Nernst equation for
a pH electrode

Nernst equation is a mathematical description of an ideal pH electrode behavior. Hermann Walther Nernst (1864 – 1941) was a German chemist that introduced in 1889 a well known equation, correlating chemical energy and the electric potential of a galvanic cell or battery.

The pH electrode potential

As explained on the pH definition page of this site, the pH value is defined as the negative logarithm of the H+ activity in a given solution (pH = log aH+).

Equation of a straight line

The equation E = E0 - kT·pH is the potential or voltage (millivolt; mV) relation of a pH electrode. It is the equation of a straight line. The slope factor is the term "kT" and it provides the amount of change in total potential (mV) for every change in pH unit.

Temperature

The equation E = E0 - kT·pH may be stated for any temperature. However, the slope or Nernst factor (kT) will change when temperature changes (T is not constant).

If T = 25 °C the equation will be: E = E0 - 0.0592·pH

Let's draw the graph of this equation:

This is the theoretical equation for an ideal pH electrode. And as you will see there is no ideal or perfect pH sensor. However, first let's read more about pH versus temperature.



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