Historical Definition of pH

The Danish chemist SLP Stirensen originally defined pH as the negative logarithm of the hydrogen ion concentration pH=-log [H+]

Sorensen was developing enzymatic studies and discovering that the degree of acidity was of fundamental importance for biochemical reactions. Later he and Linderstorm-Lang proposed a new definition of pH as the negative logarithm of the hydrogen ion activity

pH = -log aH

This definition is equivalent to the current definition of pH

pH = -log(yHmH)

where yH is the particular ionic activity coefficient of the hydrogen ion and mH is the molality of the hydrogen ion. The development of the pH scale and the methods of determining pH were described by Bates in a classic book.

Current Definition of pH

The pH of a substance is a measure of its acidity just as a degree is a measure of temperature. A specific pH value tells us the exact acidity.

The pH is defined in terms of the activity of the hydrogen ion as:
pH = - log10 aH or 10-pH=aH

Activity is the effective concentration of the hydrogen ion that is in solution. This is discussed in more detail later. Basically the difference between actual and effective concentration decreases when moving towards more dilute solutions in which ionic interaction becomes progressively less important.

The formula for pH is analogous to the relationship between absorbance (A) and transmittance (T), that is, A = -log T. In this logarithmic function, however, the interval is normally narrower than the interval for pH. The important similarity is the logarithmic relationship, that is, for every decade of change in activity, the pH changes one unit. The extent of this relationship is illustrated in Figure 1. The factor of 10 between each pH unit shows the importance of measuring pH in tenths or hundredths of a unit.

Normally, reference is made to the hydrogen ion when reference should be made to the hydronium ion (H30+). For convenience and brevity, only the hydrogen ion is mentioned, even though it normally exists in its solvated form:
H- +H2O __ H30+

The complexation of the hydrogen ion by water is a factor that affects the activity and applies to other ions, which partially complex or establish an equilibrium with the hydrogen ion. In other words. balances such as
H2CO3 __ H+ + HCO3-
HC2H3O2 __ H+ + C2H302-
they complex the ion, hydrogen such that it is not sensed by the pH measurement system. This, of course, is why an acid-base titration is performed if a total acid (H+) concentration is desired.

This effect on hydrogen ion activity is obvious, but other more subtle effects are involved in the correlation of activity and concentration.
Relationship between Activity and Concentration Because the glass electrode is sensitive to the activity of the hydrogen ion aH+, the factors that influence the activity and its definition are of great importance. The activity of the hydrogen ion can be defined by its relationship with the concentration (mH+, molality) and the activity coefficient yH+:
a H+ = yH+ mH

If the activity coefficient is unity, then the activity equals the concentration. This is close in the case of dilute solutions, where the ionic strength is low. Since the objective of most pH measurements is to have a stable and reproducible reading which can be correlated to the results of a process, it is important to know the influences of the activity coefficient and therefore of the pH measurement. .

The factors that affect the activity coefficient are the temperature T, the ionic strength 1, the dielectric constant ε, the charge of the ion Zi, the size of the ion in Angstroms A, and the density of the solvent d. All of these factors are characteristic of the solution which relate activity to concentration.

A more exact definition of the salt effect is found using the Debye-Hükel equation. The other factors mentioned are used in defining their equation, thus showing their effect on the measurement.
The second effect is the effect of the medium which is designated as log ymH+. This effect relates the influence that the solvent will have on the activity of the hydrogen ion. This reflects the chemical and electrostatic interactions between the ion and the solvent, of which the main interaction is solvation. This effect can be related by comparing the standard free energy in a non-aqueous solvent and in water. For example, the activity of the hydrogen ion in ethanol is much larger (about 220 times) than in water.

This brings up the question about pH measurements in non-aqueous solvents, which will be covered later. Most often an aqueous buffer solution is used to calibrate the pH measurement system. If the measurement is made on a non-aqueous sample, the correlation between the hydrogen ion activity in an aqueous standard and the activity in a non-aqueous sample is not valid.

However, if the obtained pH value is stable and can be related to some results, the activity of the hydrogen ion need not be known. The relative pH value can be used as an indicator to alter the process or to proceed in some corrective way if the pH value changes dramatically.

Thus, activity is related to concentration through the effect of the salt and the effect of the solvent. Activity measurement with the glass electrode is mainly influenced by ionic strength, temperature and solvent:
This means that the sample composition and conditions must be established when determining the pH if another person is to reproduce the results or if the pH value is to be compared. Solution pH is valid only at a particular temperature, ionic strength, and solvent.

Due to these influences, the pH value of a sample cannot be extrapolated to another temperature or dilution. If the pH value of a particular solution is known at 40°C, it is not automatically known at 25°C. Standard buffer solutions were tested at different temperatures and compositions to define their activity, and unless the same is done for the sample, their pH under different conditions is not known due to these variables.


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