The hydrogen ion exponent

For many purposes, especially when dealing with small concentrations, it is cumbersome to express concentrations of hydrogen and hydroxyl ions in terms of moles per litre. A very convenient method was proposed by S. P. L. Sorensen (1909). He introduced the hydrogen ion exponent pH defined by the relationships  

This must be written in the usual form containing a negative characteristic and a positive mantissa  

This relationship should hold for all dilute solutions at about 25 °C. 

The logarithmic or exponential form has also been found useful for expressing other small quantities which arise in quantitative analysis. These include (i) dissociation constants (Section 2.13), (ii) other ionic concentrations, and (iii) solubility products (Section 2.6). 

---

Its value is often quoted instead of that of K. The usefulness of pK will become apparent when dealing with the hydrogen-ion exponent or pH. 

THE HYDROGEN-ION EXPONENT (pH) In the practice of chemical analysis one frequently deals with low hydrogen-ion concentrations. To avoid the cumbersome practice of writing out such figures with factors of negative powers of 10, Sorensen (1909) introduced the hydrogen-ion exponent or pH, defined by the relationship ... 

The hydrogen ion exponents of a number of aspartic acid solutions are given in the following table. The [H+] values were calculated in three ways by the simple equation (8), by the second approximation method, and by the complicated equation (9) of Soeensen. 

Soren Peer Lauritz Sorensen (1868—1939). Danish biochemist. Sorensen originally wrote the symbol as pjj and called p the hydrogen ion exponent (Wasserstoffionexponent), it is the initial letter of Potenz (German), puissance (French), and power (English). It is now customary to write the symbol as pH. 

The principles of pH begin with a definition of the term pH. The p comes from the word power. The H, of course, is the symbol for the element of hydrogen. Together, the term pH means the hydrogen ion exponent. 

The term pH is based on p, for power, and H, representing the element of hydrogen. Therefore, pH means the hydrogen ion exponent and pH is a measure of acidity of a solution. The well-known definition of pH can be shown as ... 

The exponent (or power) to which the base number (10) has to be raised is the logarithm. To find the pH of a substance, the negative of the logarithm of the hydrogen ion concentration must be taken. 

Because the ion concentrations are small and the negative exponents make them tedious to work with, Soren Peer Lau-ritz Sorenson (1868-1939), a Danish biochemist, devised the pH concept in 1909 to express the hydrogen ion concentration. The abbreviation pH comes from the French pouvoir hydrogene meaning power of hydrogen. The pH of a solution is given by the equation ... 

Hydrogen ion exponent — Obsolete term for the numerical value of - pH used by - Serensen. 

This equation can easily be memorized and used for quick calculations. The equation is strictly valid for the pH range 0-8 over pH = 8 the dissociation of hydrogen sulphide cannot be disregarded any more, and therefore the simple treatment outlined above cannot be used. With proper mathematical treatment the sulphide ion exponent even for pH above 8 can be calculated results of such calculations are summarized on the graph of Fig. 1.12. This graph can be used if predictions on the precipitation of sulphides are required. This is illustrated in the following examples. 

A similar but less comprehensive study was published by Schoenemann and Hofmann [17]. There is agreement that the rate of xylose disappearance is proportional to the hydrogen ion concentration, and that there is an exponential temperature dependence in accordance with the law of Arrhenius, but there are minor differences in the numerical values of the proportionality factor and the exponent. 

A simple graphical method of converting [H+] into pH, or the reverse, is shown in Fig. 1. The pH scale is divided into ten equal parts from 0.0 to 1.0. Beneath it, the corresponding CH+J scale is laid off logarithmically. Each decimal of the hydrogen exponent corresponds to the value given for the hydrogen ion concentration in the lower row (see also Appendix, Table 6). 

This treatment is easily generalized and leads to the conclusion that in water or similar solvents general acid catalysis will be observable only for intermediate values of the exponent a. If a is too small, the catalytic effect of acids will be swamped by that of the solvent, while if a approaches unity, the effect of all other acids will be masked by that of the hydrogen ion. Similar conclusions apply to basic catalysis. It is possible, therefore, that those reactions in aqueous solution which appear to show specific catalysis by hydrogen or hydroxyl ions (cf. preceding sub-section) do not constitute a special class of reaction, but are actually... 

Thus, pH is simply the negative of the exponent used to express the hydrogen-ion concentration in moles per liter. 

This tiny concentration of hydrogen ions leads to difficulty in notation when expressing changes e.g. the difference between 0.00000001 and 0.0000001 M. To avoid all the zeros, the pH scale was introduced. The pH is the negative logarithm, to the base 10, of the hydrogen ion concentration in M (section A.2). Informally, pH is minus the exponent of the concentration . The pH of a neutral solution is therefore 7.0 units at 2S°C. 

---