Principles of General Physiology

There is no doubt that the dielectric constant of the solvent is, in some way, intimately involved in the process. Tt is not an easy matter to picture the way in which it acts, but the following points may possibly be of assistance to the reader. Two oppositely charged bodies, as is well known, attract one another with a certain force, which can be measured. It might be supposed that this force would be independent of the substance between the two bodies, provided that it be an insulator. But this is not so, as Faraday found. Suppose that air is the insulator between the two bodies, and that they have such a charge, and are at such a distance from one another, that the force tending to bring them together is equal to the weight of 10 g. Now put petroleum in place of air, it is found that the force is only 10/2 -2, and, if castor oil be used, it is only 10/4 '3. The denominators of these fractions are known as the "dielectric constants " of the liquids, and they play a part in other connections. The capacity of a condenser, for instance, is greater, the greater the dielectric constant of the material between the plates ; that of mica being 8, the reason for using this material instead of paraffin, with a dielectric constant of only 2'3, is obvious. According to the modern theory of electrons, the dielectric constant is the greater, the larger the number of electrons present in a given space of the substance. These act as conducting particles and are surrounded by an insulating substance of very special properties, the luminiferous ether. In the course of their propagation through a non-conductor, electric forces must exert an action on these electrons ; so that it can be understood why, the more of them there are, the greater is the obstruction to the forces. The connection between electricity and light, as the reader will remember, was worked out by Clerk Maxwell, and, in the present connection, it is of interest to recall the fact that the dielectric constant of a substance is identical with the square of its refractive index, as calculated for light of very long wave length or electric waves (Maxwdr* Law).

Of all liquids, with the exception of prussic acid, hydrogen peroxide, and formamide, water has the highest dielectric constant, about 80 times that of air, while the majority of other liquids have valves which vary between 40 for nitromethane, and 6 -46 for acetic acid. When a substance is soluble in more than one of these various liquids, it is found that its conductivity, or, in other words, the degree to which it is dissociated, is greater, the higher the dielectric constant of the solvent (J. J. Thomson, 1893, and Nernst, 1894, independently). The following numbers will serve as illustrations (Walden, 1906). The solute is tetra-ethyl-ammonium iodide, on account of its solubility in a variety of organic solvents.

Centnerszwer (1902, p. 223) gives the molecular conductivity of potassium iodide in prussic acid as 262, compared with that in water as 80. The dielectric constant of liquid prussic acid is 95. The significance of this fact in connection with the meaning of the dielectric constant as allowing charged bodies to approach nearer to one another without union of their charges is that, supposing we assume that the oppositely charged ions have been separated, a solvent with a high dielectric constant will enable them to come much nearer to one another without combination than in a solvent with a low dielectric constant. The kinetic energy they possess enables them to resist the attraction of the opposite ions when much nearer together, owing to this attractive force being less the higher the dielectric constant of the solvent ; so that, on an average, a larger number are free at any given moment.

Although considerations of such a kind enable us to form some idea of the reasons why ions do not all combine with their oppositely charged fellows, it is not obvious what causes their original separation, when a solid salt is placed in water. If we admit Faraday's view of the electrical nature of chemical affinity, it seems possible that the electronic forces of the dielectric may be involved. When molecules are separated from one another, as in the process of dissolving a solid, it may be that they are more accessible to forces tending to break the combination between their constituent ions, and as the separation is effected, the high insulating power, or dielectric constant, of the solvent prevents, to a varying degree, their recombination.

Perhaps the most serious difficulty in the Arrhenius theory is the behaviour of strong acids, strong bases and salts, as compared with that of weak acids and weak bases. In the latter case, as Ostwald showed, the proportion of dissociated to combined molecules, when the solution is diluted, obeys a law deduced from mass action simply and known as Ostwald's "dilution law." In the former case the law is quite different. In a paper by A. A. Noyes, Melcher, Cooper, and Eastman (1910, p. 375), attention is called to the fact that the electrolytic dissociation in the former case of salts, strong acids, and strong bases "is a phenomenon primarily determined not by specific chemical affinities, but by electrical forces arising from the charges on the ions ; that it is not effected (except in a secondary degree) by chemical mass action, but is regulated by certain general, comparatively simple, laws, fairly well established empirically, but of unknown theoretical significance ; and that, therefore, it is a phenomenon quite distinct in almost all its respects from the phenomenon of dissociation ordinarily exhibited by chemical substances, including that of the ionisation of weak acids and bases."

