CHAPTER III

ELECTROLYTIC SOLUTIONS

Solutions which conduct Electricity.—The laws of solution which we have studied in the previous chapter apply only to those solutions, chiefly of organic origin, which do not conduct electricity. Solutions of electrolytes such as the ordinary salts, acids, and bases, which are ionized on solution, give values for the various constants of solution which do not accord with those required by theory. If, for instance, we take a gramme-molecule of an electrolyte such as chloride of sodium, and dissolve it in a litre of water, we find that the lowering of the freezing point is nearly double the theoretical value of 1.85°. The same holds good for the osmotic pressure, and for all the constants which are proportional to the molecular concentration of the solute. The solution behaves, in each case, as if it contained more than one gramme-molecule of sodium chloride per litre. It behaves, in fact, as if it contained i times the number of molecules of solute originally introduced into it. If n be the original number of molecules, then it will apparently contain n′ = in molecules. This law is universal for all electrolytic solutions; the theoretical value for their concentration, osmotic pressure, and all the proportional physical constants must be multiplied by this quantity, i = n′/n, which is the ratio of the apparent number of the molecules present to the number originally introduced.

A similar dissociation of the molecule is observed in the case of many gases. The vapour of chloride of ammonium, for instance, is decomposed by heat, and it may be shown experimentally that the increase of pressure on heating above

that which theory demands, is due to an increase in the number of the gaseous molecules present. Some of the vapour particles are dissociated into two or more fragments, each of which plays the part of a single molecule.

Arrhenius, in 1885, advanced the hypothesis that the apparent increase in the number of molecules of an electrolytic solution was also due to dissociation. This interpretation at once threw a flood of light on a number of phenomena hitherto obscure.

Coefficient of Dissociation.—We have seen that in order to obtain values which accord with experiment we have to multiply the number of gramme-molecules of the solute by the coefficient i, which is called the Coefficient of Dissociation.

This coefficient of dissociation, i, may be found by observing the lowering of the freezing point of a normal solution, and dividing it by 1.85. i = t/1.85.

The coefficient of dissociation varies with the degree of concentration of the solution, rising to a maximum when the solution is sufficiently diluted.

If we know i, the coefficient of dissociation for a given solute, contained in a solution of a definite concentration, we can find n′, the number of particles present in a solution containing n gramme-molecules of the solute per litre, since n′ = in. On the other hand, if from a consideration of its freezing point and other constants we find that an electrolytic solution appears to contain n′ gramme-molecules per litre, the real number of chemical gramme-molecules in one litre of the solution will be only n′ / i = n.

Very concentrated solutions do not conform to these laws. In this they resemble gases, which as they approach their point of condensation tend less and less to conform to the laws of gaseous pressure.

Electrolysis.—If we take a solution of an acid, a salt, or a base, and dip into it two metallic rods, one connected to the positive and the other to the negative pole of a battery, we

find that the metals or metallic radicals of the solution are liberated at the negative pole, while the acid radicals of the salts and acids and the hydroxyl of the bases are liberated at the positive pole. The liberated substances may either be discharged unchanged, or they may enter into new combinations, causing a series of secondary reactions.

Electrolytes.—Solutions which conduct electricity are called Electrolytes, and the conducting metallic rods dipping into the solution are the Electrodes. Faraday gave the names of Ions to the atoms or atom-groups liberated at either electrode. The ions liberated at the positive electrode are the Anions, and those at the negative electrode are the Cations. The only solutions which possess any notable degree of electrical conductivity are the aqueous solutions of the various salts, acids, and bases, and in these solutions only do we meet with those phenomena of dissociation which are evidenced by anomalies of osmotic pressure, freezing point and the like,—anomalies which show that the solution contains a greater number of molecules than that indicated by its molecular concentration. These anomalies are due to dissociation, the division of some of the molecules into fragments, each of which plays the part of a separate molecule, contributing its quota to the osmotic tension and vapour pressure of the solution, in fact to all the phenomena which are dependent on the degree of molecular concentration. The electrical conductivity of a solution is therefore proved to be dependent on its molecular dissociation.

Arrhenius' Theory of Electrolysis.—In 1885, Arrhenius brought forward his theory of the transport of electricity by an electrolyte. According to this hypothesis, the electric current is carried by the ions, the positive charges by the cations, and the negative charges by the anions. In virtue of the attraction between charges of different sign, and repulsion between charges of like sign, the cations are repelled by the positive charge on the anode, and attracted by the negative charge on the cathode. Similarly the anions are repelled by the cathode and attracted by the anode.

