long as they are not brought together at the electrodes by the passage of an electric current.

§ 100. Faraday's Law.-According to the law discovered by Faraday, the passage of electricity from one electrode to the other, through the electrolytes, takes place in such a way that for a certain amount of electricity passing through the electrolyte a given fixed quantity of each 'ion' separates out at the electrodes; so that the ions are not only equivalent to one another, but also the amount of each liberated is proportional to the quantity of electricity passing through the system. From this we must conclude that every equivalent weight of the ions can be charged by a fixed and definite amount of electricity, which it carries through the electrolyte from one electrode to the other; just as a ship takes up a given load and carries it across the ocean. The anode charged with positive electricity gives up positive, the negatively charged cathode an equivalent quantity of negative electricity. The electrolyte takes up these charges, but in return discharges an amount of each ion equivalent to the electricity at each electrode, at the anode the electro-negative anion, e.g. chlorine, and at the cathode the electro-positive cation, e.g. sodium, is discharged.

The origin of the distinction of the ions as positive and negative is to be found in the observation mentioned in § 37, that different substances when brought in contact with one another become electrically excited, one becoming charged with positive, the other with negative electricity; and the greater the difference in the chemical characters of the substance, so much the stronger is the charge; and, further, those substances which by such contact become electro-negative in electrolysis appear asanions'; conversely, the electro-positive appear as 'cations.' The hypothesis has been advanced that ions united with one another in compounds are charged in like manner, and retain their charge even when dissociated. Such a supposition explains how it comes about that the positively charged anode should attract the negatively charged anion, and that the cation should be drawn to the cathode, the electrodes repelling the ions charged similarly to themselves; consequently one receives an impulse in one direction, the other in the opposite direction. When the attracted ion comes in contact with the

N

electrode the opposing electricities neutralise one another, and the ion remains in an unelectrified state. Now two ions, e.g. two chlorine atoms, which were previously charged with the same kind of electricity, and in consequence would repel one another, may combine to form a molecule of free chlorine, Cl2, and as such appear at the anode.

By this discharge of electricity at the electrodes the liquid. receives at these points an excess of the opposite electricity, that is, of the same kind as that with which the electrode is charged, and this moves with the ions through the electrolyte to the other electrode. For the transport of the electricity it is not necessary that the particles repelled by one electrode should reach the other. This movement takes place simultaneously throughout the whole of the electrolyte situated between the electrodes, the cations going always with the current, the anions against the stream; and this takes place in such a way that in every sectional area of the current there is as much electricity passing in a. given time as through any other similar section, namely, as much as each electrode gives off or takes up respectively.

§ 101. Relationship between Conductivity and Dissociation.— As the electricity is transferred by the ions, and can only pass. through the electrolyte by their aid, the undecomposed molecules taking no part in the transport, it follows that only substances. capable of dissociation can act as electrolytes; and, further, they must conduct the more readily the more advanced the dissociation. In fact, Arrhenius has shown by numerous examples that all electrolytes described in § 79, whose aqueous solutions give an abnormal depression of the freezing point, are therefore partially or entirely dissociated, and that their conductivity is proportional to the extent of the dissociation as measured by the reduction of the freezing point. Those bodies, such as the chlorides of the alkali-metals, which give a reduction almost twice as great as that produced by an equal number of molecules of non-dissociable substances, are almost completely decomposed in their dilute solutions, and therefore are good conductors of electricity. In more concentrated solutions the conductivity does not increase in proportion to the amount present, but more slowly, because in such cases the dissociation is not so great. If the share in the conduction of electricity taken by each molecule

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179

be calculated by dividing the conductivity, by the number of equivalent weights (expressed in grams) contained in the unit volume (1 litre), then we obtain a series of quotients which Kohlrausch has styled the specific molecular conductivity;1 and which increases with increased dilution, and therefore with increasing dissociation. The conclusions arrived at in § 79 find a most satisfactory confirmation in this behaviour of electrolytes.

The knowledge of the interdependence of dissociation and electrolytic conductivity enables one to explain the statement made by F. Kohlrausch that at the ordinary temperature only mixtures conduct electricity, the several constituents of which are, however, non-conductors. Thus, whilst a mixture of water and hydrochloric acid gas is a good conductor of electricity, because the hydrochloric acid gas is almost completely dissociated, still neither pure water nor liquefied hydrochloric acid gas is a conductor. At a red heat, when the tendency to decomposition is greater, many homogeneous substances are electrolytes.

