Exp. The migration of the ions throughout the whole solution may be demonstrated by the passage of a current through a large U-tube containing a mixture of a cupric salt and a permanganate,74 placed under some dilute sulphuric acid. The cupric-ion is blue, all ionized solutions of cupric salts, with a colorless negative ion, being blue, while the permanganate-ion is of an intense purple color. In the limb of the U-tube, in which the cathode is placed, a blue zone, containing cupric ions, is soon seen emerging from the purple liquid and rising toward the cathode (see Fig. 8). It will take some time for any cupric ions actually to reach the electrode and be deposited as metallic copper. On the anode side, purple permanganate ions are seen rising toward the positive electrode.

Exp.78 An electrolytic cell, having the shape of a parallelopipedon and a capacity of about one liter, is fitted with electrodes of copper, which reach from the bottom to the top of the cell and are connected with a storage cell and an ammeter. The cell is first filled with distilled water: no perceptible current passes through the water and the latter is therefore practically a nonconductor. The cell is then emptied by means of a siphon and 20 c.c. of 4-molar hydrochloric acid is brought into it. The ammeter shows that a definite current passes through the solution (0.17 ampere in an experiment79 with a cell 4.6 cm. wide and 11.5 cm. long, with copper electrodes 4.6 cm. broad and 21 cm. high). (See Fig. 9, p. 48.) [p048]

Exp. 20 c.c. of water is added to the 20 c.c. of 4-molar acid in the cell, and the mixture is stirred. The current is decidedly increased (from 0.17 to 0.22 ampere in the experiment under discussion). If 40, 80, 160 and 320 c.c. of water are added in succession to the contents of the cell, the conductivity is increased by every addition of water. But, while each addition dilutes the acid to one-half the previous concentration, the increase grows proportionally smaller and smaller with increasing dilution. In the following table, "Ratios I" are the ratios of the observed conductivities to the original conductivity, "Ratios II" the ratio of each observed conductivity to the preceding one.

The method of calculation of α in a specific case may be illustrated as follows: the resistance of a cube of 1 cm. edge of a solution of hydrochloric acid, which contains 1.825 grams hydrogen chloride in a liter, is found to be 55.55 ohms at 18°. Its conductivity then is 1 / 55.55 reciprocal ohms. Now, 1.825 grams of hydrogen chloride is 1.825 / 36.5 or 1 / 20 gram-equivalent of the acid; a whole gram-equivalent of the acid would be contained in 20 liters or 20,000 c.c. Then Λ_v = (1 / 55.55) × 20,000, or 360 reciprocal ohms. If we use the value at infinite dilution given above, α = 360 / 384, or 93.75%. That is, 93.75% of the hydrochloric acid is present in the ionized condition in such a solution, and 6.25% is not ionized.

Clausius84 also assumed dissociated molecules or ions to be the real carriers of electricity in the passage of a current through the solution of an electrolyte, but he assumed only a minute quantity of these molecular fragments or ions to be free at any moment, their existence being supposed to be transitory and dependent in particular on exchanges of atoms between molecules. As a result of the oscillations of the atoms composing a molecule, oscillations comparable with the motions of molecules assumed in the kinetic theory of gases, molecules were considered by Clausius occasionally to reach such a condition of instability, that they dissociated into smaller particles; since the atoms were supposed to be held in a molecule by attractions of electrical charges on the atoms (theory of Berzelius), the fragments of the molecule would carry the charges, positive and negative respectively, which they possessed in the molecule. Such a breaking up or dissociation of molecules was, further, supposed to occur with particular ease during the collisions of molecules, the electrical attractions and repulsions of the charged atoms favoring, at such moments, an exchange of atoms. During the exchange, the atoms were considered to be free molecules, charged with electricity—essentially ions,—capable of moving under the influence of electrical forces and of thus carrying a current. Finally, such ions were supposed, in part, to escape recombination, and to remain free, until each ion either collided and combined with an ion of opposite charge, or collided with a molecule and displaced an atom of the same charge from that molecule, a new ion being thus liberated. The theory, as usually interpreted, assumed the existence of only a very small quantity of such free ions, that being all that was supposed to be required to explain the facts known at the time it was advanced.

