Principles of General Physiology

" 2. All electrolytes (in solution in water) consist partly of molecules which are active (in electrolytic and chemical ^relationships), and partly of inactive molecules. The latter, however, on dilution, are converted into active molecules ; so that in infinitely diluted solutions only active molecules are present." We may now venture to call these hypotheses " laws," although objections have not been wanting, as we shall see. Free ions, therefore, are believed to be present in all solutions of electrolytes, whether a current is passing or not. Definite proof of their existence under ordinary conditions is naturally desirable. Since the distinguishing property of an ion is its electrical charge, the difficulty of investigating its properties by methods other than electrical, which might be supposed to introduce conditions which beg the question, is obvious. To begin with, the following reasons are given by J. J. Thomson (1888, p. 294) for concluding "that the splitting up of the molecules which allows the current to pass is not caused by the electro-motive force, but takes place quite independently of the electric field." In other words, they are already split up before the current is sent in.

(1) The smallest electro-motive force is sufficient to start a current, so that no finite electro-motive force is required to dissociate the molecules. (2) The experiments of Fitzgerald and Trouton (1886, p. 312) show that Ohm's law is obeyed exactly, " whereas, if the electro-motive force had to break up the molecules, the current would be proportional to a higher power than the first of the electro-motive force." (3) J. J. Thomson himself was unable to detect the slightest change in the osmotic pressure of a solution of an electrolyte during passage of a current through it. If the number of separate systems is increased by the current, the osmotic pressure must rise considerably ; in the case of dilute strong acids, to nearly double.

Let us further contrast the behaviour of an organic compound of chlorine, say chloroform, CHC13, with that of an inorganic chloride, CaCl.,. In the first case, chlorine cannot be detected by the ordinary tests ; the molecule has certain properties as a whole. In the second case, in dilute solution, the behaviour to reagents is not that of an individual compound with its own peculiar properties ; its reactions are simply those which are common to all calcium salts, together with those which are common to all chlorides. According to the electrolytic dissociation theory, all chlorides, in dilute solution, contain chlorine ions, and all calcium salts contain calcium ions. Calcium salts 'have also a particular action on the muscle of the heart, and it is found that it does not matter what salt is taken. Again, hydrochloric acid has no properties peculiar to itself ; it tastes sour, turns litmus red, dissolves metals, inverts canesugar, in common with all acids. It precipitates silver salts in common with all chlorides. The nitrate, chloride, and bromide of copper are all blue in dilute solution in water, but in alcohol, where very little dissociation is to be expected, they are blue, green, and brown respectively. Ostwald (1892) has shown that each ion independently contributes its share to the properties of a solution, inclusive of colour, by taking photographs of the absorption spectra of the permanganates of zinc, cadmium, ammonium, tin, potassium, nickel, magnesium, copper, hydrogen, aluminium, sodium, barium, and cobalt in dilute

FIG. 53. ABSORPTION SPECTRA OF SOLUTIONS CONTAINING THE SAME COLOURED iox. — Showing the identity of position of the band. b. Salts of diazoresorufln with various elements. e, Salts of rosaniline with the following acids : — solution, and found the absorption band in the same situation in all. Various salts of dyes show the same behaviour (see Fig. 53). Before we pass on to consider other evidence, the question of electrolytic conductivity must be dealt with.

The passage of an electric current through a solution being due to the ions present between the electrodes, it is clear that the amount of current that will pass through a given solution will depend, in the first place, on the size of the electrodes— the larger they are, the more ions there will be between them. The current that passes, other things being equal, is in direct proportion to the area of the electrodes when the column of solution between them is of the same cross section as the electrodes, so that no spreading of the current takes place. In the second place, owing to the fact that the velocity with which the ions move is finite, the greater the distance between the electrodes the longer it will take for an ion to carry its charge to the opposite electrode and the less electricity will be carried in unit time, i.e., the current will be less. In comparing the conductivity of one solution with that of another, it is therefore necessary to agree to some arbitrary dimensions. The unit of conductivity is taken, accordingly, as that of a body of which a column one centimetre long and one square centimetre in cross section has a resistance of one ohm (Nernst, 1911, p. 361). The resistance is the reciprocal of the conductivity; if one solution has twice the resistance of another, only half the current will pass through it, so that its conductivity is half that of the other.

