Engineering & Scientific
Nernst Equilibrium (Reversal) Potential & Electrochemical Driving Force
Compute ion reversal potential E_ion = (R*T / (z*F)) * LN([X]_out / [X]_in) in millivolts across temperature and valence, plus net transmembrane driving force V_m - E_ion.
Why textbook 61.5 mV log10 approximations fail away from 37 °C or for divalent ions
Across a selectively permeable membrane or electrochemical half-cell, Walther Nernst’s equilibrium voltage balances thermal diffusion against electrostatic drift: E_ion = (R * T / (z * F)) * LN(C_out / C_in), where R = 8.31446 J/(mol*K), F = 96,485.33 C/mol, T = T_Celsius + 273.15 K, and z is signed ion valence (+1 for K+/Na+, +2 for Ca2+, -1 for Cl-).
Hardcoding 61.5 * LOG10(C_out / C_in) silently assumes z = +1 at mammalian 37 °C (310.15 K, thermal voltage R*T/F = 26.73 mV), producing wrong voltages for room-temperature 20 °C squid-axon / patch-clamp recordings (R*T/F = 25.26 mV) or negative anions like Cl- (where z = -1 flips the polarity!).
| Ion at 37 °C (V_m = -70 mV) | Valence z | [Out] / [In] (mM) | Reversal E_ion & Driving Force |
|---|---|---|---|
| Potassium (K+) | +1 | 4.5 / 140 | E_K = -91.87 mV | V_m - E_K = +21.87 mV (Outward) |
| Hyperkalemic K+ | +1 | 8.0 / 140 | E_K = -76.50 mV | Depolarized +15.37 mV |
| Calcium (Ca2+) | +2 | 2.0 / 0.0001 | E_Ca = +132.34 mV | Strong inward gradient |
| Chloride (Cl-) | -1 | 110 / 10 | E_Cl = -64.09 mV | Signed z = -1 flips sign |
Exact Temperature- & Valence-Aware Nernst Potential Formula (mV)
Convert Celsius to Kelvin, compute thermal voltage (R * T_K / F) * 1000 in millivolts inside LET, divide by signed valence z, and multiply by LN(C_out / C_in).
=LET(tk, B2 + 273.15, v_th, (8.31446 * tk / 96485.33) * 1000, ROUND((v_th / B3) * LN(B4 / B5), 2))Electrochemical Driving Force (V_m - E_ion)
Subtract E_ion from resting membrane voltage V_m: positive driving force drives net outward cation current (or inward anion current), while V_m = E_ion yields zero net flux.
=ROUND(B6 - E3, 2)Try the example
Use the original values or change them to test your understanding.