An electrolytic solution contains three varieties of particles, positive ions or cations, negative ions or anions, and undissociated neutral molecules. The molecular concentration of such a solution, with the corresponding constants, depends on the total number of these particles, i.e. the sum of the ions and the undissociated neutral molecules. We may indicate an ion by placing above it the sign of its electrical charge, one sign for each valency. Thus Na⁺ and Cl^- indicate the two ions of a salt solution; Cu⁺⁺ and SO₄^-- the two ions of a solution of sulphate of copper. A point is sometimes substituted for the + sign, and a comma for the - sign. Thus Na^. and Cl^,; Cu^.. and SO₄^,,.

My friend Dr. Lewis Jones has given a very vivid picture of the processes which go on in an electrolytic solution when an electric current is passing. He compares an electrolytic cell to a ballroom, in which are gyrating a number of dancing couples, representing the neutral molecules, and a number of isolated ladies and gentlemen representing the anions and cations respectively. If we suppose a mirror at one end of the ballroom and a buffet at the other, the ladies will gradually accumulate around the mirror, and the gentlemen around the buffet. Moreover, the dancing couples will gradually be dissociated in order to follow this movement.

Degree of Dissociation.—The degree of dissociation is the fraction of the molecules in the solution which have undergone dissociation. Let n be the total number of molecules of the solute, and n″ the number of dissociated molecules. Then n″ / n = a will represent the degree of dissociation. Let k be the number of ions into which each molecule is split. Then a = n″k / nk, i.e. the degree of dissociation is the ratio of the number of ions actually present in a solution to the number which would be present if all the molecules of the solute were dissociated.

Let n′ be the total number of particles present in a solution

containing n molecules, each of which is composed of k ions. Then if a is the degree of dissociation,

n′ = n - an + ank,

n′ = n[1 + a (k - 1)],

n′ / n = 1 + a (k - 1) = i.

We thus obtain i the coefficient of dissociation, in terms of the degree of dissociation a and the number of ions in each molecule k.

If there is no dissociation, i.e. if a = 0, then n′ = n, and i = 1. If all the molecules are dissociated, a = 1, and i = k.

Faraday's Law.—Faraday found that the quantity of electricity required to liberate one gramme-molecule of any radical is 96.537 coulombs for each valency of the radical.

Electrochemical Equivalent.—The electrochemical equivalent of a radical is the weight liberated by one coulomb of electricity. It is equal to the molecular weight of the ion, divided by 96.537 times its valency.

Electrolytic Conductivity.—The conductivity of an electrolyte is the inverse of its resistance. C = 1/R.

For a given difference of potential the conductivity of an electrolyte is proportional to the number of ions in unit volume, the electrical charge on each ion, and the velocity of the ions.

The specific conductivity Δ of an electrolyte is the conductivity of a cube of the solution, each face of which is one square centimetre in area. The molecular conductivity of an electrolyte is the conductivity of a solution containing one gramme-molecule of the substance placed between two parallel conducting plates, one centimetre apart. The molecular conductivity is independent of the volume occupied by the gramme-molecule of the solute, depending only on the degree of dissociation. The molecular conductivity U is equal to the product of V, the volume of the molecule, by Δ, its specific conductivity. U = VΔ. Whence Δ = U / V, i.e. the specific

conductivity equals the molecular conductivity divided by the volume.

The conductivity of an electrolyte is proportional to the number of ions in a volume of the solution containing one gramme-molecule. Let M_∞ be the conductivity for complete dissociation and M_v the molecular conductivity at the volume V. Then

M_v / M_∞ = n″k / nk = n″ / n = a,

the degree of dissociation. This is Ostwald's law, which says that the degree of dissociation is equal to the ratio of conductivity when the gramme-molecule occupies a volume V, to its conductivity when the solution is so dilute that dissociation is complete. Hence the degree of dissociation may also be determined by comparing the electrical conductivities of two solutions of different degrees of concentration.

Velocity of the Ions.—If the electrolytic cell is divided into two segments by means of a porous diaphragm, we shall find after a time an unequal distribution of the solute on the two sides. For instance, with a solution of sulphate of copper, after the current has passed for some time there will be a diminution of concentration in the liquid on both sides of the diaphragm, but the loss will be very unequally divided. Two-thirds of the loss of concentration will be on the side of the negative electrode and only one-third on the positive side. In 1853, Hittorf gave the following ingenious explanation of this phenomenon:—

Fig. 1 represents an electrolytic vessel containing a solution of sulphate of copper, the vertical line indicating a porous partition separating the vessel into two parts. Fig. 2 shows the same vessel after the passage of the current. The acid radical has travelled twice as fast as the metal. For each copper ion which has passed through the porous plate towards the cathode two acid radicals have passed through it towards the anode. Three ions have been liberated at either electrode, but in consequence of the difference of velocity with which the positive and the negative ions have travelled, the negative side of the vessel contains only one molecule of copper sulphate and has lost two-thirds of its molecular concentration, while the positive side contains two molecules of copper sulphate and has only lost one-third of its concentration. This proves clearly that the ions move in different directions with different velocities. Let u be the velocity of the anions, and v the velocity of the cations. Let n be the loss of concentration at the cathode, and 1 - n the loss of concentration at the anode. Then

u / v = n / (1 - n),

i.e. the loss of concentration at the cathode is to the loss of concentration at the anode as the velocity of the anions is to that of the cations. Hence by measuring the loss of concentration at the two electrodes, we have an easy means of determining the comparative velocity of different ions.