If, then, a body of the dimensions given above has a resistance w in ohms (usually written o>) its conductivity (K) is -- in reciprocal ohms, frequently called mhos (i.e., ohm spelt backwards). The actual conductivity of a particular solution is called the " specific conductivity " of that solution ; but in order to compare solutions of different salts with one another, it is convenient to have an expression in which the molar concentration is taken into account. The "molecular conductivity" is now understood as the actual conductivity divided

by the concentration in gram-equivalents per cubic centimetre (77), i.e., -, and is denoted by A. It is clear that the conductivity of the solution of an electrolyte depends on its concentration, since it is the ions into which the solute dissociates that conduct the current, and the more there are in the space between the electrodes, the more current will pass. The value of taking gram-equivalents instead of gram-molecules is that salts with multivalent ions are more readily compared with those with univalent ions. Thus, if equimolar solutions of KC1 and K2SO4 are compared, we must remember that the second salt, at an equal degree of dissociation, has twice the conducting power of the first, since it gives ions with four charges, two negative and two positive, while the first only gives one negative and one positive.

It will be remembered that, in the statement of the theory of electrolytic dissociation given by Arrhenius (page 173 above), the " inactive molecules " are said to be converted into active molecules on dilution. This is the expression of the experimental fact that the molecular conductivity, or the number of ions into which a gram-equivalent is dissociated, increases as the solution is diluted. By plotting successive values of the molecular conductivity at increasing dilutions in the form of a curve, the value at infinite dilution, that is, what it would be if completely dissociated, can be extrapolated. Equivalent conductivity may also be expressed in terms of the volume of solution in cubic centimetres which contains 1 gram-equivalent; the symbol <f> is generally used, so that the equivalent

conductivity may be expressed as K<J>. <£ is, of course, equal to -. The methods of measuring conductivity may be now considered. What is actually measured is the resistance of a stratum of known dimensions. The value of these dimensions for a particular vessel is determined by measuring in it the resistance of a solution whose value in conductivity is known from previous measurements in a vessel whose dimensions can be measured directly. Actual details may be obtained from the book by Findlay (1906, pp. 144-181) or from the article by Asher (1911, pp. 161-174). In the present pages general principles only need be referred to. As is familiar to the reader, the measurement of the resistance of metallic conductors by the Wheatstone bridge method is capable of extreme accuracy. The same method, with modifications, is also employed t<>i solutions of electrolytes. These modifications are due to the fact that, if a current is sent for any appreciable length of time between metallic electrodes immersed in such a solution, the current falls off greatly in strength owing to deposition of ions on each electrode of opposite sign to themselves, polarisation, as it is called. For this reason, accurate measurements by the ordinary galvanometer method are impossible. The difficulty is got over in the method of Kohlrausch by the use of a current which rapidly changes its direction, before any appreciable polarisation has had time to develop. Fjach electrode is made anode and cathode in turn. A small induction coil, with a very rapidly vibrating interrupter, is used for the purpose and the alternating induced currents from the secondary coil are sent through the electrolyte. But this again necessitates the use, as detector of the zero point, of some instrument which responds to alternating currents, since the ordinary galvanometer does not, except when the changes of direction do not occur at frequent intervals. A telephone is generally used.

When the solutions have a very high resistance, it is found to be difficult to get enough current through to give sharp readings with the telephone. In such cases, the method of Whetham (1900) is of great value. In this, the change of direction of the current is effected by a rotating commutator, and, in order to enable a delicate galvanometer of the ordinary type to be used, the alternating current is rectified again before going to the galvanometer. This is done by a second commutator on the same axis as that which originally makes tinalternating current. It is obvious that this method allows of great variations in the electromotive force used to drive the current through the electrolyte, and in the sensibility of the galvanometer.

In practice, especially for physiological purposes, the conductivity vessels with fixed vertical electrodes, and provided with stoppers, will be found of most value (see the catalogue of Fritz Kohler, Cat, E. 1906, No. 1326). We may now return to the consideration of further evidence in favour of the electrolytic dissociation theory. Let us take the molecular conductivity of the following series of salts in O'OOOl molar concentration as given by Kohlrausch and Maltby (1899).

