How this instrument works
The Nernst equation calculates the actual cell potential, E, of an electrochemical cell operating away from standard-state conditions, starting from its standard cell potential, E deg. Standard cell potential is measured at a fixed reference point — 1 M concentrations, 1 atm gas pressures, 298 K — but real cells rarely sit exactly there, so the equation adds a correction term, -(RT/nF) x ln(Q), that shifts E up or down depending on how far the reaction quotient Q has moved from 1. When Q equals 1, exactly at standard conditions, the correction term vanishes (ln(1) = 0) and E simply equals E deg.
The correction term itself comes straight from chemical thermodynamics: cell potential is proportional to the Gibbs free energy change of the reaction, and Gibbs free energy depends on the reaction quotient through ΔG = ΔG deg + RT ln(Q). Converting free energy to potential using ΔG = -nFE, where F is Faraday's constant (the charge carried by one mole of electrons) and n is the number of electrons transferred per reaction, and rearranging, produces the Nernst equation exactly as written. R and F are both fixed physical constants — R = 8.314 J/(mol K), F = 96,485 C/mol — so temperature, electron count and the reaction quotient are the only things that actually change from one calculation to the next.
The equation explains a wide range of real behavior beyond textbook batteries: it's why a battery's voltage sags as reactants are consumed and products build up (Q moves away from favoring the forward reaction), it underlies pH electrodes and other ion-selective sensors (where E responds to the concentration of a single ion), and it governs the resting membrane potential of living cells, where Q reflects the ratio of an ion's concentration across the cell membrane rather than a chemical reaction quotient.
- Enter the cell's standard potential into Standard cell potential, E deg (V) — a tabulated value for the specific redox reaction, measured at standard conditions.
- Enter how many electrons the balanced half-reactions transfer into Number of electrons transferred, n.
- Enter the current reaction quotient into Reaction quotient, Q — 1 at standard conditions, above 1 if products are favored, below 1 if reactants are favored.
- Enter the operating temperature into Temperature (K).
- Read Cell potential, E (V) — the actual voltage the cell produces under these specific, non-standard conditions.
Worked example — the Daniell cell at standard conditions
Enter 1.1 into Standard cell potential, E deg (V), 2 into Number of electrons transferred, n, 1 into Reaction quotient, Q, and 298 into Temperature (K) — the classic Daniell cell, Zn(s) + Cu2+(aq) -> Zn2+(aq) + Cu(s), evaluated exactly at standard conditions. Cell potential, E (V) reads 1.100000: since Q = 1, ln(1) = 0 by definition, so the entire correction term vanishes and E equals E deg exactly.
That result holds regardless of the RT/nF coefficient's numeric value, because multiplying anything by zero still gives zero — it's a useful sanity check that confirms the equation reduces correctly to its standard-state case. Change Reaction quotient, Q to a value other than 1 while holding the rest fixed, and Cell potential, E (V) shifts away from 1.100000 in the direction that reflects whether reactants or products are now in relative excess.
Questions
Why does cell potential equal E deg exactly when Q = 1?
Because the equation's correction term is -(RT/nF) x ln(Q), and ln(1) equals exactly 0 regardless of what RT/nF works out to. Q = 1 corresponds to standard-state conditions (1 M concentrations, 1 atm gas pressures for the species involved), which is precisely the condition under which E deg itself was defined and measured, so the equation is built to reduce to E = E deg exactly at that point.
What does it mean if the reaction quotient Q is greater than 1?
Q > 1 means products are present in relative excess compared to standard conditions (or reactants are relatively depleted). Because ln(Q) is then positive and it's subtracted, the cell potential E drops below E deg — physically, the reaction has less driving force left to push forward when it's already partway toward its products, which is exactly what happens as a real battery discharges and its reactants are consumed.
How does temperature affect the size of the correction?
The correction term -(RT/nF) x ln(Q) scales directly with T, so raising the temperature amplifies how far E moves from E deg for any given Q away from 1 — at higher temperature, the same deviation from standard conditions produces a larger voltage shift. At T = 0 K the correction term would vanish entirely, though that's a purely mathematical limit; real electrochemical cells don't function near absolute zero.
Why does the number of electrons transferred, n, matter?
n sits in the denominator of the correction term, so it scales the size of the correction inversely: a reaction that transfers more electrons per unit reaction spreads the same free-energy change across more charge, producing a smaller voltage shift for a given change in Q. n comes directly from balancing the cell's half-reactions and must match the overall balanced equation, not just one half-reaction in isolation.
What are R and F, and why are they fixed constants?
R is the molar gas constant, 8.314 J/(mol K), the same constant that appears in the ideal gas law; F is Faraday's constant, 96,485 C/mol, the electric charge carried by one mole of electrons. Both are universal physical constants with values fixed by nature (F is defined exactly in the modern SI), not adjustable parameters, so only E deg, n, Q and T change between different Nernst-equation problems.
Why must Q and n be entered as positive numbers?
The equation takes the natural log of Q, which is undefined for zero or negative values, so Q must be strictly positive — a physically sensible requirement, since reaction quotients are ratios of concentrations or pressures, which can't themselves be negative. n represents a count of electrons transferred and must likewise be positive; the instrument blanks the reading and explains why if either constraint is violated.