The reasons for this view can be found in the original paper ; we must be content here with reference to the similar dissociation values for salts of different chemical nature but of the same ionic type, the proportion of these values to valency, the small effect of temperature on the dissociation of salts, strong acids and bases, and its parallelism with that on the dielectric constant, the exponential relation between dissociation and concentration, which is not the same as that required by the law of mass action, and the fact that the optical and similar properties of dissociated salts (in equimolar concentration) is independent of this actual concentration, and therefore of their dissociation, if the solution is even moderuti-lv dilute.

With respect to the influence of temperature, the actual effect on dissociation must be distinguished from that on the rate of migration of the ions. The temperature coefficient of conductivity of a salt is about 2 per cent, per degree, as shown by Arrhenius (1901, p. 136), but this is almost entirely accounted for by the increased velocity of the ions, due to diminution of internal friction of the solvent. The actual increase in number of ions is very small indeed. In another class of cases, which are regarded by Noyes and his co-workers (1910) as being of a more strictly chemical nature (see below), the increase in number of ions is considerable as the temperature is raised. Water itself is a striking example. According to the data of Kohlrausch and Heydweiller (1894, p. 209), the temperature coefficient of ionisation of water at 18° is 5'32 per cent. (Nernst, 1911, p. 670). This fact is in agreement with the great heat of electrolytic dissociation of water.

As remarked above, Noyes and his coadjutors (1910, p. 376) suggest that ions may form two different kinds of molecules, electrical and chemical. In the first case the union is not so strong, and the constituents still retain their electrical charges and their characteristic optical effects. " Secondarily, the ions may unite in a more intimate way to form ordinary uncharged molecules, whose constituents have completely lost their identity and original characteristics." " In the case of salts, inorganic acids and bases, the tendency to form chemical molecules is comparatively slight, so that the neutral electrical molecules predominate. In the organic acids, as a rule, chemical molecules predominate. These latter are formed in accordance with the law of mass action, while electrical molecules are formed in accordance with an entirely different principle, whose theoretical basis is not understood."

G. N. Lewis (1910, p. 218) also calls attention to the deviation of these salts, strong acids and bases, from the mass action law, and points out that it is the moderately concentrated solutions that are abnormal ; in highly dilute solutions the behaviour is in agreement. The ions themselves seem to obey the laws of perfect solutions, so that we must turn to the undissociated molecules for an explanation of the anomalies. The author refers to cases where, assuming normal behaviour of ions, correct results are predicted, although the undissociated part is neglected.

A deduction from the electrolytic dissociation theory, which has been verified by independent methods, is the constancy of the product of the concentrations of H' and OH' ions in dilute aqueous solutions. Finally, the Nernst equation for the electromotive force of concentration batteries gives good results when the concentration of the ions alone is considered. Lewis (p. 219) also refers to a calculation which he made involving the use of three principles all founded on the Arrhenius theory, viz., the Nernst equation, the solubility product, and the dissociation constant of water. The result was different from the value accepted, but independent investigation by Haber and by Nernst immediately afterwards showed perfect agreement with the calculated value. As the author remarks : " The calculation would obviously have been vitiated if any one of the principles used had been unreliable." On the whole, the evidence indicates that later and better theories will be developments of the first simple one of Arrhenius, not substitutes for it. It must not be forgotten that the propounder of the theory has always been ready to admit the difficulties. Whether the views of Noyes will be found to explain some of these remains to be seen ; there are no doubt many objections to be made to their bare present form. Perhaps this point of view may also supply an answer to the question why a concentrated solution, say of potassium chloride, in which only 25 per cent, is dissociated, exhibits only the properties of ions. Has the KC1 molecule no properties of its own 1

Arrhenius himself (1914, p. 1424) points out that the dielectric constant of the solvent is increased by the presence of strong electrolytes of higher dielectric constants than itself. This would increase its dissociating power. It must be admitted that some intemperate partisans of the electrolytic dissociation theory may have claimed too much; at any rate, the sweeping statement that all chemical reactions are between ions must not be made without the qualification that no absolute proof of the absence of the intervention of electrical forces has been given in any particular reaction.

