Principles of the pH-value measurement with Hydrogen Electrodes

Hydrogen potential and pH-value

The hydrogen potential directly depends on the activity or rather the concentration of the hydronium ions and thus on the pH-value of the solution. The pH-value itself is defined as the negative decadic logarithm of the hydrogen ions activity. The activity is the product of concentration and activity coefficient. The latter can only be defined approximately in diluted solutions. Thus, the measurement of the pH-value according to its definition can only be made approximately.

As soon as two half cells are contacted and the circuit is closed, the potential of the spontaneous happening reaction sets. Due to the higher proton concentration in the left half-cell, the hydrogen ions are reduced to hydrogen. Thereby, electrons are removed from the electrode and thus it has a more positive potential than the electrode in the right half-cell. So, the reduction takes place in the left half-cell. This cell is equivalent to the cathode and is the positive pole in the galvanic cell.
In the right half-cell, hydrogen is oxidized to hydrogen ions. The electrode has a more negative potential than the left electrode (negative pole). In the right half-cell the oxidation takes place, so the right half-cell is equivalent to the anode.
The free flow direction of the electrons is from the negative pole to the positive pole, here (in a galvanic cell) from the anode to the cathode. Electrons flow from right to left, thus from the diluted to the concentrated cell.
The potential is calculated by E = E (right) – E (left). The standard hydrogen electrode has to be the left cell according to the IUPAC.

The potential changes technically with a positive sign depending on the proton concentration. BUT: we have a logarithmic function of the protons function. At concentrations < 1 mol/L, negative potentials result, here it is -0.059 V at a concentration of 0.1 mol/L.
If you convert the protons concentration into the pH-value, the calculation of the potentials is easier: E = 0.059 pH (25°C)
Since E < 0 Volt, the reaction proceeds from right to left, as we expect due to the different concentrations. To measure negative potentials in such a concentration chain, the standard hydrogen electrode has to be connected to the negative pole (COM-port).
The platinum hydrogen pH electrode pHydrunio is such a measuring chain. The outer hydrogen electrode measures the hydrogen potential in the measuring solution. Against a normal hydrogen electrode (by definition: reference potential of 0 mV), the lower dark orange dotted line in the diagram arises, according to the calculation
E = -0.059 pH (25°C). However, the inner reference electrode of our pH electrode is placed in buffer pH 7. This has to be considered when calculating the potential. Hence, an offset of 0.414 V arises at 25°C and the measuring voltages are equivalent to the upper light orange straight.