Principles of General Physiology

Of the various hypotheses made in explanation of this effect, those of Caldwell (1906), Snethlage (1913), and Taylor (1914) may be referred to. According to Caldwell, the action of salts in increasing the rate of hydrolysis by acids is to be accounted for by a real increase in concentration of the acid. This takes place in two ways. If volume normal solutions are taken, a part of the water is displaced by the molecules of the salt, in the sense of van der Waals' constant, b. These salts also actually take up water in some way, so that it is rendered unavailable for dilution of the acid ; so that, again, the amount of water really free is less than it appears to be. Determinations of the increased quantity of water required to bring the rate of hydrolysis to the same value as that in the absence of salt leads to values of the amount used in " hydration " of the salt very close to those found in other ways, as will be described in the next chapter. Snethlage's work, in Bredig's laboratory, suggests that the undissociated part of the acid has also a catalytic action in the hydrolysis of esters and cane-sugar. As the affinity constant of the acid rises, so does the catalytic power of the undissociated part. In the weakest acids, that of the undissociated molecules is less than that of the hydrogen ions, but in the strong acids it may actually be greater. The action of chlorides in increasing the rate of hydrolysis of cane-sugar by hydrochloric acid is thus explained by the decrease of dissociation of the acid, as demanded by mass action on the Arrhenius theory. Taylor (1914) comes to conclusions similar to the last, in more detail. He also finds that the catalytic action of the undissociated acid increases with the affinity constant of the acid.

If Cj is the concentration of the hydrogen ion, C2 that of the undissociated acid, &H the catalytic action of the former, km that of the latter, then It will be noted that it is not definitely known whether the H' ion concentration is actually raised by neutral salts. As regards the part played by this " neutral salt action " in physiological phenomena, see the paper by Hober (1910, 3). For very weak acids a sensitive method has been described by Fraenkel (1907). Diazo-acetic-ester is decomposed, with evolution of nitrogen gas, by very low concentrations of hydrogen ions, and is of use even in the case of the very weak amino-acids.

A method similar to that of hydrolysis of ordinary esters, and, like it, specially useful for the stronger acids, but subject to "neutral salt action," is the inversion of cane-sugar. This consists in the hydrolysis of the disaccharide, with the formation of glucose and fructose and, being associated with a considerable fall in the power of rotating polarised light, can be followed with the polarimeter in a convenient manner. We have seen how very sensitive the various processes, both chemical and physical, taking place in the organism are to changes in concentration of hydrogen ions. Now a large number of the reactions going on result in the production of such changes, and it is not to be supposed that it would be desirable that these changes should be entirely neutralised, even if it were possible. For example, the sensitiveness of the respiratory centre to slight increase of hydrogen ion con-

centration serves to get rid of the two products of muscular activity — carbon dioxide by the increase of respiratory ventilation, and lactic acid by increased supply of oxygen. At the same time, unless there were an efficient mechanism for moderating the changes in hydrogen ion concentration, there would be serious disturbance of the delicate action of protoplasmic processes. This mechanism does in fact exist, and has been elucidated chiefly by the work of Lawrence J. Henderson, whose article on the subject (1909) should be consulted for a more detailed account than can be given here.

The possibilities of a means of soaking up, as it were, excess of hydrogen or hydroxyl ions would naturally be looked for in the more complex forms of electrolytic dissociation of the salts of the bi- or tri valent acids, in combination with the hydrolytic dissociation of salts of weak acids with strong bases. This latter process has not been as yet discussed in these pages, and will require some consideration presently. There are two systems of this kind to which early investigators turned their attention. They are both found widely spread throughout the animal organism. The first is that of the bicarbonates and carbon dioxide, which is to be met with chiefly in the blood, but also in the cells of the tissues generally. The second is that of the acid and alkaline phosphates, of greater importance in the cells. There are also, of course, interactions between the two systems, thus : —

so that there is always present a complex state of equilibrium between the two phosphates in addition to that between the bicarbonates and carbon dioxide. The proteins, as amphoteric electrolytes, and therefore capable of combination with both acids and bases, although, in all probability, only with strong acids and strong bases, except in rare instances, must also be taken into account. As we shall see, however, the part played by proteins appears to be comparatively unimportant. Adsorption, possibly, may also play a subordinate part.

