Nernst Equation

A tabulated standard potential assumes every dissolved species sits at 1 M and every gas at 1 bar — conditions almost nothing in the real world satisfies. Walther Nernst's 1889 equation supplies the correction: the potential shifts by (RT/nF) ln Q, pushing the cell voltage up when reactants are plentiful and down as products pile up. At 25 °C the factor RT/F is 0.02569 V, so multiplying by ln 10 gives the famous 0.05916/n volts per decade. A Daniell cell with E° = 1.10 V, n = 2, and Q = 0.100 reads E = 1.10 + (0.05916/2) = 1.130 V.

That "59 mV per tenfold" is the entire basis of potentiometry. A glass pH electrode is a concentration cell whose voltage moves 59 mV for every pH unit, which is exactly why a pH meter must be calibrated at the temperature of the sample — at 50 °C the slope is 64 mV, not 59, and an uncorrected reading drifts. Nernst received the 1920 Nobel Prize in Chemistry (presented in 1921) chiefly for his heat theorem, the third law of thermodynamics, but this equation is what carries his name into every teaching lab. The usual mistakes are writing Q upside down (products over reactants, always) and swapping ln for log₁₀ without changing 0.02569 to 0.05916.