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Again, the ion of chloric acid CIO: combines with another hydroxyl to form perchloric acid.

CIO; + OH' = HCIO, + 20 As this reaction depends on the previous formation of chloric acid, it occurs mainly when the electrolysis has been proceeding some time.

(F) Electrolysis of Potassium Chloride betwnno D . Electrodes.—The process at the anode in ' n preceding case. There are two catio that at the cathode discharge m these. Hydrogen is the more r

anlal O., anu potassions are discharged, the mo w ed will react with water, generating hydrogen : hence, regards the substance liberated from the electrode, it is immaterial which ion actually carries the current. The secondary reaction of the potassium on the water, however, produces hydroxyl ions

K + H,0 = K + OH' + H and the liquid round the cathode therefore turns alkaline. Further details will be considered later in dealing with the practical application of electrolysis for manufacture of caustic potash.

$ 4. MIGRATION OF IONS. In the interior of an electrolyte anions and cations are always present in equal measures; they therefore both participate in carrying the current, in the way described in § 2. According to the formula there given the cationic current density is 96600 ynuk, the anionic 96600 yqua; n, the concentration, refers to the dissolved salt as a whole, and y, the degree of dissociation, is, of course, the same for both components of the dissociating substance, so the two parts of the current are in proportion to the velocities of the cations and anions respectively.

With regard to the velocity of an ion, however, some preliminary remarks are necessary. If a charged particle be placed in an electric field, there is a definite force on it, just as


not when a heavy body is placed near the earth there is a force (of

gravity) on it tending to make it move vertically downwards. If the field is uniform, the force is (like gravity) constant. Such

a force will not cause the particle to move with uniform speed, hik but, like a falling body, with uniformly accelerated speed. But Met an ion moving in an electrolyte is not so much to be compared

with a heavy mass falling freely, as with a raindrop falling a hrough the air and suffering considerable resistance on that in lccount. A raindrop does not increase constantly in speed in its fall from the clouds, but, on account of air-friction soon reaches a limiting velocity with which it will continue to move

however far it falls. ", an ion moving through a liquid ut experiences a very lattesistance, and cannot travel any De appreciable distance wit. constant acceleration; rather, owing i to repeated collisions with molecules of solvent, its average

speed is brought down to a fixed, and—as experiment shows, very moderate amount.

The limiting velocity that a raindrop reaches will depend on the intensity of the force of gravity that draws it down ; and in the same way the velocity of an ion depends on the intensity of the electric field (known also as the potential gradient) driving it. We shall adopt the practical unit, the volt, as measure of the difference of potential between two points, and therefore express the gradient of potential in volts per centimetre length.

The precise way in which the velocity of ions depends on potential gradient is shown by the experimental result known as Ohm's law, which is that in any given conductor the electric current is proportional to the difference of potential driving it. This, of course, does not mean that other circumstances-temperature, concentration, etc.—may not affect the current, but merely that under similar conditions the potential difference affects it in the manner stated.

Ohm's law may, of course, be stated in the form that the current density is proportional to the potential gradient (this is equivalent to considering its application to a conductor i cm. long and of 1 sq. cm, cross-section).

Now, as the number of ions in a solution and the charges
T. P. C.

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on them do not depend on the application of a potential gradient, it follows that the only way in which the current density can be affected by varying gradients is in the velocity acquired by the ions. It is concluded, therefore, that the ionic velocities are proportional to the potential gradients producing them, and this may be taken as the true physical meaning of Ohm's law.

This conclusion has been verified by direct measurement of ionic velocities by the methods described below.

In accordance with Ohm's law we may express the actual velocity u of any ion as the product of two factors, the actual potential gradient, and the velocity under a gradient of one volt per centimetre; for the latter we shall use the symbol U, and refer to UA and Ug as the mobility of the anion or cation.

The mobilities of various ions are different, according to their specific character, and methods have been worked out for measuring them. We shall begin with a method, invented by Hittorf, for comparing the mobility of an anion and a cation. The method may be explained by the aid of an experiment, as follows :

Take a rectangular glass jar (Fig. 9): fix in it (by means of paraffin wax) two porous plates, in such a way as to divide it into

three chambers. Put copper plates, for electrodes, into the two end compartments, fill up the whole with copper sulphate solution, and pass a current (of several amperes) through it for a few minutes. If specimens of the liquid be taken out and analysed it will be found

that the solution in the middle chamber 1 )

is unaltered in strength, but that the

cathode liquid is weaker, the anode Fig. 9.

stronger than before. Qualitatively the change in colour of the electrolyte will be sufficient to show this.