In what follows, we shall confine the discussion strictly to such contrasts between the two theories as grow out of a consideration of the phenomena of conductivity, and particularly consider some evidence which is directly concerned with the conductivity of solutions.

In the first place, if the formation of ions occurs primarily during the exchange of atoms in collisions of molecules, then, as Whetham85 has shown, the specific conductivity (of 1 cm.³) of an electrolyte, like hydrochloric acid, must increase with the concentration and must increase, approximately, as a function of the third power of the concentration. The more concentrated the solution, the more frequent the collisions between the dissolved molecules must be. As a matter of fact, as shown in the following table, the conductivity [p053] increases a little less than proportionally to the first power of the concentration—which is in conflict with the assumption made in the hypothesis of Clausius, but in perfect agreement with the hypothesis of Arrhenius. The small decrease with increasing concentration, in the simple ratio between conductivity and concentration, is due to the decreasing degree of ionization in the more concentrated solutions, as demanded by the hypothesis of Arrhenius.

The table gives, in the first column, the specific conductivities of hydrochloric acid at 18°, and, in the second column, the concentrations; these concentrations are expressed in moles or gram-equivalents per cubic centimeter; the last column gives the ratio of conductivity to concentration.

Furthermore, facts admitted by Clausius to be inexplicable by his own assumptions receive, in the theory of Arrhenius, at least a quantitative formulation borne out by a mass of corroborative evidence. The difference in conductivity between pure water and sulphuric acid is such a fact, mentioned by Clausius. Determinations of the ionization of sulphuric acid and of water, by the conductivity methods which are based on the theory of Arrhenius, show that, while sulphuric acid is very considerably ionized (see p. 104), water is scarcely ionized at all. The ionization of water (see p. 104) has been determined quantitatively by at least four independent methods of examination,86 and, minimal as the ionization is, the results agree so well with each other that van 't Hoff87 was led to write: "If one is not previously convinced of the correctness of the theory of electrolytic dissociation, hardly any result won by means of it is so convincing, as the agreement between the conclusions reached in completely different ways as to the degree of dissociation of water itself. After such an agreement, it is hardly conceivable that the basis on which all these results rest should further be altered."

Such relative speeds of ions may be demonstrated by means of an experiment: the motion of the hydrogen ions, formed by the ionization of hydrochloric and other acids, may be observed by their action on a reddened (alkaline) solution of phenolphthaleïn, which is decolorized by them; and the motion of the hydroxide ions, formed by the ionization of sodium hydroxide and other bases, may be followed by their action on colorless phenolphthaleïn, which turns red in their presence. The hydrogen and the hydroxide ions are the fastest, in aqueous solutions, and their speeds are compared in the next experiment with that of blue cupric ions, which have a speed roughly the same as that of many common ions. In this experiment the hydrogen ions are readily seen to move about twice as fast as the hydroxide ions and five to six times as fast as the cupric ions.

Exp.88 Five grams of agar-agar are dissolved in 250 c.c. of boiling water. To 100 c.c. of the hot solution, 32 c.c. of a saturated solution of potassium chloride and about 1 c.c. of phenolphthaleïn solution are added, together with enough of a solution of potassium hydroxide, added drop by drop, to produce a deep red tint in the phenolphthaleïn. Of this mixture 50 c.c. is treated with dilute hydrochloric acid, added drop by drop, until the red color is just discharged, and then an excess of acid, equal in amount to the quantity used to neutralize the 50 c.c., is added to the mixture. This colorless solution and 50 c.c. of the red solution are poured, while still warm, into the two parts of a wide U-tube, slowly and at equal rates, so that the level on the two sides remains the same. In this way it is possible without difficulty to have the solution on one side red (alkaline) and on the other side colorless (acid). The agar-agar is allowed to congeal, and then a mixture of 0.5 c.c. of hydrochloric acid, (sp. g. 1.12), 6 c.c. of saturated cupric chloride solution and 20 c.c. of water is poured over the red half, and a mixture of 20 c.c. of saturated [p055] potassium chloride solution and 2 c.c. of 10% potassium hydroxide solution is poured over the colorless half. The U-tube is surrounded by ice water during the passage of the current, and the cathode is placed in the solution on the colorless side. In Fig. 10 the ∪-tube is shown when first charged (on the left), and after the current has been running for a short time (on the right).

