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and oxygen. The latter would be partly formed from water by the action of chlorine, i.e. —

Cl2 + H,0 = 2 Cľ + 2H + 0 and hydrogen ions would thus appear in the liquid, and would at once begin to migrate towards the cathode. At the cathode the discharge of sodions generates gaseous hydrogen, and leaves hydroxyl ions in solution, which migrate towards the anode ; in other words, the liquid turns acid at the anode and alkaline at the cathode. Now, hydrogen is the fastest of all ions, and hydroxyl the next; so that, if the process be allowed to take place as described above, it will not be possible to follow the movements of the original ions, on account of the migration of these new ions.

The more serious difficulty—that of the hydrogen-may be avoided by a device invented by Hittorf. Instead of platinum, he used cadmium for anode. The cadmium being an easily oxidisable metal, of course dissolves, so that there is no discharge of anions, and no gas formed-a preliminary advantage. The Cd" ions formed migrate, it is true, towards the cathode, but

+ NaOH as they have only about one-tenth of the mobility of hydrogen ions, this Cd is of no consequence. Indeed, as they are amongst the slowest, they remain constantly ele Na Cl + NaOH behind the ions of so-

Fig. 11. dium (or other metal studied), and cause no mixing of the different layers of liquid. The action may then be represented by Fig. II. This shows

a bent tube, originally filled with NaCl solution ; a cadmium anode Cd; and platinum cathode Pt. All the Na has migrated away from the anode, leaving a layer of CdCl, solution, and as the cadmium ions cannot overtake the sodions, the boundary between the two layers remains sharp. Ag in, all the Cl' has migrated away from the cathode, and been replaced by OH'; but as the latter travels much the faster, there is no sharp boundary between the NaOH and NaCl solutions, but an intermediate region in which the two are mixed. The cathode tube is shown bent upwards, to allow hydrogen gas to escape without disturbing the rest of the liquid.

Bein found that with sulphates and chlorides a formation of basic salt at the anode occurs, although the cadmium may appear to be unchanged. He considers that the previous measurements of Hittorf and Hopfgartner are somewhat inaccurate from not taking that into account. Hittorf used rather wide and short electrolysing tubes, in order to reduce the resistance, and thus be able to employ a small voltage ; this had the disadvantage, however, of requiring the use of partitions of porous material to prevent mixing by diffusion. Later observers, having at their disposal an electric supply at 100 volts or more, have preferred to use longer tubes without partitions (Bein usually 50 to 60 cms. from anode to cathode). Bein has made special observations to determine whether partitions modify the rate of transport of ions, and concludes that they do: porous earthenware, parchment paper, gold-beater's skin, and animal membranes were tried. These substances, and especially the last, exercise a selective action on ions, usually retarding the cation more than the anion, so that the migration ratio of the anion determined with the aid of a diaphragm is too high. The action in such cases is still obscure, but is of much importance in connection with the physiological effect of the membranes of animals and plants.

An example (from Bein) will serve to show the method of calculation. The electrolyte was NaCl containing o'01784 per cent. of chlorine. It was contained in an electrolyser provided

· Zeitschr. phys. Chem., 28. 439-452 (1899). See also Hittorf, Zeitschr. Phys. Chem., 39. 612-629 (1902); 43. 239-249 (1903).

with glass taps to separate it after the experiment into three portions. The weights of these were : anode portion, 226-99 grams; middle, 195*24; cathode, 331'49. The weights of chlorine that would be contained by these before electrolysis were o'04048,0'03482, 0'05913 respectively; the weights actually found after the experiment, 0'04671, 0'03483, 0'05289; hence the gain by the anode was o'00623, the loss by cathode o'00624, whilst the middle portion was practically unchanged. Temperature 11°; 150 volts applied for 108 minutes : weight of silver deposited in voltameter in series with electrolyser was equivalent to oʻ01021 grms. of chlorine. Hence migration ratio of chlorine

oʻ00624 = 0'01021 = = 0:611 The weakest point of such experiments is the very small weight of ions transported, and the consequent importance of small errors of analysis. Noyes 1 has suggested an improved process, and carried it out with solutions of K,SO., BaCl, and BaN,Og. The method consists in supplying the anode with measured quantities of the base which is being removed by the current, and the cathode with the acid, so as to keep the liquid as nearly as possible of uniform concentration. The electrodes were of platinum ; the vessel, a wide double U-tube; the electrolyte contained a small measured amount of phenolphthalein solution. Over the anode was supported a dropping funnel, containing (e.g.) caustic potash of concentration double that of the K,SO, solution used. Before starting, a small amount was added, and similarly sulphuric acid to the cathode ; and whenever the cathode liquid began to turn alkaline (every ten or twelve minutes) more acid and alkali were supplied. The current used was from o‘02 to 0-18 ampere, and was kept up for as much as seven hours. In this way fifty to a hundred times as many ions were transported as in Bein's experiments.

