Principles of General Physiology

These facts will suffice to show the importance of two things to which we must devote some attention. The first is the means of exact measurement of the H- ion concentration of a solution, the second is the capacity possessed by the blood and the cells to neutralise even considerable addition of acids or alkalies, in .order to maintain the state of nearly complete neutrality which is essential. If we were dealing with distilled water only, the addition of one-millionth of a grammolecule of hydrochloric acid to a litre would raise its H' ion concentration from lO"7'7 to 1Q-8, that is more than ten times, a change that would be fatal to many delicate protoplasmic processes. The mechanism which prevents such a result will be described later.

Measurement of Hydrogen Ion Concentration.— Very brief consideration will suffice to show that, in the case of weak acids and bases, or even strong ones in concentrated solutions, the ordinary methods of titration by adding a standard solution of acid or base until a certain change in a coloured indicator is produced, although giving valuable information as to the total concentration of free acid or base (i.e., dissociated plus undissociated), are not sufficient to afford the desired data as regards the H' ions of the dissociated fraction. Different acids, as we have seen, vary considerably in their degree of dissociation in equimolar solutions. This dissociated part is

always a certain proportion of the total acid present, so that the moment a part of the acid has been removed by the addition of a base, the remaining acid undergoes a further dissociation and so on, until the whole of the acid, whatever its original dissociation was, has become completely dissociated and its hydrogen ions have entered into combination with the hydroxyl ions of the base. There are, however, certain methods by which the actual hydrogen ion concentration can be estimated without causing any change in it.

We will first consider the use of Indicators. These are certain dyes which have a particular colour at a certain concentration in H' ions and another colour at another concentration which differs very little from the first. Those which change colour at points not far distant from neutrality are the most useful, especially in physiological work. That it is really the hydrogen ion concentration that these substances "indicate" is obvious if we take a series of five dilutions of hydrochloric acid, viz. , twice normal, normal, d«ci-, centi-, and milli-normal ; the colour of crystal violet will be found to be yellow in the first, yellow-green in the second, blue-green in the third, blue in the fourth, and violet in the fifth. No alkali has been added, and the only difference between the various solutions is the concentration in the acid.

The whole question of the theory of indicators cannot be entered into here, but may be found in Nernst's book (1911, pp. 533-536). Generally speaking, they are salts of either a very weak acid or a very weak base, sometimes the free acid or base itself. The change in colour is due to the electrolytic dissociation of the salt with the production of an ion which has a different colour from that of the free undissociated acid or base. Since the strength of the indicator acid or base varies in the different substances used for the purpose, it will be clear that the acidity of a given solution may be determined by the use of a series of indicators changing colour at different H' ion concentrations. In theory, the question is a little complicated by the existence of what are known as " pseudo-acids," which have a different chemical structure in the free state to fliat in their electrolytically dissociated salts ; but the explanation given, which was originally due to Ostwald, is not practically altered by this fact.

That indicators do actually vary in the acidity of the solution to which they respond can easily be seen by comparing methyl orange with phenolphthalein. If a solution of hydrochloric acid be taken it will be found that methyl orange is red in it. Alkali is now added until the colour changes to orange, that is, the solution is alkaline to this indicator. If another sample of the acid be taken, it will be found to produce no colour with phenolphthalein, and more alkali must be added to change the colour of this indicator to the red one of its salts than was required to change the colour of methyl orange

In the use of indicators there are several precautions to be observed. In the first place, the hydrogen ion concentration at which certain of them change colour is not the same in pure acids or bases as in the presence of foreign substances, especially salts and proteins. For a description of these cases, the reader is referred to the investigations of Sorensen (1909), which are concerned with the various methods of practical use for the estimation of hydrogen ion concentrations. The use of indicators for physiological purposes will be found fully treated. In the second place, it will be obvious that the total amount of the indicator present must not be so great as to neutralise, or react with, any perceptible portion of the ions to be estimated.

