+--------------------------------------------+----------------+
| | KCl | NaCl | LiCl |
+---------+-----------------+----------------+----------------+
| m | u + v u v | u + v u v |u + v u v |
+---------+-----------------+----------------+----------------+
| 0 | 1350 660 690 | 1140 450 690 | 1050 360 690 |
| 0.0001 | 1335 654 681 | 1129 448 681 | 1037 356 681 |
| .001 | 1313 643 670 | 1110 440 670 | 1013 343 670 |
| .01 | 1263 619 644 | 1059 415 644 | 962 318 644 |
| .03 | 1218 597 621 | 1013 390 623 | 917 298 619 |
| .1 | 1153 564 589 | 952 360 592 | 853 259 594 |
| .3 | 1088 531 557 | 876 324 552 | 774 217 557 |
| 1.0 | 1011 491 520 | 765 278 487 | 651 169 482 |
| 3.0 | 911 442 469 | 582 206 376 | 463 115 348 |
| 5.0 | | 438 153 285 | 334 80 254 |
| 10.0 | | | 117 25 92 |
+---------+-----------------+----------------+----------------+
These numbers show clearly that there is an increase in ionic velocity
as the dilution proceeds. Moreover, if we compare the values for the
chlorine ion obtained from observations on these three different salts,
we see that as the concentrations diminish the velocity of the chlorine
ion becomes the same in all of them. A similar relation appears in other
cases, and, in general, we may say that at great dilution the velocity
of an ion is independent of the nature of the other ion present. This
introduces the conception of specific ionic velocities, for which some
values at 18 deg. C. are given by Kohlrausch in Table X.:--
Table X.
+------------------------------------+
| K 66 X 10^-5 cms. per sec. |
| Na 45 " " |
| Li 36 " " |
| NH4 66 " " |
| H 320 " " |
| Ag 57 " " |
| Cl 69 " " |
| I 69 " " |
| NO3 64 " " |
| OH 162 " " |
| C2H3O2 36 " " |
| C3H5O2 33 " " |
+------------------------------------+
Having obtained these numbers we can deduce the conductivity of the
dilute solution of any salt, and the comparison of the calculated with
the observed values furnished the first confirmation of Kohlrausch's
theory. Some exceptions, however, are known. Thus acetic acid and
ammonia give solutions of much lower conductivity than is indicated by
the sum of the specific ionic velocities of their ions as determined
from other compounds. An attempt to find in Kohlrausch's theory some
explanation of this discrepancy shows that it could be due to one of two
causes. Either the velocities of the ions must be much less in these
solutions than in others, or else only a fractional part of the number
of molecules present can be actively concerned in conveying the current.
We shall return to this point later.
_Friction on the Ions._--It is interesting to calculate the magnitude
of the forces required to drive the ions with a certain velocity. If
we have a potential gradient of 1 volt per centimetre the electric
force is 10^8 in C.G.S. units. The charge of electricity on 1
gram-equivalent of any ion is 1/.0001036 = 9653 units, hence the
mechanical force acting on this mass is 9653 X 10^8 dynes. This, let
us say, produces a velocity u; then the force required to produce unit
velocity is PA = 9.653 X 10^11/u dynes = 9.84 X 10^5/u kilograms-weight.
If the ion have an equivalent weight A, the force producing unit
velocity when acting on 1 gram is P1 = 9.84 X 10^5/Au kilograms-weight.
Thus the aggregate force required to drive 1 gram of potassium ions
with a velocity of 1 centimetre per second through a very dilute
solution must be equal to the weight of 38 million kilograms.
Table XI.
+-------------------------------+
| Kilograms-weight. |
+-------------------------------+
| PA P1 |
|K 15 X 10^8 38 X 10^6 |
|Na 22 " 95 " |
|Li 27 " 390 " |
|NH4 15 " 83 " |
|H 3.1 " 310 " |
|Ag 17 " 16 " |
|Cl 14 " 40 " |
|I 14 " 11 " |
|NO3 15 " 25 " |
|OH 5.4 " 32 " |
|C2H8O2 27 " 46 " |
|C3H5O2 30 " 41 " |
+------------- -----------------+
Since the ions move with uniform velocity, the frictional resistances
brought into play must be equal and opposite to the driving forces,
and therefore these numbers also represent the ionic friction
coefficients in very dilute solutions at 18 deg. C.