In the further treatment of the question, I follow closely that of Lawrence J. Henderson. We must remenyber that, contrary to what happens in simple homogeneous systems, such as true solutions in water, we have to deal in the blood and tissues with the complication due to phases and the phenomena, such .as adsorption, which take place at their contact surfaces. It is well, however, to understand the less complex case to begin with. The results can afterwards be modified, if necessary, by the introduction of further factors.

It has long been known that the blood is able to withstand the addition of considerable amounts of free acid or alkali without much change in its reaction. This has been correctly described as being chiefly due to the carbonates and phosphates present, although the mechanism could not receive a satisfactory explanation until the electrolytic dissociation theory was propounded. Let us consider first the phosphate system. The mono-sodium phosphate (NaH2PO4) behaves as a very weak acid owing to the way in which it dissociates, while the di-sodium phosphate (Na2HPO4) is a very weak base. The dissociation of these salts may be represented as taking place in stages, thus (marking the equations for convenience of future reference) : —

Hydrolytic Dissociation. — With respect to the two last equations, we note that the source of the OH' ions giving alkalinity to solutions of Na.,HPO4 is the reaction in which the ion HPO4" combines with the H- ion of water, leaving OH' in excess. The electrolytic dissociation of water itself has not yet been discussed, but the evidence that such is the case is sufficiently strong to warrant us in making use of the phenomenon in the explanation of many facts, an explanation which it gives in a simple and reasonable way. The actual evidence itself will be given in the following chapter of this book.

A salt of a weak acid with a strong or weak base, or of a weak base with a strong or weak acid, that is, any salt of which one or both components is a weak one, is hydrolytically dissociated to a certain extent in water. There are present in the solution free acid and free base. In this connection the designation "strong" and "weak" should be understood. in a somewhat relative sense. For example, ammonium hydroxide behaves as a weak base towards the strong acid, hydrochloric, but as a fairly strong base towards the very weak acid, leucine. I refer to this point here on account of the fact that salts of weak acids with weak bases are not so highly dissociated hydrolytically as might have been expected. The question will be discussed below.

In order to understand the process a little more detail is desirable. Remembering that the dissociation constant of an electrolyte expresses the proportion in which the non-dissociated part is capable of existing in the presence of its ions, let us see in the first place what happens when a strong acid, such as hydrochloric, is added to a solution of a salt of a weak acid, say to sodium acetate. Both of these are highly dissociated electrolytically, but when mixed, opportunity is given for the formation of two other electrolytes, sodium chloride and acetic acid, the former of which is highly dissociated, but the latter very feebly so. The low dissociation constant of acetic acid means that acetic ions and hydrogen ions can exist together only to a very small extent. Hence, in our mixture, they unite almost completely to form acetic acid, the result being that the hydrogen ions of the hydrochloric acid very nearly disappear. For practical purposes the reaction may be expressed thus : —

.Further, owing to the great affinity of H* for OH' ions, the minutest quantity only of either can exist in the presence of the other. Hence, the neutralisation of a strong acid by a strong base may be represented by an equation similar to that above : — Now water contains the small concentration of both H- and OH' ions which can exist together. Applying the law of mass action to this equilibrium, we have:— where CH., CHO', and CH.,0 are the concentrations of the H- ions, the OH' ions and the water respectively. Since the latter is always very large in relation to the others, it may be taken as invariable, so that the product CH. x COH/ is constant in any aqueous solution. It is numerically equal to 1-2 x 10~14.