This will be made clear if we take a dilute solution of Congo-red, the sodium salt of an acid whose coloured ion is red and whose undissociated free acid is blue. Add a drop of this solution to a very dilute solution of hydrochloric acid, a blue colour is given. Take again a concentrated solution of the indicator and add it in rather large amount to a small quantity of the very dilute acid. The colour will remain red, because the whole of the free hydrochloric acid present has been used up to combine with a portion only of the dye, and the colour of tl itsalt still left in excess masks the bluish colour or the very small amount of the free dye-acid. This fact is especially liable to mislead when test papers are used, and a drop of very dilute solution, or one containing only a very small amount of hydrogen ions, is applied to the paper, as has been pointed out by Walpole (1913, 1). In such cases the reaction will appear to be different when a drop is placed on the paper and when the paper is immersed in a large volume of the solution.

Walpole (1910) has also described an ingenious artifice by which it is possible to use an indicator with solutions containing coloured substances. This method consists essentially in comparing the colour of the solution to which an indicator has been added with that of the light which has first passed through an equal depth of the coloured solution alone, and afterwards through water containing the indicator alone. When used for titration, for which purpose the arrangement is particularly adapted, the acid or alkali is added to the cell containing the indicator alone until the change in colour corresponding to the required concentration in H' ion is obtained. This cell is then observed by light which

has passed through a depth of the coloured solution equal to that to which the indicator has been added. Acid or alkali is then added to the latter until its colour is the same as that , ot the combination of the coloured solution with the indicator solution in separate vessels, absorption due to the coloured substance is obviously identical in the two cases. The table given in Fig. 56, which is extracted from the results of Salm (1906) and of Sorensen (1909), may be useful. With the exception of those indicators

in brackets, it contains only those found by the latter investigator to be unaffected by the presence of moderate amounts of such substances, proteins or neutral salts, as are likely to be present in physiological solutions. I have omitted two of those recommended by Sorensen on account of the difficulty of obtaining them, and have inserted in place of them, where the series would otherwise be incomplete, other indicators in common use, but more sensitive to the disturbing presence of neutral salts and proteins. These are marked by brackets.

Neutral red is an extremely valuable indicator for many physiological purposes. It changes colour at the neutrality of water, and has obvious changes at points just above and just below this concentration in hydrogen ions. It is practically unaffected by the presence of protein and is innocuous to living protoplasm. The cautions to be exercised when neutral salts or proteins are present in any considerable quantity may be found in the paper by Sorensen (1909, pp. T'2-120). Attention may be called to phenol- and thymol-phthaleins as being least affected thereby, and especially to the new indicator, a-naphthol-phthalein, which changes colour between the H' ion concentrations of 10"7''-* and 10"8'68, i.e., a very little on the alkaline side of neutrality (Sorensen and Palitzsch, 1910).

The Hydrogen Electrode. — This method, although somewhat elaborate in the apparatus required, and demanding careful work if small differences in H* ion concentration are to be measured, is the most direct and the least liable to disturbance by foreign substances. In order to understand the principle of it, the reader may be glad of a few words on the theory of electrode potential. When a solid is placed in water, it has a certain tendency to send off its molecules into the water so as to form a solution. The intensity of this varies greatly in different cases, and is known as the solution pressure of the substance in question. It occurred to Nernst (1889, pp. 150-151) that the electrical phenomena shown by metals immersed in solutions of their own salts might be treated quantitatively from a similar point of view, on the assumption of the truth of the electrolytic dissociation theory. When a metal, say copper, is immersed in a solution of one of its own salts, say the sulphate, the copper has a tendency to give off Cu" ions into the solution. There are already ions of the same kind in the solution, which, by their osmotic pressure, oppose the passage of similar ions from the metal. The force with which the metal tends to send out ions into the solution is called by Nernst its " electrolytic solution pressure," and may be greater or less than the osmotic pressure qf the metallic ions in the solution. It will be plain that, in the former case, the metal will become negatively charged, owing to its giving off positive charges on the ions which leave it. Its potential will depend on the difference between its electrolytic solution pressure and the osmotic pressure of the ions in the solution. If the latter is the greater, the electrode will have a positive charge, owing to the receipt of positive ions from the solution. It is to be remembered that the ions given off from the metal cannot travel beyond an infinitesimal distance from the oppositely charged mass of metal, owing to electrostatic attraction, as has been pointed out above.