When we come to consider the part which electrolytes play in the processes of the living organism, we have to note that there are three modes in which they may act. In the discussion of the colloidal state, we saw that, in the intervention of neutral salts in such phenomena, we may distinguish, in the first place, an effect connected with the electrical charge on the ions, specially marked with ions of valencies above one, and not in relation to the chemical nature of the ions ; so that the effect, say, of Ca* * is not to be distinguished from that of Ba' '. Especially in the case of multivalent ions, this action is manifested by very small concentration. It may be illustrated by the effect of simple trivalent ions on tlie heart, an action which does not seem to be associated with the chemical nature of these ions, since it is shown by a large number of them, and in extraordinarily low concentrations (Mines, 1911).

In the second place, there is an action shown by salts usually in somewhat high concentration, which is not directly connected with their electrical charges as such, and is most satisfactorily explained as being an action of some kind on the solvent, " lyotropic," as it is called by Freundlich. This is shown in the " salting out " of proteins, and in the various effects of anions and cations on such processes as imbibition, in which the " Hofmeister series " is followed.

In the third place, there are the actions in which differences of a more chemical kind come into play. Such cases are those of potassium and sodium salts on the heart muscle. In these, we know that it is the ions which are concerned, and not the molecules of the salts, by the facts that the action is shown by solutions so dilute that undissociated molecules are nearly absent, and that it does not matter what particular salts of these metals are used.

Other instances that may be given are the effect of calcium ions on the clotting of blood, in which even closely related elements, such as barium, are unable to replace calcium ; and the powerful action of barium in producing contraction of smooth muscle. The great activity of acids and bases in various ways is a familiar fact, so that, in our consideration of the various ions of physiological importance, it is natural to take these first. It is also a matter of common experience that the properties associated with them are much more strongly marked in the case of certain chemical individuals than in others. Some acids will turn out others from combination ; their solutions, in equal strength, taste much sourer, and some invert solutions of cane-sugar more rapidly than others, in the same molar concentration, do.

It is here that the electrolytic dissociation theory has shown itself to be of especial value, in that it is able to give precise numerical values to express the acid or alkaline properties of a solution. Now what, according to this doctrine, is the character common to all acids and what to all bases'? Obviously, the hydrogen ion in the first case and the hydroxyl ion in the second. Hydrochloric and acetic acids in solution are dissociated into H' and Cl' and into H' and acetic anion respectively ; the only chemical substance common to both is the H' ion. But why is hydrochloric acid the stronger of the two, as is so obvious in many ways'? The answer is given by measurements of the electrical conductivity of the two. Hydrochloric acid is a much better conductor ; it is therefore more highly dissociated and contains a much higher concentration of hydrogen ions. Here we

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 PH. Thus, 5 x 10~6 is the same as jQ-8.3 anfj a solution having this concentration in H- ions is said to have a PH. 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 PH. 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 PR. 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 PH. 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 development 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 concentration, 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.

The law of mass action means that, other things remaining constant, doubling the concentration of any one of the reacting substances doubles the rate of the reaction, so that, if two are doubled, the rate is four times as fast, and so on. The necessity of this fact on the kinetic theory is obvious. Thus, the rate at which a reaction goes on depends on the number of collisions, per unit of time, that occur between the reacting molecules. Clearly, if the number of one kind of these molecules in a given space is doubled, the number of collisions is doubled, and if, also, the number of the other kind is then doubled, this rate itself will be doubled; so that the effect of doubling the concentration of both is to multiply by the rate due to the increase of both, that is, by four.