The precise units in which these are expressed does not matter for our present purpose, since all are in the same units. The difference between KC1 and NaCl is 20-99 and between KNO3 and NaNO3 is 20-96, practically identical. Again, the difference between KC1 and LiCl is 30-99 and between KNO3 and LiNO3 is 31-11. What does this imply? Obviously that it does not matter whether, in changing Na or Li for K, we take a chloride or a nitrate; that is, the metallic part of the salt makes a certain contribution to the conductivity which is independent of the acidic radical associated with it. Similarly, the difference between KC1 and KNO3 is 3-56, between NaCl and NaNO3 3-53, and between LiCl and LiNO3 3-68, so that the same consideration applies to the other radical. This fact may perhaps be clearer if put in a symbolic form :

can only hold, if K, Na, Cl and NO3 each has a definite value independent of that of any of the others. We may conclude, then, that the conductivity of a highly diluted solution is made up of the independent conductivities of the individual ions and, if this is so, these ions must be present as separate entities. Kohlrausch expresses this in what is generally known as his law of the independent migration of the ions. The symbol u is given to the part contributed by the cation and v to that contributed by the anion, so that the molecular conductivity at infinite dilution of a binary electrolyte (that is, one that dissociates into two univalent ions) is u + v. These are constant values for the same ions, whatever salts they may form constituents of.

Referring back to the table on page 176, we notice that the conductivity of the Li ion is less than that of the Na ion and this again is less than that of the K ion. Since each of these ions carries the same charge, it follows that they must travel at different rates. A little consideration will show that, if this be so, after electrolysis by passage of a current has gone on for some time, there will be a different concentration of the electrolyte around the two electrodes and, by this means, measurements of the rates of the various ions have been made by Hittorf. Details of these measurements will be found in the textbooks (Philip, 1910, pp. 143, etc. ; Nernst, 1911, pp. 362, etc.).

The following table gives the molecular conductivities of a number of ions at the temperature of 18° (Nernst, 1911, p. 366). In the case of large organic ions it is interesting to note that the rate of migration diminishes comparatively little with increasing size. Thus, according to Bredig (1894), at 25°, the values of certain anions are as follows : — The practical use of these facts is that we can calculate the values of the molecular conductivity at infinite dilution in cases where it cannot be obtained experimentally. Thus ammonium hydroxide, even when diluted so far that the accuracy of the measurements becomes uncertain, is a considerable distance from complete dissociation. But from the law of Kohlrausch we can obtain the value as the sum of those of the constituents, NH4' and OH', viz. : —

Knowing the conductivity of salts when completely dissociated, we can thus determine the degree of dissociation at any concentration from measurements of its conductivity at that concentration. Suppose that we find that a binary salt at a known concentration has a molecular conductivity half that which we obtain from Kohlrausch's law as the limiting value at infinite dilution, we know that only half of its molecules are taking part in the conduction of the current.

The actual rate of movement of the various ions is of some interest. As Nernst points out (1911, p. 363), the small dimensions of ions would lead us to expect that the frictional resistance to their movements is very great. Their velocity is therefore proportional to the force acting on them. If the fall of potential in the solution is 1 volt per centimetre, that is, if the electrodes are 10 cm. apart and a potential difference of 10 volts exists between them, the hydrogen ion moves at the rate of 0'0033 cm. per second and the potassium ion at 0-00067 cm. per second. The actual manner in which this is determined is beyond the scope of this book.

This slow movement of ions allows another piece of evidence to be brought in favour of the actual existence of ions in solutions of electrolytes apart from any passage of current through them. Take a solution of copper sulphate and place in it two elect rodes at '2"1 cm apart. Let the anode consist of copper and the cathode of platinum. As soon as the current is established, copper is deposited on the platinum plate and dissolved from the anode by the >SO4" ion. Now, if. the electrical current itself split up the CuS04 molecules and the two oppositely charged parts were attracted to the two opposite poles, according to the old view, it follows that the >S04" ion belonging to a particular copper ion at the cathode has to travel in our case 2^2 cm. in less than one second. Suppose that the potential difference were 2-2 volts and that we ascribe to the SO4" ion as great a velocity as that of the OH' inn (G'0018 cm. per second) (it is really much less), twenty minutes will be required for it to travel the distance of 2'2 cm. between the electrodes.