In 1876, Kohlrausch compared the conductivity of the chlorides, bromides, and iodides of potassium, sodium, and ammonium respectively. He found that altering the cation did not affect the differences of conductivity between the three salts, thus showing that these differences of conductivity were dependent on the nature of the anion only, and not on the particular base with which it was combined. The difference of conductivity between an iodide and a bromide, for example, is the same whether potassium, sodium, or ammonium salts are compared. A similar experiment has been made with a series of cations combined with various anions. The difference of conductivity of the salts in the series is the same whichever anion is used, i.e. the difference of conductivity between potassium chloride and sodium chloride is the same as that between

potassium bromide and sodium bromide. Hence we may conclude that the conductivity of any salt is an ionic property.

Kohlrausch's law may be expressed by the formula c = d(u + v), where c is the conductivity of the salt, d the degree of dissociation, i.e. the fraction of the electrolyte broken up into ions, and u and v the velocity of the anions and cations respectively. When all the molecules of the electrolyte are dissociated, d = 1, and the formula becomes c_∞ = u + v.

As we have already seen, a salt is formed by the union of a metal M with an acid radical R. Potassium sulphate, K₂SO₄, consists of the metal K₂ and the acid radical SO₄. Ammonium chloride, NH₄Cl, consists of the basic radical NH₄ and the acid radical Cl. The various acids may be considered as salts of the metal hydrogen. Thus sulphuric acid, H₂SO₄, is the sulphate of hydrogen. Bases may be considered as salts with the hydroxyl group, OH, replacing the acid radical. Thus potash, KOH, is the hydroxyl of potassium. The various electrolytic combinations may be represented by the following symbols:—

Salts = MR.

Acids = HR.

Bases = MOH.

The various chemical reactions of an electrolyte are all ionic reactions, the chemical activity of an electrolytic solution being proportional to its electric conductivity, i.e. the degree of dissociation of its ions. The acidity of an electrolytic solution is due to the presence of the dissociated ion H⁺, and its strength is determined by the concentration of these free hydrogen ions. Hence the greater the degree of dissociation the stronger the acid.

The basic character of a solution is determined by the presence of the hydroxyl radical OH^-. The greater the concentration of the hydroxyl ions, i.e. the greater the dissociation, the stronger is the base.

The ions H⁺ and OH^- are of special importance, since they are the ions of water, H₂O = H⁺ + OH^-. The degree of

dissociation of pure water is but small. Water is, however, the most important of all the various agents in the chemical reactions of life, since a large number of organic substances are decomposed by water by a process of hydrolysis, and a vast number of organic substances are but combinations of carbon with the ions H⁺ and OH^-, their diversity being due to variations in the relative proportions and grouping.

The Chemical, Therapeutic, and Toxic Actions of Ions.—The chemical, therapeutic, antiseptic, and toxic actions of electrolytic solutions are almost exclusively due to ionization. Take, for instance, a solution of nitrate of silver in which the addition of chlorine produces a white precipitate of chloride of silver. This precipitate occurs only when the solution added is one such as NaCl, where the chlorine is present as the free ion Cl^-. No such precipitate is produced in a solution of chlorate of potassium or chloracetic acid, where the chlorine is entangled in the complex ion ClO₃ or C₂H₃ClO₂.

Since, then, the toxic and pharmacological properties of an electrolyte depend entirely on the ionic grouping, it behoves the physician and the biologist to study the structure and grouping of the ions in a molecule, rather than that of the atoms. Consider for a moment the totally different properties of the phosphides and the phosphates. The former are extremely toxic, while the latter are perfectly harmless. There is not the slightest analogy between their actions on the living organism. On the other hand, all the phosphides produce the same toxic and therapeutic effects, whatever the cation with which they are united. Their toxic properties are derived from the presence of the free phosphorus ion P^---. The phosphates contain phosphorus in the same proportion as the phosphides, but this phosphorus is harmlessly entangled in the complex ion PO₄^---, whose properties are absolutely different from those of the ion P^---.

The above considerations apply equally to the chlorides and chlorates, the iodides and iodates, the sulphides and sulphates, and in general to all chemical salts.

