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

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Electrolytic conductivity meters

An operational principle of electrolytic conductivity meters is based on the relationship between electrical conductivity and concentration of solutions.

The ability to conduct electricity is called electrical conductance, which is reciprocal of electrical resistance:

electrical conductance = 1/electrical resistance.

The unit for electrical conductance is Siemens: 1S = 1/Ohm.

Electrical conductivity is equal to electrical conductance of a volume of the material of unit length and area:

electrical conductivity = electrical conductance*length/area.

The unit for electrical conductivity is S/m. Few solutions exhibit electrical conductivities as great as 1 S/cm. So, the most commonly used units are mS/cm and mS/cm.

Electrolytic conductivity is usually defined as electrical conductance of a unit cube of solution as measured between opposite faces. It has the same units as electrical conductivity.

In conductive or electrolytic solutions positive ions (cations) move toward the cathode, and negative ions (anions) move toward the anode. Reduction and oxidation take place on the cathode and anode, respectively. Electrolytic conductivity of a solution mostly depends on the concentration and mobility of all ions in the solution. The latter depends on the ion size, charge, dielectric constant of the solvent, temperature and viscosity of the solution. Electrolytic conductivity of a mixture of solutions is proportional to the sum of relative concentration of each components and the mobility of ions. Therefore, conductivity meters are used for electrolytic conductivity measurements of one component solutions only. Fig. 7.4 shows typical conductivity curves for NaCl solution in water.


Electrolytic conductivity is usually measured by placing electrodes in contact with an electrolytic solution. In this case electrical conductance between electrodes is related to electrolytic conductivity of the solution. Since the conductivity cell has unchanged dimensions, so by measuring electrical conductance of the solution in this cell, and thus determining the cell constant, we can relate thus measured electrical conductance to the actual value of electrolytic conductivity.


Fig. 7.5 schematically shows an electrolytic conductivity meter, which employs an alternating current Wheatstone bridge in order to avoid polarisation of measuring electrodes. A conductivity cell is immersed in the solution 1. This cell consist of an insulating shield 2 made of either glass or epoxy, or polystyrene, or Teflon. Two metal electrodes 3 are placed inside this shield. These electrodes are made of either stainless steel or nickel, or platinum, or gold, or platinum-plated metals. The shield is perforated to provide good contact of solution with these electrodes. The operational principle of a Wheatstone bridge is described in 3.5. We measure an electrical resistivity (r) of the electrolytic solution between cell electrodes. An electrical resistivity is defined as an electrical resistance of a conductor of unit cross-sectional area and unit length, as follows: r=R*A/L, (Ohm*m), where, R is the electrical resistance of the conductor (Ohm), A is the cross-section area of the conductor (m2), and L is the length of the conductor (m).

Figure 7.4. Electrolytic conductivity of NaCl solutions. 

Since temperature of an electrolytic solution has influence on its electrolytic conductivity, therefore, we should be able to introduce temperature correction (compensation). For this purpose an electrode sensor filled with a reference liquid, which has a thermal coefficient of electrolytic conductivity approximately equal to that of the measuring solution, is employed. This sensor is immersed in the measuring electrolytic solution near the measuring conductivity cell, and through conductors is connected to the side of the bridge adjacent to that side of the bridge which is connected to the measuring conductivity cell. Since temperatures of the conductivity measuring cell and the sensor cell are equal, then variations of temperature of the electrolytic solution will not have influence on the results of electrolytic conductivity measurements.

Figure 7.5. Electrolytic conductivity meter.

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

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