Ostwald (1888, p. 272) directs attention to another similar experiment. It is well known that, if amalgamated zinc be immersed in dilute sulphuric acid, it is not attacked. But if a piece of platinum be also immersed in the same solution, even at a considerable distance, as soon as the two metals are connected by a wire, hydrogen appears on the platinum and zinc goes into solution. The hydrogen cannot arise from the same sulphuric acid molecule whose S04 attacks the zinc, since it cannot travel the distance in the time. It must come from the immediate neighbourhood and have been already present as dissociated ionic hydrogen.

Another fact which is readily explained by the different rate of migration of ions already present and for which no other explanation is at hand, is that, when a solution of an electrolyte is in contact with water, a potential difference is nearly always found to exist at the boundary surface. This is due to the unequal rate of diffusion of the two ions, so that either the anion or the cation is in advance of the other, forming a Helmholtz double layer. Of course, they cannot separate far from one another, on account of electrostatic attraction. We shall meet with this phenomenon again in connection with the sources of electrical changes in living ' tissues.

When we look at the numbers in the table of ionic conductivities on page 177 above, we are struck by the fact that lithium, with an atomic weight of 7, moves at a much slower rate than potassium, with an atomic weight of 39. The explanation is probably that the lithium ion carries with it a larger number of water molecules than the potassium ion, so that greater friction is experienced. The chief work on this question has been done by Bousfield (1905, 1906, 1912), to whose papers the reader is referred. An interesting fact, which is worth quoting, comes out from the results of the last paper (1912, p. lb'8). The number of molecules of water combined with both ions at infinite dilution is for

There are reasons for supposing that the number combined with the Cl' ion is f>, since its transport number is just a little greater than that of potassium, so that its share must be a little more than half of the total 9 of KC1. If this is so, we have for the number of molecules of water associated with the ions of The chief evidence for the truth of the electrolytic dissociation theory is, undoubtedly, the fact that it is capable of giving correct quantitative explanation of so many phenomena, and even of predicting the numerical values of the factors in these phenomena. It is not surprising that deductions from it have not always been verified, since modifications and additions are always necessary in theories of such far-reaching application.

Objections have been brought against it, but no rival theory has been shown able to afford the accurate quantitative results that it does in so simple and direct a manner. At the present time it may safely be said to be indispensable. There are many phenomena which, without it, could not even be described except with difficulty, much less treated quantitatively. Of these we shall presently meet with some striking examples. One only need be mentioned now. As we shall see, the " acidity " of a solution is readily expressed on our theory by the number expressing its concentration in H' ions. The difficulty found by those who do not accept the theory is seen on p. 576 of the paper by E. F. and H. E. Armstrong (1913), where mixtures of acid and alkaline phosphates in certain proportions have to be used, giving a set of numbers, having only a meaning relative to one another.

Some of the difficulties may be referred to, chiefly for the purpose of keeping in mind where further research is needed, but also on account of their instructive nature. At the time of the first publication of the theory, objection was made to it on the ground that, in the case of ammonium chloride, it was possible to separate by diffusion the products of dissociation, NH3 and HC1, whereas this could not be done in the case of Na and Cl ions in water. Although, at the present time, the explanation given by Arrhenius (1901, p. 176) is generally accepted, it is instructive to refer to it on account of the fact that it turns up in various forms. This explanation rests on the existence of the electric charge on the ions, whereas the products of ordinary dissociation are devoid of charge. This charge is the very large one of 96,500 coulombs per equivalent. Suppose, then, that we have in a tube a stratum of water lying over one of a solution of sodium chloride. If the Na and Cl had no charge, the latter, which diffuses much more rapidly than Na (in the ratio of 68 to 45), would be found in excess in the water layer after a short time. But when only 10 ~13 gramequivalents of Cl in excess of Na ions have passed to the upper layer, this layer would have a negative charge of 96,500 x 10~13 coulombs or 96,500 x lO"13 x3xlO'° = 290 electrostatic units, a quantity of electricity which would, on a sphere of 10 cm. radius, give a spark of 0'3 cm. Now it is easy to calculate that the electrical forces produced by the undetectable amount of 10 ~13 gram-equivalents of Cl far exceed any possible osmotic force which would cause unequal diffusion of the two ions. The electrostatic unit of electromotive force is about 300 volts, so that the above-mentioned 290 units would give a potential of