It is usual to express the concentrations of the reacting substances by the use of brackets : thus the rate of the reaction : — in which A and B react with the production of C and D, while C and D react to form A and B, is expressed as : — A, B, C, D may stand for the concentrations of acetic acid, ethyl alcohol, ethyl acetate, and water, and the formula would then read : — where K and K' are the velocity constants of the two reactions respectively. We note further that the ratio of these two quantities will define the composition of the system in equilibrium ; if one reaction proceeds twice as fast as the other, it will be clear that, in order to bring up the rate of the slower reaction to that of the faster, as must be the case in equilibrium, the concentration of the reacting substances in its case must be correspondingly increased.

Now it was pointed out by Arrhenius that electrolytic dissociation must be governed by the law of mass action. In order to understand its application to this case, let us consider the ethyl acetate reaction in equilibrium, thus : — where K is the ratio of the two velocity constants of our previous formulae and is known as the "equilibrium constant" and the names in brackets mean the respective concentrations of these substances. Suppose that we increase the concentration of any one of the components, it is easy to see that it involves simultaneous changes in all the others ; for example, if we increase water, ester is diminished, in order to maintain constant value of the product, and ester cannot be decreased without increase of acid and alcohol. Perhaps the matter will be made clearer if we put the equation given above into the form : —

If water is increased, the value of the fraction may be kept constant by increase of either alcohol or acid, but neither of these can occur without the other nor apart from hydrolysis of part of the ester. Take next acetic acid in water ; the reversible reaction is : — Put a = degree of dissociation, so that if a = CK5, half the molecules of the acid are dissociated ; then, if V is the volume of the solution containing one molecule of the electrolyte : —

This result was worked out by Ostwald (1888), and is known as his "Dilution Law." It is found experimentally to apply to weak acids and bases. To salts, strong acids, and bases a different law applies, a law which is not dependent on mass action, as described above (page 182). It will be seen that, when the dilution law applies, the constant K (known as the "dissociation constant" or "affinity constant") is independent of dilution and is valuable in comparing the strength of the electrolytes concerned. The following series may be found useful. The basic constants, of course, indicate the strength as bases, and are obtained from the concentration in OH' ions. The substances with both acidic and basic properties are known as " amphoteric," and will be discussed later.

Physiological Action of Hydrogen and Hydroxyl Ions.— The great activity of these ions in physiological processes will be seen in various phenomena to be described in. later pages. This activity is undoubtedly in many cases connected with their great rate of migration, as compared with other ions. It has been suggested that this unusual rate is due to a special effect on the molecules of the solvent. We have already had occasion to refer to the action of even very small concentrations of H' or OH' ions on the sign of the electrical charge of colloidal particles. Especial attention may also be called to the great sensitiveness of enzymes in this respect, probably in great part due to the colloidal nature of

agents. Means will be indicated later by which changes in acidity due to the products of their activity may be neutralised, and their activity kept constant, in so far as it is affected by this change of acidity, — Even enzymes such as emulsin, which do not, like pepsin or trypsin, require fairly strong acid or alkaline reaction, are greatly affected in their rate of action by changes such as are brought about by the addition of blood serum. This is not generally recognised in testing for the presence of " anti-enzymes," and has led to the belief in their existence when the result obtained was due merely to reduction of H* ion concentration (see Bayliss, 1912, 2, pp.

The heart of the frog is affected by so small a change of H- ion concentration as that from neutrality (10~~77) to one of 10~6'5, and is killed by one of 10~6 (Fig. 55). On the alkaline side, an H* ion concentration of 10~10 is fatal. The addition of 0'036 mgm. of hydrochloric acid to 1 litre of distilled water would raise its H* ion concentration from 10~~ " to lO"6. The respiratory centre is extremely sensitive to very minute changes in the carbonic acid pressure of the blood, i.e., in all probability, to changes in H' ion concentration from dissociation of H2CO3.

A, Perfused with normal Ringer's solution, with H' ion concentration of 10-7-7. B, After perfusion for twenty minutes with faintly acid Ringer's solution, H' ion concentration, lO-11'8. C, After perfusion of the acid solution for eighty minutes. The upper curve in each is that of the auricle. The lower one, that of the ventricle. The signal gives time in seconds. As shown by the time signal, the rate of movement of the surface was quickened on two occasions in order to show details of the curves better.