Water, then, is both a very weak acid and a very weak base ; that is, it is what we shall learn later to call an "amphoteric electrolyte." When a neutral salt AB (using A' for the anion and B* for the cation) is dissolved in water, there is the possibility of the formation of two new compounds with the ions of water, viz., HA and BOH. How far this will occur depends on the strength of the acid and the base. Suppose we take NaCl, the quantities of HC1 and of NaOH will be very small, because of their great dissociation, and approximately equal quantities of H' and OH' will be removed from the water for the purpose, being replaced by a slight further dissociation to keep CH. x COH- equal to l'2xlO 14. Again, suppose that we take borax instead of sodium chloride. Here HA is a very weak acid, while BOH is a strong base. We have now in solution A', B", H', and OH' ions, and HA and BOH will be formed as before. But, since HA is very slightly dissociated, while BOH is highly dissociated, there will be excess of OH' ions. As before, a little water will dissociate, but only to preserve the equilibrium CH. x COH, equal to 1-2 x 10'14, and this cannot get rid of the OH' ion.«, so that the solution will have an alkaline reaction. The case where the acid is strong and the base weak may be treated in a similar way, and the result will be

found to be that the solution has an acid reaction. .Such a case is that of aniline hydrochloride. The degree of hydrolytic dissociation may be determined by methods involving the estimation of the concentration of hydrogen or hydroxyl ions, such as the hydrogen electrode, rate of hydrolysis of esters, etc. The treatment of tinsubject given above is that of Philip (1910, p. 260). The U>ok of Nernst (1911, pp. .~>.SO-fi.'W| may also In- consulted with advantage. It will In- noticed that the process essentially depends <m the slight electrolytic dissociation of weak acids and weak l>u-i---.

From the equation for the reaction constant of hydrolysis given l>y Nernst (1911, p. 531). which is — where K4 is the dissociation constant of water, K2 that of the acid, and K:! that of the base, we see that the degree of hydrolysis can be calculated when the strengths of the acid and lia*e are known, and that it may have the same value with very various relative values of K.2 and K3, being greatest when both are low. Moreover, if the one or the other of the non-dissociated components is insoluble, it may happen that nearly the whole of the solute is hydrolysed. An instructive case, where the process of Ii3'drolytic dissociation is visible, is that of mercuric acetate; a fresh solution is clear, but gradually becomes more and more turbid and red oxide is deposited.

The fact is sometimes overlooked that this process of hydrolysis in water rarely amounts to more than 3 to 5 per cent, of the total content of solute. When both acid and base are weak, as in aniline acetate, the hydrolysis may amount to 28 per cent. (Bayliss, 1909, 2, p. 359). But, as a rule, it is a small thing compared with electrolytic dissociation, and indeed is not always to be found when it might be expected. For example, it appears that sodium stearate is considerably hydrolysed, sodium palmitate is not. Congo-red is not so to any appreciable degree, neither is the sodium salt of caseinogen. The acids in these cases are insoluble in water, so that it is a matter of much difficulty to know a priori what are to be reckoned as strong acids.

We may now return to the consideration of the phosphate system. In a solution of NaH9PO4, which has an acid reaction, the only source of H- ions is the stage of dissociation numbered (4) in the list above. (2) must precede this, so that, combining the two, we have : — If we add Na.,HPO4 to a solution of NaH2PO4, we add an excess of HPO4" ions. Therefore, since these solutions, as weak acids and bases, obey the law of mass action, we reverse the dissociation of equation (4) —

and the H1 ion concentration of the acid phosphate is reduced. Similarly, the alkalinity of a solution of Na.,HPO4 is due to the OH' ions derived from hydrolysis of HPO4" ions, according to equation (6). Perhaps it would be more correctly expressed by saying that the HPO4" ion combines with H- ions of water to form H2PO4' ions, in a way analogous to that in which acetic anions combine with hydrogen ions to form non-dissociated acetic acid. In any case the result is an excess of OH' ions. If, then, NaH.,PO4 is added to Na.,HPO4, the excess of H.,PO4' ions throws back equation (6), and the alkalinity is reduced.

The mono sodium phosphate, as a weak acid, gives off very few H' and HPO4" ions by (2) and (4), go that a very small amount of the di-sodium salt, which, as a sodium salt, gives many HPO4" ions by (1) and (3), has considerable power of diminishing the acidity of the former. Again, the di-sodium salt as a weak base gives rise to very few OH' ions by (1), (3), and (6). Hence a very small amount of NaH0PO4, which, in its character as a sodium salt, dissociates with the production of many H.,PO4' ions, diminishes considerably the hydroxyl ion concentration of the di-sodiura salt by throwing back equation (6).

