# IONOMETRY AND ELECTRODYNAMICS

Alexander M.Nemirovsky (novedu@yahoo.com)

A profound knowledge of literature sources on ionometry reveals the fatal inclination of authors to using the Nernst’s law to explain absolutely all the phenomena in the ionometric experiment. Mentioning the law seems become a point of good manners. But manners in some cases cannot reliably explain the observed effects. In this connection I got interested with the problem of the interaction of the ionometric and the electrodynamic laws. In my opinion, ionometrists do not pay proper attention to electrodynamic laws, getting absorbed in the chemical aspect of the problem.

Let us consider the following example. Suppose we are going to work with a nitrate ion-selective electrode on a polyvinylchloride matrix. But we got to know that the medium in which we are going to perform measurements reacts with the membrane plasticizer, thus contributing to the overall electrode potential. What should we do? There is no hope to describe such a system by the Nikolsky equation because the electrode-active agent and the plasticizer can hardly have a relation to chemical mass exchange. On the other hand, there is no ground to suppose that the potentials from the potential-determining ion and the plasticizer are simply added.

For this type of cases I suggest the model of parallel voltage sources. In this model a fraction of potential-determining reactions are considered as voltage sources in the way that is common in electrodynamics:

where
ε 1 is the voltage of the current source organized by the potential-determining ion;
ε 2 is the voltage of the current source organized by an alternative chemical reaction;
R1 and R2 are internal resistance of the current sources;
R is the resistance of the measuring instrument.

Using the Kirchhoff’s laws for calculation in closed electric circuits we get the following equations set:

where I is current strength at a subcircuit with resistance R.

If R>>R1+R2, then the voltage measured by the instrument is equal to

Since we agreed that ε 1 is caused by the potential-determining ion, then

or

Consequently, the potential (voltage) of the parallel reaction reduces the electrode function slope (S), provided the potential is independent of the potential-determining concentration. This is supported by experimental evidence, of which it is enough to mention nitrate-selective electrodes based on quaternary ammonium salts, chloride electrodes based on a mixture of silver sulphides and chlorides etc.

Evolving the hypothesis of parallel electrodynamic processes, let us consider another example. Suppose the analyzed solution consists of a mixture of salts of the main and the interfering ions, and the ions have different mechanisms of potential generation (which is possible to imagine, even if not easy). Then

where B1 and B2 are constants.

This example is interesting due to the fact that, if calibration is built by the main ion in a solution of the interfering one, it does not affect the calibration linearity. In addition, the given example admits such electrochemical systems where the interfering ion has a stronger influence on the absolute value of the potential rather than on the electrode functions slope. This is a very important analytical conclusion extending the capabilities of the addition method. (As it is known, in the addition method the weak affect of the interfering ions on the electrode function slope is very important.) It goes without saying that the classical model (the Nikolsky equation) does not cover such cases because the interfering ion affects the analysis results in the following way:

U = const + S * lg ( C + KCm ),

where C and Cm are the concentrations of the main and the interfering ions;
Kis selectivity factor.

However, leaving hypotheses alone, are there any signs to confirm the correctness of the considerations stated above? Also, is it legitimate to use the Kirchhoff’s laws for real chemical electric sources?

I’ll tell you right away that I have performed experiments on the "TOSHIBA" batteries. Measuring batteries connected in parallel showed that the Kirchhoff’s laws were valid. The results of the experiments are given in the table.

 R1, MOm R2, MOm ε 1, V ε 2, V U, V Utheor,V 8,09 8,17 1624,5 1614,4 1619,4 1619,5 1624,5 3274,3 2445 2445,3 1624,5 4898,7 3252,9 3253,5 3,33 8,17 1624,1 1614,3 1621,1 1621,3 1624,1 3274,2 2101,1 2101,9 1624,1 4898,7 2570,7 2572,3 0,942 0,788 1619,4 1658,6 1641,2 1640,7 1619,4 3282,8 2526,1 2525,1 1619,4 4906,6 3410,9 3409,3 0,01067 0,0952 1588,1 1655,1 1594,8 1594,9 1588,1 3275,9 1759,5 1758,2 1588,1 4898,6 1924,1 1921,7

As for my hypotheses, one should remember the way modern ionometry explains the existence of ion-selective electrodes with an electrode function slope different from the theoretical one. The explanation is that the greater the mass exchange with the membrane, the greater the deviation in the electrode function slope. However, this version is not always valid, because some glass electrodes, as well as electrodes with polyvinylchloride membranes have an insufficient slope, although their mass exchange is incomparable. My hypothesis explains the fact in a less contradicting manner because it admits a parallel chemical process which is not connected chemically with the main process.

In conclusion, I would like to briefly outline the advantages provided by the new hypothesis.

• The hypothesis about the effect of a parallel electrodynamic process on ionometric measurements explains the electrodes’ having an electrode function slope different from the theoretically predicted value.
• In some cases the hypothesis does not rule out a different influence of the interfering ions on the potential of the ion-selective electrode as does the Nikolsky equation.