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particular instance might conceivably be due either to the rapid motion of a few dissociated particles, or to the slow motion of many.
That it does measure a real velocity of convection is demonstrated by a method of experiment devised by Lodge, which we must now proceed to describe.
A tube is filled with a jelly, made of gelatine and water, containing sodium chloride and a little phenolphthalein. One end of the tube is placed in contact with a solution of hydrochloric acid, and a current passed in from a platinum electrode, so that it flows from tht, to the NaCl. The current involves transport of the cations in its own direction; H ions, consequently, penetrate the jelly, and, as they proceed, decolorise the phenolphthalein; this makes the movement of the ions visible, so that it can be measured by direct observation. Lodge found in this way that the velocity of the hydrogen ions was of the order of magnitude calculated by Kohlrausch.
Lodge's method, however, also only gives the effective mobility, for no single ion would produce an observable decolorisation; it is the general drift forwards of the multitude of ions that is observed, and this, of course, takes place with the average effective velocity, as defined above.
The velocity is a very small one, as we have seen (p. 63). Lodge's measurements gave oʻ0024 to o‘0029 cm. per second, under a potential gradient of i volt per centimetre. The potential gradient was not correctly determined, so that the numbers can only be regarded as a demonstration of the existence of ionic movements; but the method has been developed with success by Whetham and others.
Whetham 2 avoided the use of gelatine, which offers a certain though small additional resistance to the ions. To do this the tube was arranged vertically, with the denser liquid below. It is, of course, easy to measure by a voltmeter the potential difference between the ends of the tube ; but the gradient in the tube will not be uniform unless the conductivity is uniform through its length; so, to avoid difficulties in
i Brit. Ass. Rep., 1886, p. 389. 2 Phil. Trans., A, 1893, pp. 337-359.
determining the potential gradient, Whetham used a pair of solutions, e.g. potassium bichromate and potassium carbonate, and adjusted their strengths so as to make the conductivity the
same. As, further, there must be a colour difference between -them, the choice is limited. There is, moreover, another
condition that was not attended to in Lodge's experiments : :- the following ion must be specifically slower than the leading. : Thus, e.g., if copper ions are arranged to follow sodions, the
former will be constantly behind the latter, and the boundary
remain sharp; but if the directi? 1 of movement be reversed, - the individual sodions, being rapid, will gradually pene
trate into the cupric solution, and cause the boundary to ; become diffused, and impossible to measure accurately. By
paying attention to these points, Whetham succeeded in getting in certain cases a satisfactory agreement with the calculated mobilities. He gives these results in aqueous solution :
Cu" 0.000309 cm. per second
Cr,O," 47 . . He also made measurements with CoCl, and CoN,0. in alcoholic solution, and found that the mobilities, about to those in aqueous solution, were at least of the order of magnitude to be expected from the conductivity.
Orme Masson has modified the method so as to make it available for a wider range of substances. His apparatus consists of a horizontal tube placed between two flasks with side tubes. The tube-15 cm. long by 2 mm. wide—is filled with a jelly of the material to be studied, say NaCl; the jelly was of agar-agar, 12 per cent., and contained enough salt to make a half-normal, normal, or twice normal solution. The flasks contained two indicating solutions, and large platinum electrodes placed just opposite the endings of the tube. The anode solution was normal CuSO,, the cathode solution contained i equiv. K,Cr,O, and equiv. K,CrO, per litre. A potential difference of about 40 volts was applied ; it causes the Na: to move along the tube towards the cathode, and Cu“ ions to follow them,
1 Zeitschr. f. phys. Chem., 29. 501-526 (1899), or Phil. Trans., 1899, 331-350.
thus turning the jelly blue : the chlorions to move along the tube towards the anode, and the chromate- and bi-chromate ions to follow them, turning the jelly yellow. The time of passage of the coloured boundaries past each half centimetre of the tube was noted. The whole must be immersed in water, as a considerable amount of heat is generated in the narrow tube.