_Direct Measurement of Ionic Velocities._--Sir Oliver Lodge was the
first to directly measure the velocity of an ion (_B.A. Report_, 1886,
p. 389). In a horizontal glass tube connecting two vessels filled with
dilute sulphuric acid he placed a solution of sodium chloride in solid
agar-agar jelly. This solid solution was made alkaline with a trace of
caustic soda in order to bring out the red colour of a little
phenol-phthalein added as indicator. An electric current was then passed
from one vessel to the other. The hydrogen ions from the anode vessel of
acid were thus carried along the tube, and, as they travelled,
decolourized the phenol-phthalein. By this method the velocity of the
hydrogen ion through a jelly solution under a known potential gradient
was observed to about 0.0026 cm. per sec, a number of the same order as
that required by Kohlrausch's theory. Direct determinations of the
velocities of a few other ions have been made by W. C. D. Whetham
(_Phil. Trans._ vol. 184, A, p. 337; vol. 186, A, p. 507; _Phil. Mag._,
October 1894). Two solutions having one ion in common, of equivalent
concentrations, different densities, different colours, and nearly equal
specific resistances, were placed one over the other in a vertical glass
tube. In one case, for example, decinormal solutions of potassium
carbonate and potassium bichromate were used. The colour of the latter
is due to the presence of the bichromate group, Cr2O7. When a current
was passed across the junction, the anions CO3 and Cr2O7 travelled in
the direction opposite to that of the current, and their velocity could
be determined by measuring the rate at which the colour boundary moved.
Similar experiments were made with alcoholic solutions of cobalt salts,
in which the velocities of the ions were found to be much less than in
water. The behaviour of agar jelly was then investigated, and the
velocity of an ion through a solid jelly was shown to be very little
less than in an ordinary liquid solution. The velocities could therefore
be measured by tracing the change in colour of an indicator or the
formation of a precipitate. Thus decinormal jelly solutions of barium
chloride and sodium chloride, the latter containing a trace of sodium
sulphate, were placed in contact. Under the influence of an
electromotive force the barium ions moved up the tube, disclosing their
presence by the trace of insoluble barium sulphate formed. Again, a
measurement of the velocity of the hydrogen ion, when travelling through
the solution of an acetate, showed that its velocity was then only about
the one-fortieth part of that found during its passage through
chlorides. From this, as from the measurements on alcohol solutions, it
is clear that where the equivalent conductivities are very low the
effective velocities of the ions are reduced in the same proportion.
Another series of direct measurements has been made by Orme Masson
(_Phil. Trans._ vol. 192, A, p. 331). He placed the gelatine solution of
a salt, potassium chloride, for example, in a horizontal glass tube, and
found the rate of migration of the potassium and chlorine ions by
observing the speed at which they were replaced when a coloured anion,
say, the Cr2O7 from a solution of potassium bichromate, entered the tube
at one end, and a coloured cation, say, the Cu from copper sulphate, at
the other. The coloured ions are specifically slower than the colourless
ions which they follow, and in this case it follows that the coloured
solution has a higher resistance than the colourless. For the same
current, therefore, the potential gradient is higher in the coloured
solution and lower in the colourless one. Thus a coloured ion which gets
in front of the advancing boundary finds itself acted on by a smaller
force and falls back into line, while a straggling colourless ion is
pushed forward again. Hence a sharp boundary is preserved. B. D. Steele
has shown that with these sharp boundaries the use of coloured ions is
unnecessary, the junction line being visible owing to the difference in
the optical refractive indices of two colourless solutions. Once the
boundary is formed, too, no gelatine is necessary, and the motion can be
watched through liquid aqueous solutions (see R. B. Denison and B. D.
Steele, _Phil. Trans._, 1906).