The most extensive series of experiments on migration ratios is that of Hittorf,2 the earliest worker in the field. Hittorf considered particularly the degree of constancy of the ratios that he measured, and found that they are independent of the

1 Zeitschr. phys. Chem., 36. 63-83 (1901).
? Pogg., 89. 177; 98. 1 ; 103. 1; 106. 338, 513.

strength of current used. In the simplest cases, such as alkaline chlorides, they are also independent of concentration, at least when the concentration is moderate (see table, p. 256). When either ion is divalent a much greater change is produced by concentration; thus KCl gives o‘508 for decinormal, o'514 for normal solution, a difference of only o‘006; but K2CO3 gives 0:40 and 0.434 for the same concentrations, showing a difference of oʻ034 ; and BaCl, oʻ585 and 0:640, a difference of oʻ055. These anomalies are usually associated with the formation of intermediate ions, and will be further considered later. Besides the experiments already referred to may be mentioned those of Kümmell,who measured zinc and cadmium salts in greater dilution than previously. He found that the halogen compounds attain to a constant value of x before reaching to normal, and so presumably retain that value for all smaller concentrations; but that in the sulphates a constant value is not reached even for that dilution. Further references are to be found in Bein's paper.2 Measurements of migration ratios have also been made indirectly by means of concentration cells (vide infra, p. 210). This has been done by—amongst othersKendrick 3 and W. Stark 4 for the ions of the lead accumulator, and D. Macintosh” for acids.

For a discussion of migration phenomena in mixed electrolytes, see McGregor and Archibald.6

Before leaving the subject, one instance may be considered in detail, in which the effect on migration ratio of changes in the reaction at the electrodes is seen. In the tripartite cell of p. 34 let sulphuric acid be used as electrolyte, but lead for electrodes. This makes no difference to the behaviour at the cathode, but at the anode there may be (i.) evolution of oxygen, as when a platinum anode is used, or (ii.) formation of lead sulphate, or (iii.) formation of lead peroxide. In the second case the action in the anode chamber must be written

i Wied., 64. 655-679 (1898).
? Zeitschr. phys. Chem. 27. 1.
3 Zeitschr. f. Elektroch., 7. 52 (1901).
4 Zeitschr. Phys. Chem., 29. 385-400 (1899).
5 J. phys. Chem., 2. 273–288 (1898).
6 Phil. Mag. (5) 45. 151-157 (1898).

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Discharge of 1 equiv. So", which combines with i equiv.

lead to form the solid sulphate.
Export of 1 x equiv. H: to middle chamber.
Import of x equiv. SO," from middle chamber.
Net result :-
Loss of 1 x equiv, each of H: and SO.", i.e. loss of i

equiv. H.SO

Taking the migration ratio of the sulphion as o‘19, we see that reaction (ii.) at the anode causes a loss of 0·81 equiv. of acid, while reaction (i.) causes a gain of o'19 equiv. If the actual change be measured, the result shows how much of the current is spent on each of these reactions; it is found that the strength of the acid is the principal condition on which the result depends.

$5. CONDUCTIVITY OF ELECTROLYTES.

The most important means towards determining the mechanism of electrolytic conduction, and the nature of electrolytes, is measurement of conductivity. We have seen that the current density in an electrolyte is the product of three factors : (i.) the charge on an ion, (ii.) the number of ions per cubic centimetre, (ii.) the velocity with which the ions are moving; or in symbols 96600 y un +10)

(p. 21) Further, that the essential meaning of Ohm's law is proportionality between the current density and the potential gradient producing it; so that we may write the current density under unit potential gradient

96600 m (UA + U) where UAU, are the mobilities of the ions, i.e. their velocities under unit potential gradient; and in any other case the current density will be this amount multiplied by the actual gradient. The amount just written—the current density under unit potential gradient-is called the conductivity of the liquid. If the current density be expressed in amperes per square centimetre and the

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