Masson only used the method to compare the mobilities of two ions, such as Na' and Cl. He points out that it is not the mobilities of the indicator ions that are compared in this way, for their conductivities being different, the potential gradients acting on them are different too; but the Na and Cl ions being together in the same part of the tube are exposed to the same gradient, and their mobilities will be strictly in the same ratio as the velocity with which they move. That these velocities are truly measured by the movement of the coloured ions following was shown by chemical analysis of the coloured jellies; all the Na: had disappeared from the blue jelly, all the Cl' from the yellow. The method is therefore applicable to all ions which move faster than the cupro- and chromate ions.
Masson's measurements on alkaline chlorides and sulphates show agreement to about 2 or 3 per cent. with the numbers deduced from conductivity measurements. The method does not appear to be capable of a much greater accuracy.
B. D. Steele l has extended the work of Masson. He succeeded in dispensing with gelatine in the solution to be measured, and at the same time found that even colourless solutions could be satisfactorily observed on account of the differences of refractive index between them, thus avoiding the use of coloured indicators. Fig. 26 shows the apparatus which he used for most of his experiments. A and B are tubes of uniform bore, in which the movement of the boundary is to be observed. They are filled with an aqueous solution, bounded above by jellies (G) containing the "indicator ions:” the jellies are covered by a little liquid containing the same salt, in which the electrodes are immersed. When the tubes CC are employed for the jellies, FF are closed ; but, if the indicators
| Phil. Trans., 198. 105-145 (1902), or Zeitschr. phys. Chem., 40. 689736 (1902).
are heavier than the solution experimented on, DD are used instead of CC, and the measuring-tubes closed at the top. The whole is placed in a waterbath with good plate-glass sides, and the height of the boundaries read by a cathetometer.
E.g. MgSO, was measured by placing its solution between jellies of CASO, and NaAc, or between CuSO, and K,CrO,, or between CuSO, and NaAc, the same result being obtained in each case. To avoid difficulties as to distribution of the potential difference in the apparatus, the current flowing through it was measured, and the crosssection of the tubes being known, the current density could be calculated: this was divided by the known conductivity of the solution
Fig. 26. used, to give the potential gradient (p. 44). The electrical arrangements consisted of a battery (70 volts), an adjustable resistance, an ammeter, and the measuring cell, all in series. The current should not exceed about o'03 ampere; the size of the tubes should be chosen to allow of this, otherwise the heat generated may be sufficient to melt the jellies ; but, on the other hand, it is difficult to observe the boundary if the section of the tube be less than o'08 sq. cm.
Steele discusses at length the conditions necessary for the production and maintenance of a good boundary. These differ in different cases, and reference must be made to the original memoir for details ; but it appears that for each particular boundary the potential gradient must be within certain limits, even if all the other conditions are satisfied. Thus the boundary between BaCl, and BaAc, (the Ac' following the Cl') is fairly good with i volt per centimetre; very sharp and easy to read with 1.2; at 1'5 shows signs of " washing ;” at 2 is undulating, and obscured by little eddies. The correct
conditions for 38 pairs of salts are given, but in several other cases no good boundaries could be obtained. The results obtained by Steele areMigration ratio 1
Normality. of anion.
MgSO4 0·184 0·646
0*737 KOH 0-574 0730
0-73 BaCl2 05
K.,Cr0, 0.5 0447
KFe''Ox 0.603 0'331 The results appear to agree with Kohlrausch's conductivity measurements about as well as, or perhaps better than, those of migration ratios by Hittorf's method.
For a criticism of Steele's work, see Abegg and Gaus, who give a method for measuring very slow ions, i.e. ions for which the usual method is impracticable for want of a still slower ion : and Denison.2
A theoretical discussion of the conditions on which direct observation of ionic velocities is based has been given by Kohlrausch.
$ 7. ARRHENIUS' THEORY OF DISSOCIATION
So far we have hardly touched on the question as to what fraction of the dissolved salt molecules is broken up into ions. The effective mobility dealt with in the last section is no means of estimating the actual velocity with which ions travel when
i Zeitschr. phys. Chem., 40. 737-745 (1902).