The conductivity of a solution must be made up, therefore, of the sum of the shares which the positive ions and the negative ions, respectively, take in carrying the current. This principle was first advanced by Kohlrausch. The share of each kind of ion in conducting a current may be determined, for hydrochloric acid for instance, in the following way: A porous diaphragm may be used to divide the solution in an electrolytic cell into two halves, the concentration of the acid being the same in both halves (represented, as indicated in Fig. 11, by 15 molecules89 of ionized acid in each half). A measured current is passed through the solution, say, sufficient to liberate 3 molecules of hydrogen H₂, and 3 of chlorine Cl₂, corresponding to 6 ions of each, and the concentration of the acid in each half is then again determined by analysis. Say it is found to correspond to 14 molecules of hydrochloric acid in the half of the solution on the side of the cathode and 10 molecules in the half on the side of the anode (see Fig. 12). Then the anode half has lost 5 ions of hydrogen, which must have passed through the diaphragm toward the cathode and taken the place of five of the six hydrogen ions discharged at the cathode. Similarly, the solution around the cathode has lost one chloride ion, which must have passed through the diaphragm toward the anode, and the hydrogen-ion corresponding to it, remaining on the right side without a compensating negative ion, must be the sixth hydrogen-ion discharged at the cathode. In other words, five hydrogen ions passed to the right, while one chloride ion passed to the left. The hydrogen ions then carried five-sixths of the current through the diaphragm, and consequently through the solution, and the chloride ions only one-sixth of the current. Since the solutions were of equal concentration to start with, the hydrogen ions have moved five times as fast toward the cathode as the chloride ions have moved toward the anode.

The equivalent conductivity of 0.1-molar hydrochloric acid is 351 at 18°, and experiment shows that the hydrogen-ion carries 84% of the current, the chloride-ion only 16%. The conductivity may then be considered to be the [p056] sum of the share the hydrogen-ion has in carrying the current, i.e. 0.84 × 351, or 295, and of the share of the chloride-ion, 0.16 × 352.5, or 56. These values may be called the equivalent partial conductivities or mobilities of the ions in this solution.

In a similar way, the conductivity of every solution of an electrolyte may be shown to represent the sum of the mobilities of the ions carrying the current (principle of Kohlrausch). The limit of the conductivity of one equivalent of an electrolyte is the sum of the mobilities of the ions composing the electrolyte. The frictional forces being constant for infinitely dilute solutions, at a given temperature, an ion will always show the same mobility, irrespective of the nature of the ion of opposite charge, with which it forms the electrolyte. We may then put Λ_∞ = (l⁺_∞ + l⁻_∞), if l⁺_∞ and l⁻_∞ are used to designate the limits of the mobilities of gram-equivalents of the positive and negative ions forming the electrolyte. The following table90 gives the limits of the mobilities for gram equivalents of some of the most important ions at 18°.

For quite dilute solutions, in which the friction may be assumed to be approximately constant, the conductivity will depend, not only on the mobilities of the ions, which may be taken to be the same as for solutions of extreme dilution, but also on the proportion of electrolyte that is ionized, i.e. on the degree of ionization, α. Then Λ_v = α (l⁺_∞ + l⁻_∞), which is an elaboration of the original equation given on page 50.