It is obvious that we cannot make use of any one of these electrodes alone, since we must have metal at both ends of our cell in order to form the circuit for the purpose of measurement. If we form our battery by joining up two electrodes of the same metal in solutions of the same concentration, there will be no electromotive force in the combination, since the two electrode potentials are equal and in opposite direction to one another. If, however, the concentrations of the' metallic ion in the two solutions are unequal, the electromotive force of the battery is equal to the difference between that of the two electrodes. This arrangement is known as a "concentration battery." If we know the concentration of one of the solutions, and can measure the electromotive force of the combination, we can obtain the concentration of the other solution by difference, supposing that we know the law which governs the relation between the potential and the concentration of the solution. Now it has been shown by Nernst (1889), originally from thermodynamic considerations, although the assimilation by van't Hoff of solutions to the gas laws would lead to the same result, that this relation is given by a similar expression to that for the work

done in compressing a gas isothermally from a pressure p to P. This is, as we have seen (page 35 above), We may, in fact, regard the two pressures of the formula as being the osmotic pressure of the metallic ions of the solution (;:>) and the electrolytic solution pressure of the metallic electrode (P). We have, then, merely to express the terms of this formula in the appropriate electrical units in order to obtain the relation between potential and concentration of ions in the solution. This is done by dividing by the charge in coulombs on one gram ion, the Faraday constant ; by doing this, we convert pressure in mechanical units into electrical force. If the ion in question is multivalent, the Faraday constant (F) must naturally be multiplied by the number of charges carried, that is by the valency (n). R, the gas constant, must also be expressed in electrical units. We have, then : —

Another method of calculating this number will be found in the book by Nernst (1911, p. 753). We need, then, only to know P, the electrolytic solution pressure of the metal used, in order to be able to determine p, the osmotic pressure of the ions in the solution and, therefore, their concentration. P has been determined for a number of metals. In the case of a concentration battery, it is eliminated thus : — where p1 and p2 are the respective concentrations of the two solutions.

We may note that the electrolytic solution pressure may be looked upon as that osmotic pressure of the ions in the solution which just balances the tendency of the ions of the electrode to pass out ; so that the electrode would have zero potential if it were possible to obtain a solution of the correct concentration. Certain metals, such as platinum and copper, have a very low electrolytic solution pressure, so that they are always positive in solutions of their salts, and it will be clear that the higher the concentration of the salt is, the greater will be its tendency to send positive ions into the metal, or, in other words, the greater will be its potential. Ziuc, on the other hand, is an example of a metal with a very high electrolytic solution pressure, so that the osmotic pressure of the ions in solutions of its salts will always be lower than its own ; in this case the potential will be higher, the lower the concentration of the solution, since it is due to the sending out of ions by the electrode.

We may now proceed to the description of the hydroyen electrode. It will have been sufficiently obvious from the preceding pages that, if we could make an electrode of this gas and immerse it in a solution containing hydrogen ions, that is, an acid solution, we should have the means of measuring the concentration of the hydrogen ions by the potential of the electrode. It will probably occur to the reader that, if we saturate palladium with hydrogen, we have what is required so long as our solution does not attack the metal chemically. It will, of course, be remembered that the potential is determined only by ions common to both electrode and solution. Palladium, however, is attacked by some acids which we require to take account of — hydrochloric acid, for example. We must therefore use platinum, which also takes up hydrogen, although in less amount than palladium does, so that it needs more care to saturate it and keep it saturated. In practice, the electrode is sometimes made of gold, merely plated with platinum

black, in order that it may be rapidly saturated with hydrogen. The gold, of course, merely serves as a conducting support for the platinum. It is unnecessary for both electrodes to be hydrogen electrodes, or to have a concentration battery in hydrogen, although in some cases it may be desirable. So long as the opposing electrode is of a known electromotive force, it may be of any form. In practice, the Ostwald calomel electrode, described on p. 202 of Findlay's book (1906), is generally used. The tables givt-n in the paper by Schmidt (1909) will be found to save much time in calculation.

