Nernst Equation Calculators

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The Nernst equation calculates the actual electrode potential based on standard potential and ion concentrations: E = E° − (RT/nF) × ln(Q). In electrochemistry it adjusts the standard cell potential for non-standard conditions. In biology, it predicts the equilibrium membrane potential for each ion: E_ion = (RT/zF) × ln([ion]_out/[ion]_in). K⁺ equilibrium potential ≈ −90 mV; Na⁺ ≈ +60 mV. These Nernst potentials set the driving force for ion flow through open channels. The pH electrode applies the Nernst equation with a sensitivity of 59.16 mV/pH unit at 25°C.

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Nernst Equation

Electrochemistry: E = E° − (RT/nF) × ln(Q)

At 25°C simplified: E = E° − (0.05916/n) × log(Q). R = 8.314 J/mol/K; T in K; n = electrons; F = 96,485 C/mol.

Biological Nernst Equation

E_ion = (RT/zF) × ln([ion]_out / [ion]_in)

At 37°C: E_ion = (25.7 mV / z) × ln([ion]_out / [ion]_in). K⁺ (z=+1): [K⁺]_out = 5 mM; [K⁺]_in = 140 mM: E_K = 25.7 × ln(5/140) ≈ −86 mV ≈ −90 mV. Na⁺: [Na⁺]_out = 145 mM; [Na⁺]_in = 15 mM: E_Na = 25.7 × ln(145/15) ≈ +58 mV ≈ +60 mV.

pH Electrode

E = E_ref + 0.05916 × pH at 25°C. Nernst slope = 59.16 mV per pH unit. Calibrate with pH 4 and pH 7 buffers.

Equilibrium and ΔG

At equilibrium: E_cell = 0 → log Keq = n × E°/0.0592. ΔG = −nFE; ΔG° = −nFE°.

Glossary

Nernst Equation
E = E° − (RT/nF)ln(Q); adjusts electrode potential for non-standard concentrations; at 25°C: E = E° − (0.0592/n)log(Q); equilibrium when E = 0, giving log Keq = nE°/0.0592.
Nernst Potential (E_ion)
(RT/zF)ln([ion]_out/[ion]_in); the membrane voltage at which no net ion flow occurs; E_K ≈ −90 mV; E_Na ≈ +60 mV; E_Ca ≈ +130 mV in mammalian neurons at 37°C.
Nernst Slope
59.16 mV per pH unit at 25°C for pH electrodes; = RT ln(10)/F; decreases with electrode aging; used for electrode calibration with standard pH buffers.

Frequently Asked Questions

The Nernst equation relates actual electrode potential to the standard potential and ion concentrations: E = E° − (RT/nF) × ln(Q) or E = E° − (0.0592/n) × log(Q) at 25°C. Used when: ion concentrations are not at standard (1 M) conditions; to determine spontaneity of electrochemical reactions (positive E = spontaneous); to calculate equilibrium constants from standard potentials; to calibrate ion-selective electrodes (pH meters); to find biological equilibrium membrane potentials for individual ions.

E_ion = (RT/zF) × ln([ion]_out/[ion]_in). z = charge (+1 for Na⁺, K⁺; −1 for Cl⁻; +2 for Ca²⁺). These equilibrium potentials represent the membrane voltage at which no net ion flow occurs for that ion. K⁺: [K⁺]_out = 5 mM; [K⁺]_in = 140 mM → E_K = 25.7 × ln(5/140) ≈ −86 mV. Na⁺: E_Na ≈ +58 mV. Ca²⁺: E_Ca ≈ +130 mV. When K⁺ channels open: membrane potential is driven toward −86 mV. When Na⁺ channels open: potential driven toward +58 mV. The resting membrane potential (≈ −70 mV) reflects the weighted average of these potentials, dominated by K⁺ permeability.

A glass pH electrode has a membrane selectively permeable to H⁺. The potential across the glass: E = E_ref + (RT/F) × ln[H⁺] = E_ref − (RT/F) × 2.303 × pH. At 25°C: E = E_ref − 0.05916 × pH. Each pH unit change corresponds to 59.16 mV change in electrode potential — the Nernst slope. Calibration with pH 4 and pH 7 buffers determines the electrode's actual slope (may be slightly < 59.16 mV due to aging). Temperature affects slope: pH meters require temperature input for accurate readings (the RT/F term changes with T).

At equilibrium the cell potential = 0: 0 = E° − (0.0592/n) × log(Keq). Rearranging: log Keq = n × E° / 0.0592. Connection to thermodynamics: ΔG° = −nFE°; ΔG = −nFE. Spontaneous reaction: E > 0 (ΔG < 0). Example: Zn-Cu cell E° = 1.10 V; n = 2: log Keq = 2 × 1.10/0.0592 = 37.2; Keq = 10^37.2 — the reaction strongly favors products. Biological relevance: standard potentials of biological redox couples (NAD⁺/NADH = −0.32 V; O₂/H₂O = +0.82 V) determine the free energy available from electron transfer in the electron transport chain.