Now, Kohlrausch discovered the principle of the summation of the mobilities of ions a number of years before the theory of Arrhenius was advanced, and the proportion in which the ion is present in a given solution being unknown, the effect of what is here known as the degree of ionization was included empirically in the value of the mobility. It is not surprising, then, that an ion was found to have approximately the same mobility only in solutions of the same concentration of strictly analogous and closely related salts, which, according to present methods of investigation, are now found to have approximately the same degree of ionization. For instance, the mobility of the gram-equivalent of the chloride-ion was found to be approximately the same, 47.3 and 50.5 respectively, in molar solutions of sodium and potassium chloride at 18°, no account being taken of the degrees of ionization. However, the degrees of ionization of the two salts are approximately the same, 66.9% and 74.9% respectively, and might be ignored in a comparison of the conductivities, without affecting the result of the comparison in any marked way. [p057]

When the conductivities of unlike electrolytes are compared, the introduction of the conception of the degree of ionization (by Arrhenius,) into Kohlrausch's principle of the independent conductivities of specific ions, shows most striking results and demonstrates the value of the new conception. For instance, the equivalent conductivity of potassium chloride at 18° in 0.075 molar solution is 113.8 reciprocal ohms and the partial conductivity of the chloride-ion in the solution is 57.4. But the conductivity of an equivalent solution of mercuric chloride at 18° is only 1.51, which is very much less than the conductivity of the chloride-ion alone in the potassium chloride solution. Now, mercuric chloride, according to investigations of its conductivities and of its effect in depressing the freezing-point of water,91 is one of a very few salts that are difficultly ionizable (p. 107); according to the data mentioned, it is ionized, at most, to the extent of 2.5 per cent in the solution in question, whereas 87.5 per cent of the potassium chloride is ionized in such a solution. When the difference in the degree of ionization is taken into account, the conductivity which mercuric chloride should show may be calculated, on the assumption that the chloride-ion has the same mobility in the two solutions, but that there is less of it in the mercuric solutions. We put Λ_HgCl2 = α (l_Hg + l_Cl) = 0.025 (48 + 65.9) = 2.8. We thus find that the conductivity of the mercuric chloride should be, approximately, only 2.8 reciprocal ohms, which is of the same order as that found (1.51).92

In the same way, when we compare the conductivity of a strong acid, like hydrochloric acid, with that of a weak acid, like acetic acid—the conductivity of 0.1 molar hydrochloric acid is 351, of 0.1 molar acetic acid only 4.6—the principle of the specific, characteristic mobility of the hydrogen-ion, which is present in both solutions, has significance only if we take into account the very different concentrations of the hydrogen-ion in the two solutions, resulting from the different degrees of ionization of the two acids—91% for the hydrochloric and only 1.7% for the acetic acid. The same relations hold in the comparison of the conductivity of a solution of a strong base like sodium hydroxide with that of an equivalent solution of a weak, i.e. much less ionized base like ammonium hydroxide, or in comparing the conductivity of a weak acid or a weak base with the conductivities of their much more highly ionized salts.

In all these cases the use of the conception of the degree of ionization of the electrolytes makes possible a much broader and more general application of the principle of the independent migration or mobility of the ions than was possible before the theory of Arrhenius was proposed, and marks a distinct advance in the theory of conductivity, over what was possible on the basis of the theory of Clausius. [p058]

Exp. The lower plate in an Arrhenius cell is covered with concentrated hydrochloric acid. Very dilute acid is allowed to flow slowly on to the surface of the concentrated acid, from a pipette with a curved, narrow point, until the upper plate is submerged. The two plates are connected with a sensitive galvanometer. The current flows in the direction demanded by the observed mobilities of the ions, the positive current entering the galvanometer from the plate covered by the dilute solution, which is charged positively by the faster moving hydrogen ions coming from the concentrated solution. If the cell is [p061] connected with the electrodes of a very small cell containing copper sulphate, in the course of twenty-four hours quite a deposit of metallic copper is formed on the electrode connected with the concentrated solution of hydrochloric acid.