So far, we cover the basic principle of pH. Have you added to your knowledge of pH?
By the way, subsequent studies showed that the electromotive force of the battery Sorensen used to calculate pH was found to have a relationship with not only with the concentration of hydrogen ions, but also with activity of the hydrogen ions. The march of progress in the understanding of thermodynamics and actual measurement of pH played an important role in this study.

So, there was great scientific progress, although it was found that theoretical calculation of pH based on activity was impossible and that activity could not be measured directly. So, the classical definition of pH (meaning the notion that pH could be determined according to the concentration of hydrogen ions) proposed by Sorensen was subject to slight modification as science progressed. However, such modification did not detract from the advantages of using the pH scale, or from its practical value and biological and chemical meaning.

So, what is activity of hydrogen ions? Let's try to clear that up.


Imagine a box of known size that contains one steel ball. If you move the box back and forth or side to side, the ball rolls around freely within the box. Then, suppose you have two balls in an identical box. These two balls will sometimes collide, which places certain limits on possible directions of movement of the balls. But movement is not severely restricted with only two balls. However, as the number of balls increases, the movement of the balls becomes more and more limited. Suppose we call the degree of this restriction f. If we multiply the degree of restriction f by the number of balls in the box, the result will correspond to the number of balls that have freedom of moment at a given instant.

Next, apply this example to hydrogen ions within a solution, where the balls are hydrogen ions (H+), the number of balls is hydrogen-ion concentration ([H+]) and the number of balls that can move about freely is the activity of hydrogen ions . And "moving about freely" means that an ion can "exert its particular characteristics." We use f as the activity coefficient.
This leads us to the following formula:


As already mentioned, activity cannot actually be measured directly. Thus, when measuring pH in actual practice, we measure pH by defining a solution of known pH as a standard solution (in this case, a solution whose pH is very unlikely to vary) and comparing it with pH of the target solution.


With the widespread need for measuring the pH of various solutions, the problem of getting different measured values from identical samples became prominent. Therefore, it became necessary to establish a clear definition of pH and a standard selection method. Also, it was decided to try to define JIS standards as early as possible for methods for measuring pH. JIS standards for methods for measuring pH were established in March of 1957, after a lot of research and surveys and with the participation of people from a wide variety of fields.
In preparation for the planning of the JIS standards, the standards regarding pH in the U.S., England and France were studied. Since pH was used not only in Japan but also abroad, they couldn't just set arbitrary standards, but needed to consider the future international validity of any proposed standards. Compatibility was needed so as not to hinder academic and commercial activities.
This concludes our briefing on pH


A list of books follows, where you can find further information on this subject.
We have also provided an excerpt from "JIS Z 8802--Methods for Measuring pH" on the next page. The JIS standards are established for industrial application; however, it's a good idea to read it in order to clarify the subject.

Theory and Application of Electric Chemistry, Volume I, Maruzen (1963), Kameyama
Theory and Measurement Method of pH, Maruzen (1968), Yoshimura, Matsushita, Morimoto
Measurement of pH and Automatic Control, Nikkan Kogyo ?? (1960), Kishimoto, Matsushita
Measurement of pH, John Wiley & Sons (1964), Bates
Reference Electrodes, Academic Press (1961), Ives, Janz
JIS Z 8802--Methods for Measuring pH, Japanese Standards Association
JIS Z 8805 Glass Electrodes for Measuring pH, Japanese Standards Association