§ 102. Migration of the Ions.-As the positive electricity is alone transported by the cations, and the negative by the anions, and as exactly equal amounts of each are simultaneously deposited at both electrodes, one might be inclined to think that what holds true for the different kinds of electricity will also apply to the ions, and that equal quantities of each ion must pass simultaneously through any section of the current. This is, as Hittorf has shown, not the case; nor is it necessary that it should be, for, as far as the transport of electricity is concerned, it is immaterial whether a number of positive ions move to one side or an equal number of negative ions pass to the other side. A deficiency of one kind may therefore be compensated by an excess of another. The transference of electricity, however, is proportional to the sum of the quantities of both the ions deposited; the electrolytic conductivity is also proportional to this amount, which consequently may be used as a measure of the conductivity.

The ratio of the velocities of the anions and cations may also be determined. It is only necessary, after the electrolysis has

Strictly speaking, the addition 'molecular' is not correct, as the specific conductivity is given in terms, not of molecular, but of equivalent weights.

gone on for a little time, to determine, by an analysis of those portions of the liquid surrounding the electrodes, what quantities of each ion have passed through the central and still unaltered portion of the liquid. Hittorf has made a large series of such determinations, and found that the migration of the ions, as he styles it, takes place with very unequal velocities. If the anion and cation were to move at equal rates, then for every single equivalent weight of each deposited at the electrodes one half of this amount of each must during this time pass through the intermediate layers of the electrolyte; for by the complete symmetry of the operation one half of the positive electricity released at the cathode is provided by the positive ions, coming from the side of the anode; the other half is thus free, so that the negative ions may pass from the cathodes towards the anode. This, according to Hittorf's investigations, happens in some cases, for example, in a moderately dilute solution of potassium chloride, in which for every equivalent of potassium, K=39-03, deposited at the cathode, and every equivalent of chlorine, Cl=35-37, deposited at the anode, and giving up their charge of electricity, the half of each of these quantities passes from one half of the solution to the other. If now we take the case in which, for instance, the cation of an electrolyte is entirely or almost completely immovable, electrolytic conduction and decomposition may still take place; in such a case, however, the transport of electricity is effected by the anion entirely, of which, therefore, an entire equivalent must pass from the side of the cathode to the anode, so that a loss of anion takes place in the portion of the liquid surrounding the cathode, and the loss in that portion surrounding the anode produced by the deposition of the anion is completely compensated for by this migration. Moreover, as one equivalent of the cation is deposited at the cathode, it is evident that the entire expenditure is borne by that portion of the electrolyte surrounding the cathode. At this point the liquid must become very much diluted, whilst in other parts the concentration will remain unaltered. Such an extreme case has certainly never been observed; but all those hitherto investigated lie between this and the first case considered.

The number expressing the fraction of an equivalent of an ion transferred from one electrode to the other in the time during

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181

which an equivalent of each is liberated at the electrodes Hittorf has styled the 'transport number, and represents it by 'n.' For example, from a solution of 1 part of crystallised copper sulphate, CuSO4+5H2O, whilst 0-2955 gram of copper is deposited on the cathode, 0·0843 gram only passes through the intermediate and unaltered layers of the liquid from the side of the anode to the cathode. In this instance, then, we have n for copper equal to 0.285.

0.0843
0.2955

= 0.285.

Instead of half an equivalent of the metal passing through the unaltered section of the current, little more than a quarter passes. This portion of the electrolyte does not contain the free ions but simply the neutral salt, proving that the ions exist in equivalent proportions; it therefore follows that the quantity of the anion passing against the current has proportionately increased-in fact, 0.715 equivalent of SO1, thus :—

1-n1-0.285 0.715 equivalent SO..

The sum of the transport numbers of the two ions is always equal to unity. They are not quite invariable, but vary somewhat with the concentration, and in some cases considerably.

For instance, in the case of potassium bromide, the 'transport number' for bromine changes. For a solution of 1 part of the salt in 2-36 parts of water it is 0.493, in 116.5 parts of water it is 0.546. The transport number of the potassium falls in a corresponding manner from 0.507 to 0.454. In the more dilute solutions the velocity of the bromine compared to that of the potassium is somewhat increased.

§ 103. Velocities of the Ions.-By the aid of these numbers and the determinations of the conductivity of solutions, F. Kohlrausch has calculated the velocities of the single ions. The electrical conductivity of a body depends not only on its material composition, but also on its dimensions and the temperature. According to Ohm's Law it is proportional to the sectional area, and inversely proportional to the length of the conductor; in electrolytic conduction it rises with increased temperature, but decreases with rise in temperature in case of metallic conduction. By maintaining the temperature and dimensions constant,