In order to account for these changes of concentration, let us make a list of the actions occurring in the three chambers. We will assume that x is the fraction of the whole current conveyed by the anion, so that 1- x is conveyed by

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the cation. Hence, when one faraday of electricity is passed through the liquid, requiring on the whole one gram-equivalent of ions to convey it, there migrate across any section in the interior of the liquid, 1 - x equivalents of cations in the direction of the current, and x equivalents of anions in the opposite direction. x is called the migration ratio, or Hittorf's number (for the anion). Its relation to the mobilities of the ions is easily found, for we have seen that the currents produced by movement of the cation and anion are proportional to their mobilities. Hence

Cationic current _ Uc _ I – X

Anionic current UA X The actions in the three chambers during the passage of one faraday are then

Anode Chamber. Middle Chamber. ; Cathode Chamber. Formation of i equiv. Import of 1 - x equiv. Discharge of i equiv.

Cu“ from anode. ' Cu“ from anode Cu" on cathode. Export of 1 – x equiv. chamber.

Import of 1 -- x equiv. Cu" to middle cham- | Export of 1 – x equiv. Cu" from middle ber.

Cu“ to cathode chamber. Import of x equiv. ' chamber.

Export of x equiv. 50" from middle Export of x equiv. SO," to middle chamchamber.

SO," to anode ber.

chamber. Net result:

Import of x equiv. Net result :Gain of x equiv. Cu" | SO," from cathode Loss of x equiv. Cu " and SO,", i.e. x equiv. chamber.

and SO.",i.e. x equiv. CuSO,

Cuso, | No change. In the experiment, if correctly carried out, there ought to be no change in the middle chamber, while of the others, the anode chamber should gain just as much salt as the cathode loses. If, e.g., o‘2 faraday be used (conveniently measured by a copper voltameter put in series with the migration cell) and it be found that the change in each chamber is o'124 equivalents, it follows that

x = 124 = 0.62

02 Again, suppose in the tripartite cell, the electrodes of platinum, the electrolyte dilute sulphuric acid ; the action in anode

Net result :

and cathode chambers is as follows (the middle chamber is always unchanged) :Anode Chamber.

Cathode Chamber. Discharge of i equiv. SO,", which Discharge of i equiv. H:.

reacts with water, forming i equiv. Import of 1 - * equiv. H: from gaseous oxygen + i equiv. H', middle chamber. and reforming the SO,"

Export of x equiv. SO," to middle [SO, + H2O = 2H: +'so," +01

chamber. Export of 1 – x equiv. H. to middle

chamber. Import of x equiv. SO," from middle

chamber. Net result:Gain of x equiv. H. and the same of Loss of x equiv. H. and the same SO,", i.e. of x equiv. H SO, of SO,", i.e. of x equiv. H,80,.

In this case, too, the anode solution increases in strength at the expense of the cathode ; the change is easily followed by titration. It is found that about 0:19 equivalents of acid migrate for each faraday, so that x = 0'19.

On comparing the results of such experiments with the changes occurring at the electrodes, we find that quite different conditions regulate the flow of current in the two cases, although the total current must be the same at each part of the circuit. At the electrodes when there are several available ions, the current will be conveyed by that whose formation or discharge is the least difficult, i.e. involves the least expenditure of energy. The whole current may be, and often is, conveyed by a single kind of ion, so that it may be exclusively anionic or exclusively cationic. In the interior of the solution, on the other hand, all the ions present necessarily share in the current, and the share that each takes is determined merely by the amount of it present and by its specific mobility. This is true, not merely in considering the relation of anion to cation, but also with regard to the shares taken by the various ions of the same sign, if more than one be present; for the expressions of p. 21 still hold, however many ions may exist in the solution. Thus, in the case of copper sulphate, besides Cu" there is H: in the liquid, although in very small proportion; hence a small part of the cationic current is carried by the hydrogen ions, and similarly a small part of the anionic by hydroxyl ions.

In passing from an electrode to the interior, then, each

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