These considerations show that phosphate mixtures vary comparatively little from neutrality, even with considerable excess of the acid or alkaline constituent. For this reason they make useful standard mixtures for hydrogefr ion concentrations not far removed from neutrality, as we shall see later. The Bicarbonate System. — Similar considerations may be applied to the bicarbonate and carbon dioxide system. In actual dissociation the conditions are not so complex, since we have to deal with a dibasic acid instead of a tribasic one. On the other hand, there is a new complication added in the escape of CO9 as a gas.

The equations of dissociation may be written thus, to correspond with those of the phosphates : — Since carbonic acid, H2CO3, is a very weak acid, few hydrogen ions are formed by equation (4). Sodium bicarbonate, as a weak base, produces few hydroxyl ions, but as a sodium salt, produces a considerable number of HCO3' ions. Suppose that CO2 is added to a mixture of bicarbonate and CO9.H0CO3 is formed, and this increases the concentration of HCO3' by dissociation. The result of this will be increase of non-dissociated NaHCO3 by throwing back equation (3).

The way in which these facts work in the maintenance of moderate changes only in H' ion concentration will best be seen by taking a numerical example. We must first, however, refer to the principle of isohydric solutions. This states that, if two solutions have an ion in common and in the same concentration in both, no change in the concentration of this ion will take place when the solutions are mixed. Suppose that H2CO3 and NaHCO3 are present together in a solution. From the low value of the dissociation constant of the former we may assume that the concentration of the non-dissociated H9CO3 is almost exactly the same as that of the dissolved CO2 ; practically all the HCO3' ions, therefore, come from the strongly dissociated NaHCO3, and their concentration is proportional to it— that is, in decimolar concentration, about 0'8 of it, since this is the proportion dissociated. The dissociation of NaH2PO4 is also 0-8, and that of Na.2HPO4, as regards H* ion, is 0'04.

Hence, to obtain a hydrogen ion concentration of 1 x 10'7 (i.e., neutrality at an expression which gives the proportion of the constituents necessary for neutrality in a solution containing all four, or either pair, since they are isohydric. The absolute concentrations may vary so long as the ratios are kept constant, and the latter can only change if dissociation constants change. For the sake of simplicity, we will take for further consideration the first

(CO.2) system, having a total concentration in CO., of decimolar strength, which corresponds very closely to that of blood. Let us see what change is necessary to raise the H* ion concentration from 0*5 x 10~~ to 1'Ox 17"", keeping, for ease of calculation, the total CO2 constant hy dilution. In the manner described above we have — From the previous calculation, we have, for 1 x 10~~, a value for the ratio of O~=-T, so that the concentration of NaHCCX in this case must be 0-046 molar. 3-7o

The difference between this and the value for 0'5 x 10- 7 is 0'088 - 0-046 = 0-042 grammolecules of NaHCO3 or CO2. This shows that nearly half as much CO., as the bicarbonate present is required in order to produce a change of hydrogen ion so small as that from 0"5 x 10"" to 1 x 10~", which is about what would be produced by the addition of O'OOl gram-molecule of hydrochloric acid to 10,000 litres of water. A similar calculation can be made of the amount of bicarbonate required to reduce the hydrogen ion concentration from 0-5 x 10"" to 0*2 x 10"". Thus : —

