1 84 PRINCIPLES OF GENERAL PHYSIOLOGY 



have, then, a numerical value for the acidity, namely, the concentration in H' ions. 

 Similar considerations apply to bases, say sodium or ammonium hydroxides, and 

 here the concentration in OH' ions gives a measure of the alkalinity of a solution. 

 As will be shown later, the product of the H" and OH' ion concentrations in 

 solutions in water is a constant quantity ; it is clear, therefore, that along with 

 any OH' ion concentration a definite H* ion concentration is connected. For the 

 sake of uniformity it is the custom to express both acidity and alkalinity in terms 

 of H* concentration. Thus, neutrality means the concentration of the two ions 

 as they are present in pure water, i.e., 1 x 10~" at 25, and any concentration of 

 hydrogen ion less than this means alkalinity and any greater means acidity. 



It is rather troublesome to write repeatedly such expressions as I'SxlO" 6 , etc., so that 

 Surensen (1909, p. 28) has advocated the use of the negative exponent as a whole number, and 

 the designation of it as the "hydrogen-ion-expanent" or P H . Thus, 5 x 10~ 6 is the same as 

 jQ-8.3 anf j a solution having this concentration in H- ions is said to have a P H . of 5'3. A 

 centinormal solution of hydrochloric acid is 0*00916 normal in H' ions, which may be expressed 

 as 10- 2< % the index being the logarithm of 0'00916 and the P H . value is 2'04. Otherwise, the 

 exponent of the hydrogen ion concentration of a solution is the common logarithm of the 

 reciprocal value of the normality in hydrogen ions. This method is frequently made use of, 

 but it has certain disadvantages, at all events for those commencing the study of the subject. 

 The first is that the P R . value decreases as the acidity increases. The second is that, while 

 it is easy to see that a hydrogen ion concentration of 4 x 10~ 6 is double that of 2 x 10~ 8 , it is 

 not at once obvious that a P H . of 5 '398 is double that of 5 '699. One has to get accustomed 

 to thinking in negative logarithms. 



Perhaps one of the most striking facts with regard to acids, and in itself strong 

 evidence of the truth of the Arrhenius theory, is that the heat produced by the 

 neutralisation of equivalent amounts of the most various acids is practically 

 identical. This is easily accounted for if due to the union of the H* ions of the 

 acid with the OH' ions of the base. On the other hand, the fact has been brought 

 as an objection to the view. A weak acid is said to be such because it contains 

 a less number of H* ions than a strong one ; hence, it is said, if the heat of 

 neutralisation is due to the combination of these ions, it should be less in the 

 former case. The nature of electrolytic dissociation as an equilibrium is lost sight 

 of in this objection ; as soon as the free ions, say of half the acid present, are 

 neutralised, the remaining undissociated acid at once becomes half dissociated, its 

 ions are then neutralised, and so on, until the whole of the acid has passed through 

 the stage of ions and all the hydrogen ions have combined with the hydroxyl ions of 

 the base. 



To return to the question of strong and weak acids. We remember that the 

 reason why hydrochloric acid is so much stronger than acetic acid in the same 

 concentration is because the former is so much more highly dissociated. Since in 

 very great degrees of dilution even weak acids are almost completely dissociated, 

 it is clear that the difference between strong and weak acid becomes less as the 

 concentration is diminished. While, therefore, it is sufficient, in order to define 

 the acidity of a particular solution, to state the value of its concentration in 

 hydrogen ions, it is useful to be able to compare the strength of different acids by 

 numbers independent of concentration. 



This can be done, in the case of a large number of acids, by means of their 

 dissociation constants. To understand the significance of these values, we must, 

 at some risk of repetition, refer to the law of Mass action. The historical develop- 

 ment of this law will be dealt with in Chapter X., and a brief description only 

 will be given here. The law in its simplest form states that the rate at which 

 any reaction proceeds is directly proportional to the amount, or rather concentra- 

 tion, of the reacting substances. We have already seen cases where the whole 

 mass of a substance present is not concerned in the chemical reaction, as, e.g., 

 in heterogeneous systems, where the " active mass " depends on the surface, but, 

 if we understand " mass " in the above statement of the law to mean the mass 

 actually taking part in the reaction, we may regard it as unconditionally true for 

 all kinds of reactions. It is, of course, unnecessary to remark that the actual 

 rate of any particular reaction depends on all kinds of conditions, which can be 

 grouped together in the form of a constant (K), as long as they remain unchanged. 