There is one circumstance to be taken into consideration which has so far been omitted, for simplicity, in our account. We saw above (page 178) that when the two ions of an electrolyte have different velocities, there is a difference of potential at the contact surface of such a solution with water, and also when two solutions of different concentrations are in contact. This electromotive force is allowed for in the complete Nernst formula for a concentration battery by the factor —

where u and v are the mobilities of the two ions in question, and cl and c0 the concentrations of the two solutions in contact ; B and T have their usual meaning (Nernst, 1911, p. 752). In the case of the complex physiological solutions with which we often have to deal, calculations on the basis of this expression are practically impossible, since we are uncertain as to the actual ions concerned. The contact difference is therefore rendered as small as possible .by the interposition of a saturated solution of potassium chloride in the manner described by Bjerrum (1905), between the solutions of the two electrodes. It appears that the great excess of ions, having very nearly the same rate of migration, makes the two contact potential differences between this solution and the solutions in the electrode vessels practically equal and opposite to one another, while the dissociation of the electrode solutions is greatly diminished at the contact. When great accuracy is required, determinations are made of the total electromotive force of the combination when potassium chloride solutions of different concentrations are interposed. From the data obtained the true value can be determined by xtrapolation. Other very soluble salts, such as ammonium nitrate, are sometimes used.

The measurement is made by a compensation, or potentiometer, method. A wire, best made of platinum-iridium, is stretched along a scale, and through it a current is passed from a constant battery, such as a partially discharged storage cell. By means of a sliding contact, any fraction of the electromotive force between the two ends of this wire can be tapped off and opposed to that of the electrodes until the whole is brought to zero. Some means of detecting this point of balance is necessary, and, owing to the high resistance usually present in the circuit, the capillary electrometer, to be described in Chapter XX., is generally used. The value of the reading on the scale of the slide wire is obtained by determining at what reading the electromotive force of a standard cell is balanced. The value of each scale division is then known.

For further practical details the reader is referred to Findlay's book (1906), for the general method, and to the paper by Sb'rensen (1909) for the physiological applications. A diagram of the circuit is given in Fig. 204 (Chapter XXII. ). The most important of these applications may now be referred to, that of estimating the true hydrogen ion concentration of the blood, which it is impossible to determine in any other way. The difficulty here is that a part of the hydrogen ions arise from carbon dioxide dissolved in the liquid, so that, if the usual method of passing hydrogen gas through the solution in which the platinum electrode is immersed for a part of its area be used, carbon dioxide gas is driven off and the acidity decreased. In the earlier determinations of the reaction of the blood this circumstance was not duly taken into account. The difficulty is obviated by taking a closed volume of hydrogen in contact with the electrode, which has been previously saturated with it, shaking this limited volume of gas with a portion of blood, so that the carbon dioxide tension of the gas phase becomes equal to that of the liquid. This blood, which has lost a part of its carbon dioxide, is replaced by a fresh portion, which will need to part with only a minute fraction of its carbon dioxide to the hydrogen. This was first done by Michaelis, and an improved method has been described by Hasselbalch (1910). More recently, \Valpole

(1913, 2) has invented a simple form of hydrogen electrode, which can be used for various purposes ; with care, it can be made to serve the purpose of the Hasselbalch form. Fig. 57 shows the Walpole electrode. In a later paper Walpole (1914, 1) describes improvements in this electrode. Peters (1914) uses another excellent form. In the case of blood, or other solution containing haemoglobin, there is another difficulty. Platinum takes up oxygen as well as hydrogen, and, in pure oxygen, it serves as a hydmxyl ion electrode, although not so accurately defined as the hydrogen one, owing to its sensibility to various disturbing conditions. When in use as a hydrogen electrode, it is obvious that the potential which it assumes in a solution of given hydrogen ion concentration will not be the same if the gas in contact with it contains oxygen, as must be the case if shaken with a solution of oxyhfemoglobin. At present it seems impossible to devise a method of removing oxygen without producing other changes in the blood. Perhaps carbon monoxide would srrvr.