the same if the charge were given to a cube of liquid (Arrhenius.) Let us take now a stratum of half normal sodium chloride solution one centimetre high and one square centimetre in section, and imagine a potential of 104 volts at the end A and zero potential at B (Fig. 54). The sodium chloride is further supposed to be distributed in such a manner that its concentration at A is zero and at B normal, half normal midway. It is assumed to be completely dissociated for sake of simplicity. On the Cl ions

there is acting an electrical force of 7X6, where 7- is the fall of potential per centimetre, i.e., 104 volts, and e is the amount of charge on the ions, i.e., =r = 48*2 coulombs, since the solution contains per cubic centimetre 48'2 x 104 volt-coulombs per centimetre (Arrhenius, 1901, p. 6) = 48'2 x 1011 dynes. The osmotic force, on the other hand, which acts on the same Cl ions is given by the difference between the osmotic pressures of the normal solution at B and

23-9 x 106 dynes. The osmotic force is therefore 2 x 105 times less than the electrostatic force preventing diffusion ; in other words, the latter is 200,000 times as strong. We see then how an extraordinarily minute excess of Cl over Na ions would suffice to prevent any further diffusion. If one ion moves on, the opposite one must follow it at an infinitesimal distance. A more difficult question arises from considerations of energetics. We know that sodium and chlorine combine with the evolution of heat in considerable amount, so that, in order to separate them as ions when the compound is dissolved in water, a corresponding amount of energy must be supplied from some source. The fact that ions are hydrated seems to offer a possibility, if we regard the hydrates as chemical compounds, formed with evolution of heat.

Bousfield and Lowry (1907, p. 125) suggested that the affinity of the "ionic nucleus" for water is the main source of the energy required. Further evidence for this view is given by Bousfield (1912, p. 149). The argument may be put very briefly thus : Atoms, being composed of large numbers of more minute bodies or corpuscles, may be regarded as compressible. The heat of formation of a compound is found to be approximately equal to the sum of certain "calorific constants" of the components, together with 0'875 <5V, where 5V is the change of atomic volume which takes place. From this fact, the internal energy of an atom is to be regarded as the sum of the kinetic energy of the corpuscles, and of the potential energy due to their mutual attraction. The factor, 0'875 5V, therefore represents the change in internal energy of the atoms due to their change of volume on combination. How compression or contraction diminishes the internal energy of an atom by approximation of mutually attractive corpuscles may be found on p. 151 of the original paper. Applying these considerations to the estimation of the components of the heat of formation of solid, liquid, and ionic molecules, it is found that 5V is considerably greater in the ionic state than in that of solid or liquid ; thus, the value for KC1 in the ionic state is 42 '7, for the solid state, 32 '5.. That is, the contraction which takes place on combination in the ionic state is greater than that in the solid state, and may well be the source of the energy required for electrolytic dissociation.

Larmor (1908, p. 37) states the possibility that "internal potential e,nergy is released owing to the ions entering into relations of closer affinity with the solvent. There is, of course, no doubt as to the capacity of molecular forces to afford the energy required, hut the question still remains, what should cause them to give it up for the purpose of dissociating dissolved salts ? We may say that the affinity of an ion for water is greater than that which it has for an opposite ion, but is this any more than a re-statement of the problem in another form?

A further difficulty that has been put forward is this. Granting that, by some means or other, the ions have been separated, what is to prevent the opposite electrical charges from neutralising one another with production of the salt again ? We have seen that an analogous process does actually occur in the mutual precipitation of oppositely charged colloids. The answer is probably bound up with that to the previous question. The forces which caused the dissociation are presumably continually active in preventing recombination.