pH meters (hydrogen ion concentration)

Acids and bases are significant in food and chemical industries, water and sewage treatment, biology, medicine, etc. Therefore, we need to be able to measure concentration and strength of acid and base solutions. Instrumentation has been developed to measure pH of solutions using special selective electrodes that can develop an electromotive force, which is proportional to the hydrogen ion concentration in the solution where these electrodes are immersed.

What we understand under the term of pH? How is it related to the concentration and strength of solutions?

It is known, that acids and bases produce conductive solutions, when dissolve in water, because charged ions are formed. Here are ionisation equations for hydrochloric acid and sodium hydroxide dissolved in water:

If we mix these two aqueous solutions, the acidic and basic properties of the solution will be lost, so the neutralisation reaction occurrs:

Water is formed as the result of this reaction. However, the resulting solution is still conductive, because of the presence of sodium and chloride ions. If the quantities of initial acid and base are equal, then this resultant solution will be neither alkaline, nor acid.

In the case of dissociation of pure water, ions of hydrogen and hydroxyl are formed:

Pure water is very weak regarding to dissociation. So, very small amount of water molecules break into ions. The symbol Û  in (7.4) indicates that the process consists of two reactions, namely, dissociation of molecules into ions and recombination of ions into molecules. 

Fig 7.6A : Dissociation and formation of hydronium.

For pure water the rates of these two reactions are equal, and we can write an equilibrium equation as follows:

where,

Since pure water is neutral, then according to (7.5) the activity of hydrogen and hydroxyl ions should be equal, ie, 10-7  mole/l. No matter what compounds form an aqueous solution, the product of activities of hydrogen and hydroxyl ions should always be equal to 10-14  mole/l at 25 °C.

With an addition of a strong acid (such as HCl) to pure water we add many hydrogen ions. As the result of this addition, the number of hydrogen ions will increase, let’s say to 10-2  mole/l, and the activity of hydroxyl ions then will be equal 10-12  mole/l. As we can see, the product of activities is still equal to 10-14  mole/l at 25 °C.

Since the use of ion activities in the form of a power representation is not convenient, a Danish biochemist S.P.L. Sørensen in 1909 proposed to use the expression of pH, which was originally derived from the phrase “power of hydrogen”. The pH is defined as a negative common logarithm (with the base of ten) of the hydrogen ion activity, as follows:

Therefore, the pH of pure water is equal to 7 at 25 °C. Acid solutions contain more hydrogen ions than hydroxyl ions, so the activity of hydrogen ions will be greater than 10-7 , that is, 10-6, 10-5, 10-4, 10-3, etc., with pH equal to 6, 5, 4, 3, etc., respectively. pH values for basic solutions will be 8, 9, 10, 11, etc., respectively.

Instrumentation for pH measurements use an electrometric method. A glass pH-responsive electrode immersed in a solution under measurement will vary electric potential (voltage) on the boundary between the electrode and solution as a function of pH of this solution. However, it is not possible to measure the potential between this electrode and solution only. Why? Because when we connect a measuring device, another potential is developed between the solution and a conductor which connects the measuring device and the solution, this new potential being also dependent on the pH of the solution. Therefore, we need to use one more electrode, the reference electrode, which potential is not dependent on the pH of the solution. In order to make the potential of the reference electrode not dependent on the pH of the solution, it should be filled with a saturated solution.

Figure 7.6. Schematic of a pH-meter with the glass and reference (calomel) electrodes.

Fig. 7.6 shows schematic of a pH-meter. A glass electrode 1 and a reference electrode 2 are immersed in a solution 3 under measurement. The potential difference between these two electrodes which is proportional to the pH of the solution is measured by a potentiometer 6. The glass electrode is filled with the solution 4 with a known value of pH. A silver-silver chloride electrode 5 is placed inside the glass electrode. The reference electrode presents a dielectric enclosure 2 filled with pure mercury 7. A low soluble mercury-mercury chloride 8 (calomel) is placed above mercury. The reference electrode is filled with a saturated solution 9 of KCl. A semipermeable membrane 10 is used to produce an electrical contact between KCl solution and the solution under measurement 3. Potassium chloride diffuses or leaks into the solution under measurement, so the concentration of KCl in the reference electrode is not changed. An electrical circuit consists of several elements connected in series, and an overall electromotive force is equal to the sum of these potentials, as follows:

where,

E_S - the overall electromotive force developed in the circuit, mV;
E₁ - potential between a silver-silver chloride electrode and the solution 4, mV;
E2 - potential between the solution 4 and an internal surface of the glass electrode, mV;
E3 - potential between mercury and calomel in the reference electrode, mV;
Ex - potential between an outside surface of the glass electrode and the solution under measurement, mV.

E1, E2 and E3 are not dependent on the pH of the solution under measurement, but vary with temperature. Ex depends on the pH of the solution under measurement and its temperature, and can be evaluated by the Nernst equation:

where,
R - the gas law constant, R = 8.31451 J/(mole*K);
T - absolute temperature of the solution under measurement, K;
F - Faraday’s number, F = 96485.309 C/mole, C - coulomb.

The overall electromotive force at a constant temperature is the function of the pH of solution only. However, one need to introduce a temperature compensation element (usually a suitable packaged resistor, thermistor, or resistance temperature detector), which is placed close to the glass electrode in the solution under measurement and connected to the electrical circuit for electromotive force measurement.

Article Source:: Dr. Alexander Badalyan, University of South Australia