Engineering
Nernst equation: electrochemical cell potential and reaction quotient
Calculate a reversible cell potential from a supplied standard potential, temperature and dimensionless activity-based reaction quotient.
Use a temperature-consistent standard potential and reaction quotient
The Nernst equation is E=E0-(RT/nF)*LN(Q). Supply E0 for the same temperature as T; changing temperature while holding an arbitrary E0 fixed is not a complete temperature model. Q is dimensionless and based on activities for the balanced reaction. Concentration ratios approximate activities only under suitable assumptions.
For the supplied hypothetical Daniell-cell parameters at 25 degrees Celsius, E0=1.1 V, n=2 and Q=0.01 give 1.1592 V. This is a reversible equilibrium potential, not a prediction of a loaded battery terminal voltage: resistance, kinetics and overpotentials are omitted. Q=1 gives E=E0 without proving every species has unit activity.
| Daniell Cell State (E0 = 1.100 V, n = 2, 25 °C) | Reaction Quotient Q | Cell Potential E (Volts) |
|---|---|---|
| Low reaction quotient | Q = 0.01 | 1.1592 V |
| Unit reaction quotient | Q = 1 | 1.1000 V |
| High reaction quotient | Q = 100 | 1.0408 V |
Nernst potential with supplied temperature-consistent E0
A2=E0_V (1.10), B2=Electrons n (2), C2=Temp_C (25), D2=Quotient Q (0.01), E2=R (8.31446), F2=Faraday F (96485.3).
Use a positive integer electron count for the balanced reaction, temperature above absolute zero, positive Q and positive R and F. E0 may be negative.
=IF(OR(COUNT(A2:F2)<>6,B2<=0,B2<>INT(B2),C2<=-273.15,D2<=0,E2<=0,F2<=0),"Invalid inputs",ROUND(A2 - ((E2 * (C2 + 273.15)) / (B2 * F2)) * LN(D2), 4))Thermal voltage slope (RT / nF in Volts per natural-log unit)
Evaluates ~0.01285 V at 25 °C for n = 2 (equivalent to 0.02958 V per decade LOG10).
=IF(OR(COUNT(A2:F2)<>6,B2<=0,B2<>INT(B2),C2<=-273.15,D2<=0,E2<=0,F2<=0),"Invalid inputs",ROUND((E2 * (C2 + 273.15)) / (B2 * F2), 5))Try the example
Use the original values or change them to test your understanding.