# pH Temperature Compensation

The output of a pH electrode is effected by the temperature of the solution being measured, and whether temperature compensation is needed will depend on the pH accuracy required.

The relationship between the pH and temperature is given by the Nernst equation:

• E = Total potential (in mV) developed between the sensing and reference electrode
• E0 = Standard potential of the electrode at aH+ = 1 mol/l
• R = Gas constant
• T = Temperature
• n = Valency of ion
• aH+ = Activity of the hydrogen ion in solution

At 25°C, the change in each additional pH unit represents a +/- 59.16 mV change in the potential of the electrode. As the temperature of the solution changes the relationship between the measured mV value and the pH changes as can be seen in the graph above.

#### Solution Temperature Effect vs Electrode Temperature Effect

The solution temperature effect describes the changes in viscosity and mobility of the ions which induces a change in the pH of the solution. The change in pH due to temperature is not an error, but the true pH of the solution. Hence there is no need to compensate for this change.

However, the temperature effect on the pH electrode will result in an error and need to be compensated for by the pH meter. This effect is caused by changes in the resistance of the glass as the solution temperature varies.

In an ideal pH electrode, with an isoelectric point at pH 7, there is no temperature effect at pH 7. However, as the pH of the solution deviates away from pH 7 and 25°C the error increases. This can be seen in the table below, which shows the error as a function of pH and temperature.

 pH T(°C) 14 0.53 0.42 0.32 0.21 0.11 0 0.11 0.21 0.32 0.42 0.53 0.63 0.74 0.84 0.95 1.05 1.16 13 0.45 0.36 0.27 0.18 0.09 0 0.09 0.18 0.27 0.36 0.45 0.54 0.63 0.72 0.81 0.90 0.99 12 0.38 0.30 0.23 0.15 0.08 0 0.08 0.15 0.23 0.30 0.38 0,45 0.53 0.60 0.68 0.75 0.83 11 0.30 0.24 0.18 0.12 0.06 0 0.06 0.12 0.18 0.24 0.3 0.36 0.42 0.48 0.54 0.60 0.66 10 0.23 0.18 0.14 0.09 0.05 0 0.05 0.09 0.14 0.18 0.23 0.27 0.32 0.36 0.41 0.45 0.50 9 0.15 0.12 0.09 0.06 0.03 0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 0.33 8 0.08 0.06 0.05 0.03 0.02 0 0.02 0.03 0.05 0.06 0.08 0.09 0.11 0.12 0.14 0.15 0.17 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0.08 0.06 0.05 0.03 0.02 0 0.02 0.03 0.05 0.06 0.08 0.09 0.11 0.12 0.14 0.15 0.17 5 0.15 0.12 0.09 0.06 0.03 0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 0.33 4 0.23 0.18 0.14 0.09 0.05 0 0.05 0.09 0.14 0.18 0.23 0.27 0.32 0.36 0.41 0.45 0.50 3 0.30 0.24 0.18 0.12 0.06 0 0.06 0.12 0.18 0.24 0.3 0.36 0.42 0.48 0.54 0.60 0.66 2 0.38 0.30 0.23 0.15 0.08 0 0.08 0.15 0.23 0.30 0.38 0,45 0.53 0.60 0.68 0.75 0.83 1 0.45 0.36 0.27 0.18 0.09 0 0.09 0.18 0.27 0.36 0.45 0.54 0.63 0.72 0.81 0.90 0.99 0 0.53 0.42 0.32 0.21 0.11 0 0.11 0.21 0.32 0.42 0.53 0.63 0.74 0.84 0.95 1.05 1.16 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

#### Automatic vs manual temperature correction

There are typically two ways to compensate for errors due to temperature:
Automatic: uses a sensor to measure the temperature of the solution and transmits it back to the meter where the pH readings are corrected for the temperature. There are typically two types of temperature sensors used. External sensors which measure the solution temperature directly and internal sensors found in 3-in-1 style electrodes, which measure the temperature of the pH electrolyte. So when using internal sensors it is important to ensure that the electrode and solution have been given sufficient time to equilibriate.
The change in the Nernst slope can be compensated by the meter using automatic or manual temperature correction.

Manual: requires the user to key in the solution temperature in to the pH meter so that the reading can be correct for the inputted temperature. However, if the temperature of the solution changes it needs to be manually updated in the meter.