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Ion activity of electrolytes in the physiological concentration range

Ion activity
Ion activity is a measure of the effective concentration of an ion, i.e., in contrast to the measurement of the amount-of-substance concentration, the measurement of the ion activity also includes the interaction of ions and the influence of the solution in which they are found. In clinical chemistry, ion activity is therefore a measurand which delivers important information on a patient's condition. For that reason, its precise and reliable measurement is of particular interest. Mathematically, the amount-of-substance concentration ci and the activity ai of the ion species i have the following relation:

 ai = γi ci

Hereby, γi is the dimensionless activity coefficient (which is a characteristic quantity for each ion species, concentration and solvent).

Ion activity can be measured directly by using so-called ion-selective electrodes (ISEs).
Figure 1 below illustrates the principle of such a measurement:

Fig. 1: Basic principle of an ISE measurement

The ion-selective membrane reacts to the activity of a certain ion species in the measurement solution, which leads to the formation of a potential difference in front of and behind the membrane. This potential difference depends on the activity of this ion species in the measurement solution and is measured against a reference electrode. By calibrating the measuring arrangement with solutions of a known ion activity, it is possible to determine the ion activity of an aqueous sample solution.

ISE primary measuring set-up of PTB
Our Working Group measures the activity of the ions calcium, magnesium, sodium, potassium and chloride, which are the most relevant ones in laboratory medicine, by means of the apparatus shown in Fig. 2 below. This apparatus was developed within the scope of the European metrological research project Opens external link in new windowimera+ T2J10 "Tracebioactivity". The core of the apparatus is an arrangement of ion-selective electrodes that are contained in the small white containers in the bottom row on the left in the photograph and a silver/silver chloride reference electrode (the container with the red cap in the bottom row). The temperature is measured at the far right side of the row. The calibration standards in the large bottles (which contain mixtures of the above-mentioned ions in different concentrations in the physiologically relevant range) or an aqueous test sample that is to be measured are pumped through the apparatus by means of a peristaltic pump. The whole apparatus is located in a temperature-controlled box where  the temperature is maintained constant within a deviation  range of  approximately 5 mK.

Fig. 2: ISE primary measuring set-up of PTB


Traceability of the activity to the SI System of Units
The calibration standards are prepared gravimetrically from the ultra-pure chlorides of calcium, magnesium, sodium and potassium whose purity grades and ion concentrations were previously determined by means of different methods of characterization (e.g. coulometry). These methods are primary methods, or standards were used that are traceable to the SI System of Units. The ion activities of the calibration standards are calculated by means of the semi-empirical Pitzer model for electrolyte solutions that is based on the Debye-Hückel theory. Since the uncertainty of the Pitzer model was determined within the scope of an international research project, each calculated and/or determined ion activity is traceable to the SI System of Units. The Pitzer model contains the so-called MacInnes convention. This is why the determined ion activity is rightly called "conventional activity". For this measurand, PTB has a CMC entry in the BIPM database.

To calibrate the apparatus, the electric potentials of each ISE are measured for all calibration standards and are plotted against the logarithm of the ion activity (see Fig. 3).

Fig. 3: Calibration curve using the example of potassium

Then, the ion activities of the sample can be calculated from the equation of the calibration curve that was adapted to the measurement points and the measured electric potential of a sample.

Ei,j = m ⋅ log (ai,j) + E´
Ei,j:    measured electric potential of the ion species i in the calibration standard j
m:     slope of the calibration curve
ai,j:    activity of the ion species i in the calibration standard j
E´:    approximately constant electric potential (sum of the standard electrode potential
         and the diffusion potential)

Ion activity in human blood serum
So far, the above-mentioned work has been limited to aqueous solutions. The aim was, above all, to investigate whether it is feasible to trace ion activities to the SI system. To measure the activity of ions in human blood traceable to the SI, it should be taken into account that the value of their activity coefficient in water differs from that in blood. Since blood is a much more complex medium than water, the activity coefficients can, to date, not be calculated, so that the calibration curve cannot be used for blood measurements and the measurement result can no longer be traced to the SI. It is therefore intended to investigate in a future project whether ion activity measurements in human blood serum can be traced to the SI.