s) electrodes) and pure liquid solvents have unit thermodynamic activity (a = 1).