The phosphate equilibrium can be treated in the same -way, so that we can understand the great capacity of blood and cells to preserve an almost complete neutrality. The results of the preceding calculations may be further realised in the following way. In a bicarbonate system with a constant pressure of CO.,, in order to change an acidity of 0-0000002 molar into an alkalinity of the same value, an extremely small change, it is necessary to add a volume of decinorrnal sodium hydroxide nearly equal in volume to the solution itself. On account of the importance of the question, another example may be given (see L. J. Henderson, 1913, pp. 147-152). Consider 1 kg. of CO9 dissolved in 100 litres of water and that sodium hydroxide is added in quantities of 50 g. at a time. Before any addition, the hydrogen ion concentration is about 10~4, or about 1,000 times that at neutrality. The addition of 50 g. of NaOH reduces this to 50 times that at neutrality. After the addition of 200 g. more, the H- ion concentration is only 10~6, merely 10 times that at neutrality, although there are still present 682 g. of free CO2. An acidity of this order is produced by the addition of only 0-004 g. of hydrochloric acid to 100 litres of pure water. We can continue to add NaOH without causing any change, more than just perceptible, until 450 g. more have been added. When 700 g. in all have been added, the reaction is practically that of pure water, and a further 50 g. may be added without any greater change in the H- ion concentration than from 0'9 x 10~" to 0'6 x 10~", and in the OH' ion concentration from 1*1 x 10~" to 1'7 x 10~", although in pure water one ten -thousandth part of the amount would reduce the H- ion concentration from 1-1 x 10~7 to 0-1 x 10~T and raise that of the OH' ions from M x 10~7, to 12 x 10~7. The same amount (50 g.) added to pure water would raise the OH' ion concentration to 120, 000 x 10~7.

Suppose now that we take a case which is analogous to that of the blood of air-breathing animals. The state of affairs will be found to be still more striking. In the experiment described by L. J. Henderson (1913, pp. 149-151) we take a solution of 1 kg. of sodium bicarbonate in 100 litres of water and allow it to attain equilibrium with an unlimited atmosphere containing 1 g. of CO., per litre. Let hydrochloric acid be added in small portions at a time, constantly shaking the solution so that there shall always be equilibrium with the CO., in the gas phase. Further, let the temperature be such that

the absorption coefficient of CO2 is unity, that is, about 17°. Then the stages will be about as given in the following table : — Until nearly 250 g. of hydrochloric acid have been added, neither the acidity nor the alkalinity is greater than twice that of a perfectly neutral solution. The cause of this constancy is simple enough. At the beginning the free CO2 of the solution is in equilibrium with that of the gas phase. Accordingly when hydrochloric acid is added and reacts to form sodium chloride and more .CO.,, the whole of the latter escapes to the gas phase and the total amount of acid is what it was before, viz , saturation with CO2 at a partial pressure of 1 g. per litre of air, since all the hydrochloric acid has combined with the bicarbonate. Thus the concentration of the alkaline salt (bicarbonate) is diminished, but there is no increase of free acid. Not until all the bicarbonate is decomposed does the hydrochloric acid begin to show its effect, and then the addition of 2 g. causes nearly as much rise in acidity as the previous 318 g. had done, or about 200 times the rise caused by 100 times the amount at the first stage of the experiment.

A remarkable fact was noticed by Henderson (1908, p. 176) in comparing the relative amounts of alkali necessary to produce a given change in the H' ion concentration, as shown by indicators, in the cases of various weak acids. With the single exception of hydrogen sulphide, it was found that NaHzPO4 and ff2CO3 required the largest quantities. Acids both weaker and stronger than these required very much less, there being a large step between the three mentioned and the next in the series.

The "Fitness" of Carbon Dioxide. — It will probably not have escaped the reader that, as is insisted upon by L. J. Henderson (1913), it is a remarkable fact that it should be carbon dioxide, the universal product of oxidation in the living organism, that is the most efficient regulator of neutrality. Of course it is clear that organisms would not have been able to develop to their present degree of perfection without some mechanism of this kind, and that it is in adaptation to a system in which carbon compounds play the chief part that their mechanisms have been evolved. None the less it is calculated to excite a certain amount of wonder that the element carbon, which is, as pointed out above (page 41), so peculiarly adapted for the formation of a great variety of complex compounds, should also include amongst these an acid with the properties which carbon dioxide alone, with the exception of hydrogen sulphide, possesses. Especially is this so when we remember that there is no reason to suppose that this property is necessarily connected with the other properties of carbon. In the next chapter we shall see that similar remarks apply with even more force to the case of water.