E_cell = E_cathode - E_anode
Cell potential equals the reduction potential at the cathode minus the reduction potential at the anode.
Cell potential from reduction potentials of the cathode and anode.
- E_cathode
- reduction potential of the cathode half-reaction (V)
- E_anode
- reduction potential of the anode half-reaction (V)
Use when — Both values are written as reductions under matching conditions.
Common trap — Reversing one value's sign and subtracting again, double-correcting the orientation.
ΔG = -nFE
Reaction Gibbs-energy change equals negative n times Faraday's constant times cell potential.
Reaction Gibbs-energy change for a cell reaction transferring n electrons.
- n
- number of electrons transferred in the balanced reaction (mol)
- F
- Faraday constant (C mol^-1)
Use when — The reversible cell relation applies to the written, balanced reaction.
Common trap — Using stoichiometric coefficients that do not match the n actually used in the electron balance.
E = E° - (RT / nF) ln Q
Cell potential equals standard potential minus RT over nF times the natural log of the reaction quotient.
Nernst equation relating cell potential to standard potential and reaction quotient.
- R
- gas constant (J mol^-1 K^-1)
- T
- temperature (K)
- Q
- reaction quotient of the balanced cell reaction
Use when — Activities are defined, the reaction is balanced, and temperature is stated.
Common trap — Building Q for the reverse reaction instead of the reaction as written for the cell.
E = E° - (0.05916 / n) log Q
This is the 298 kelvin numerical form of the Nernst equation only.
Base-10 numerical form of the Nernst equation at approximately 298 K.
- n
- number of electrons transferred (mol)
Use when — Temperature is approximately 298 K.
Common trap — Using the 0.05916 constant at a temperature that is not approximately 298 K.
ln K = nFE° / (RT)
The natural log of the equilibrium constant equals n times Faraday's constant times standard cell potential, divided by RT.
Relation between the standard cell potential and the equilibrium constant of the cell reaction.
- K
- equilibrium constant of the balanced cell reaction
Use when — Same standard states and reaction orientation are used throughout.
Common trap — Substituting a nonstandard E in place of E° in this relation.
G = 1/R; κ = Gℓ/A
Conductance equals one over resistance; conductivity equals conductance times length over area, removing geometry.
Conductance from resistance, then conductivity from conductance and cell geometry.
- ℓ
- distance between electrodes (m)
- A
- electrode area (m^2)
Use when — Cell geometry (length and area) is uniform and known.
Common trap — Confusing conductance (geometry-dependent) with conductivity (a material property).
Λm = κ / c
Molar conductivity equals conductivity divided by molar concentration.
Molar conductivity normalizes conductivity per amount concentration.
- c
- molar concentration (mol m^-3 for strict SI)
Use when — Concentration is expressed in mol m^-3 for strict SI consistency.
Common trap — Using concentration in mol L^-1 directly without converting to mol m^-3.
Λm° = Σ νi λi°
Limiting molar conductivity equals the sum of each ion's stoichiometric count times its limiting ionic molar conductivity.
Kohlrausch law: limiting molar conductivity is the sum of independent ionic contributions.
- λi°
- limiting ionic molar conductivity of ion i
Use when — Independent ionic migration applies at limiting dilution.
Common trap — Applying limiting values at concentrated, not infinitely dilute, conditions.
m = MIt / (nF)
Mass deposited equals molar mass times current times time, divided by n times Faraday's constant.
Mass deposited or liberated during quantitative electrolysis.
- M
- molar mass of the species deposited or liberated (kg mol^-1)
- I
- current (A)
- t
- time (s)
Use when — Quantitative electrolysis is assumed to run at 100 percent current efficiency.
Common trap — Confusing the number of electrons transferred with the ionic charge sign.