How to Use the Nernst Equation

Two forms of one equation

The Nernst equation gives the potential of an electrode, cell or membrane when concentrations are not at their standard values. Chemists and biologists write it in two ways.

Electrochemical cell: E = E° − (RT ÷ nF) × ln Q

Ion across a membrane: E_ion = (RT ÷ zF) × ln([ion]_outside ÷ [ion]_inside)

R is 8.314 J/(mol·K), T the temperature in kelvin, F 96,485 C/mol, n the electrons transferred, z the ion's charge and Q the reaction quotient.

The shortcuts

Changing ln to log₁₀ multiplies by 2.303. RT/F × 2.303 is 59.16 mV at 25 °C and 61.5 mV at 37 °C, so:

• at 25 °C: E = E° − (0.05916 V ÷ n) × log Q
• at 37 °C: E_ion = (61.5 mV ÷ z) × log([out] ÷ [in])

Example: a zinc–copper cell

Zn | Zn²⁺ (1.0 M) || Cu²⁺ (0.010 M) | Cu at 25 °C, with E° = 1.10 V and n = 2. Q = [Zn²⁺] ÷ [Cu²⁺] = 100, and log 100 = 2.

E = 1.10 − (0.05916 ÷ 2) × 2 = 1.10 − 0.059 = 1.04 V. Lowering the copper ion concentration lowers the cell voltage.

Example: ions across a neuron's membrane

With typical mammalian concentrations at 37 °C:

The resting potential, around −70 mV, sits near the K⁺ value because the resting membrane is mostly permeable to potassium. To combine several ions weighted by their permeabilities, use the Goldman–Hodgkin–Katz equation instead.

Common mistakes

• The sign of z. For an anion such as Cl⁻, z is −1, which flips the sign.
• Outside over inside. The membrane form puts the outside concentration on top. Swapping them flips the sign.
• Temperature. Using 59 mV at body temperature makes every result about 4% too small.
• Activities. The equation strictly uses activities, not concentrations. In concentrated solutions the two differ noticeably.

Calculators

The Nernst Equation Calculator does both forms at any temperature. For hydrogen ion concentration and pH, use the pH Calculator.