THE HYDROGEN ion concentration of human plasma usually ranges from about 35 to 45 billionths molar. This might easily and usefully be expressed as 35 mμM to 45 mμM. In disease states it may range from about 10 mμM to 200 mμM.
Logarithms are convenient to express very large or very small numbers, particularly if these cover a wide relative range. The logarithm of a decimal fraction is a negative number which increases in size as the decimal fraction becomes smaller. It is inconvenient to retain negative numbers, so pH was defined as the negative logarithm of the hydrogen ion concentration. Two negatives yield a positive number for pH, which however, still increases in magnitude as the hydrogen ion concentration decreases.
We are so accustomed to pH notation that it seems "natural," but it is certainly a nuisance to calculate. Moreover, some properties of the hydrogen ion are not
GLEASON DF. pH Measurements. Arch Intern Med. 1965;116(5):649-653. doi:10.1001/archinte.1965.03870050003002