The general method of determining the concentration of particular ions in a solution by the use of appropriate electrodes is probably capable of wider application in physiology than it has yet received. Thus the changes in the concentration of chlorine ions due to separation and dissociation of chlorides and changes in the tension of oxygen can be investigated on these lines. These are processes which occur in physiological activity, and Roaf (1913) has already obtained valuable information with regard to changes in contracting muscle by these methods. Reference will be made to these results later.

In the description of the Nernst theory of the metallic electrode, it must not be forgotten that the process is not the same as that of ordinary solution. Owing to the forces of electrostatic attraction, the ions given off from the metal cannot actually pass beyond the immediate proximity of the electrode itself, thus giving rise to a Helmholtz double layer. The case of a solution enclosed by a membrane permeable only to one of the ions into which the solute dissociates is a completely analogous one. The surface of the metal itself in the Nernst electrode may be regarded as permeable to its own positively charged ions, but not to the oppositely charged mass of metal. The former ions, however, are held fast by electrostatic attraction until the circuit of the battery is completed, when they are able to pass out from the one electrode, which is dissolved, and are deposited on the opposite one, losing their charges and increasing the mass of the metal.

There is one point in connection with the Nernst formula which may have struck the reader, although it is not alluded to in the usual descriptions of the theory. It had, however, not escaped the notice of the original author (Nernst, 1911, p. 139). If pl in the expression : — becomes zero, i.e., if the liquid in one electrode is in infinite dilution, or, in other words, is water, the value of the potential difference becomes infinite. Nernst points out thai, theoretically, the diffusion of any substance into a space which is, for it, a vacuum, should take place with infinite velocity. In the case of a gas this condition would last only for an infinitesimally short time. Water is practically never a vacuum for electrolytic diffusion, since there are always ions in it. There are, moreover, other reasons connected with the conditions at the surface, which make measurements with solutions of less than O'OOl molar strength unreliable as indicating the state of the solution as a whole (see the remarks by Nernst referred to above).

Certain other methods of estimating the hydrogen ion concentration of a solution require a brief account.- These are of a more chemical nature, and are occasionally useful. As a rule they necessitate a previous knowledge of the composition of the solution apart from its concentration in hydrogen ions. Hydrolysis of Enters. — The rate at which methyl or ethyl acetic esters are hydrolysed in water is found to be proportional to the hydrogen ion concentration present. It may be used as a convenient method for the comparison of fairly high concentrations of these ions, but with weak acids the rate is too slow to be of much practical value. The presence of neutral salts affects the rate of the reaction in an anomalous way. If we return for a moment to the equation for the dissociation of a weak acid in equilibrium with its ions, viz. : —

it will be seen that any increase in the concentration of the acetic ion leads to diminution in that of the hydrogen ion, in order that K may remain constant. This increase may be produced by the addition of a salt of the weak acid, in our case say sodium acetate, which dissociates into acetic and sodium ions. Experimentally this is found to be the case. It is, indeed, a deduction from the law of mass action. But it does not apply to strong acids and their salts. In fact, the addition of sodium chloride to a solution of hydrochloric acid increases,

instead of decreasing, the hydrolysis of an ester by the solution. This difficulty in the electrolytic dissociation theory was noticed by Arrhenius himself (1889, 2, and 1899), and called "neutral salt action." It shows that neutral salts of a strong acid increase the effect of the acid itself in some way not yet clear. Attention has already been called to the anomalous behaviour of salts, strong acids, and strong bases, and the views of Noyes, etc., on the question (see page 182 above). Some suggestions made by Senter (1910), at the conclusion of a paper which bears on the subject, may be of interest. The influence of neutral salts may be supposed to be exerted on the water or on the substance being hydrolysed, sugar or ester. In the former case the dissociation may be increased, or the action may be of some unknown kind on the non-dissociated molecules. In the latter case the effect may be due indirectly to an effect on the dissociative force of the medium. Senter himself favours the latter view, but regards it as probable that there may be several causes acting together. Possibly hydration of the ions of sodium chloride may increase the effective concentration of both acid and sugar, but it is doubtful whether the effect would be large enough.