The question has an intimate bearing on practical pharmacology. When we prescribe a cacodylate or an amylarsinate, we are not prescribing an arsenical treatment whose effects can be compared with those of an arsenide, an arsenite, or an arsenate. This fact is sufficiently indicated by the difference in the toxic doses of the different salts. Each variety of arsenical ion has its own special physiological and therapeutic properties. We do not expect to obtain the results of a ferruginous treatment from the administration of a ferrocyanide or a ferricyanide. Both contain iron, it is true, but neither possess the properties of the cation Fe⁺⁺⁺, but rather those of the complex anion of which they form a part.

We have already said that most of the therapeutic, toxic, and caustic actions of an electrolyte are due to ionic action, and the substances can therefore have no toxic action unless they are dissociated. Many of the solvents employed in medicine, such as alcohol, glycerine, vaseline, and chloroform dissolve the electrolytes but do not dissociate them into ions, and these solutions therefore do not conduct electricity. Such solutions have no therapeutic action. With the absence of dissociation all the ionic toxic and caustic effects also disappear entirely, and only re-appear as the water of the tissue is able slowly to effect the necessary dissociation.

Carbolic acid dissolved in glycerine is hardly caustic and but very slightly toxic. We have met with several instances in which a tablespoonful of carbolized glycerine, in equal parts, has been swallowed without any ill effect, either caustic or toxic, whereas the same dose dissolved in water would have been fatal. This absence of dissociation has enabled the surgeon Mencière to inject carbolic and glycerine in equal proportions into the larger joints, the part being subsequently washed out with pure alcohol. Thus by employing vaseline, oil, or glycerine as a solvent, and avoiding the access of water, we are able to use electrolytic antiseptics in very concentrated form. Their action is brought out very slowly, as the water of the organism effects the necessary dissociation of the electrolyte.

Since all chemical, toxic, and therapeutic actions are ionic, they are proportional to the degree of ionic concentration, i.e. to the number of ions in a given volume. The only point of importance, that which determines their activity, whether chemical or therapeutic, is the degree of ionization or dissociation. For example, all acids have the same cation H⁺. They have all identical properties, but they differ widely in the intensity of their action. There are weak acids such as acetic acid, and strong acids like sulphuric acid. The stronger acids are those which are more thoroughly dissociated, and in which the ion H⁺ is very concentrated; whereas the feeble acids are but slightly dissociated, so that the ion H⁺ is less concentrated.

Paul and Krönig have shown that the bactericidal action of different salts also varies with their degree of dissociation, i.e. with the concentration of the active ions. They made a series of observations on the bactericidal action of various salts of mercury, the bichloride, the bibromide, and the bicyanide, on the spores of Bacillus anthracis. The following results were obtained from a comparison of solutions containing 1 gramme-molecule of the salt in 64 litres of water. With the bichloride solution, after exposure to the solution for twenty minutes, only 7 colonies of the bacillus were developed. After exposure to a similar solution of the bibromide the number of colonies was 34. The antiseptic action of the bichloride was therefore five times as great as that of the bibromide. The bicyanide of mercury, however, even when four times as concentrated, permitted the growth of an enormous number of colonies, showing that it had no appreciable antiseptic action whatever. Nevertheless, the proportion of Hg is the same in all the solutions, and if there were any difference one would naturally expect that the ion Cy^- would be more toxic than Cl^- or Br^-. The real condition which varies in these solutions and determines their activity is the degree of dissociation. The whole of the antiseptic property resides in the ion Hg⁺⁺. This ion is very

concentrated in the highly dissociated solution HgCl₂, less concentrated in the less ionized solution HgBr₂, and exceedingly dilute in the HgCy₂, which is hardly ionized at all.

What is true of the bactericidal action of the salts of mercury is equally true of their therapeutic effect. It is a great mistake to estimate the medicinal activity of a solution of a salt of mercury, or indeed of any electrolytic solution, simply by its degree of molecular concentration. The important point is the degree of dissociation, which is the only true measure of its activity. In the intramuscular injection of mercury salts it is by no means a matter of indifference what salt we employ. A salt should be used such as the bichloride or the biniodide, which is easily dissociated. Other salts are often employed because they occasion less pain at the site of injection; but the pain is a sign of the degree of activity of the preparation. The pain, it is true, may be avoided by using a salt which is less easily dissociated, or in which the mercury is bound up in a complex ion, but by so doing we diminish the efficacy of the remedy. It is moreover quite easy to diminish, or even entirely to suppress, the pain, by using a very dilute solution of an active ionized salt. A one-half per cent. or even one-quarter per cent. solution of the bichloride or biniodide of mercury may be injected very slowly in sufficient quantity without producing the slightest discomfort. Local action depends entirely on ionic concentration. One drop of pure sulphuric acid will destroy the skin, whereas the same amount if diluted in a tumblerful of water will furnish a refreshing drink.