All the direct measurements which have been made on simple binary
electrolytes agree with Kohlrausch's results within the limits of
experimental error. His theory, therefore, probably holds good in such
cases, whatever be the solvent, if the proper values are given to the
ionic velocities, i.e. the values expressing the velocities with which
the ions actually move in the solution of the strength taken, and under
the conditions of the experiment. If we know the specific velocity of
any one ion, we can deduce, from the conductivity of very dilute
solutions, the velocity of any other ion with which it may be
associated, a proceeding which does not involve the difficult task of
determining the migration constant of the compound. Thus, taking the
specific ionic velocity of hydrogen as 0.00032 cm. per second, we can
find, by determining the conductivity of dilute solutions of any acid,
the specific velocity of the acid radicle involved. Or again, since we
know the specific velocity of silver, we can find the velocities of a
series of acid radicles at great dilution by measuring the conductivity
of their silver salts.
By such methods W. Ostwald, G. Bredig and other observers have found
the specific velocities of many ions both of inorganic and organic
compounds, and examined the relation between constitution and ionic
velocity. The velocity of elementary ions is found to be a periodic
function of the atomic weight, similar elements lying on corresponding
portions of a curve drawn to express the relation between these two
properties. Such a curve much resembles that giving the relation
between atomic weight and viscosity in solution. For complex ions the
velocity is largely an additive property; to a continuous additive
change in the composition of the ion corresponds a continuous but
decreasing change in the velocity. The following table gives Ostwald's
results for the formic acid series:--
Table XII.
+----------------------+----------+---------------------+
| | Velocity.| Difference for CH2. |
+----------------------+----------+---------------------+
| Formic acid HCO2 | 51.2 | .. |
| Acetic " H3C2O2 | 38.3 | -12.9 |
| Propionic " H5C3O2 | 34.3 | - 4.0 |
| Butyric " H7C4O2 | 30.8 | - 3.5 |
| Valeric " H9C5O2 | 28.8 | - 2.0 |
| Caprionic " H11C6O2 | 27.4 | - 1.4 |
+----------------------+----------+---------------------+
_Nature of Electrolytes._--We have as yet said nothing about the
fundamental cause of electrolytic activity, nor considered why, for
example, a solution of potassium chloride is a good conductor, while a
solution of sugar allows practically no current to pass.
All the preceding account of the subject is, then, independent of any
view we may take of the nature of electrolytes, and stands on the basis
of direct experiment. Nevertheless, the facts considered point to a very
definite conclusion. The specific velocity of an ion is independent of
the nature of the opposite ion present, and this suggests that the ions
themselves, while travelling through the liquid, are dissociated from
each other. Further evidence, pointing in the same direction, is
furnished by the fact that since the conductivity is proportional to the
concentration at great dilution, the equivalent-conductivity, and
therefore the ionic velocity, is independent of it. The importance of
this relation will be seen by considering the alternative to the
dissociation hypothesis. If the ions are not permanently free from each
other their mobility as parts of the dissolved molecules must be secured
by continual interchanges. The velocity with which they work their way
through the liquid must then increase as such molecular rearrangements
become more frequent, and will therefore depend on the number of solute
molecules, i.e. on the concentration. On this supposition the observed
constancy of velocity would be impossible. We shall therefore adopt as a
wording hypothesis the theory, confirmed by other phenomena (see
ELECTROLYSIS), that an electrolyte consists of dissociated ions.
It will be noticed that neither the evidence in favour of the
dissociation theory which is here considered, nor that described in the
article ELECTROLYSIS, requires more than the effective dissociation of
the ions from each other. They may well be connected in some way with
solvent molecules, and there are several indications that an ion
consists of an electrified part of the molecule of the dissolved salt
with an attendant atmosphere of solvent round it. The conductivity of a
salt solution depends on two factors--(1) the fraction of the salt
ionized; (2) the velocity with which the ions, when free from each
other, move under the electric forces.[12] When a solution is heated,
both these factors may change. The coefficient of ionization usually,
though not always, decreases; the specific ionic velocities increase.
Now the rate of increase with temperature of these ionic velocities is
very nearly identical with the rate of decrease of the viscosity of the
liquid. If the curves obtained by observations at ordinary temperatures
be carried on they indicate a zero of fluidity and a zero of ionic
velocity about the same point, 38.5 deg. C. below the freezing point of
water (Kohlrausch, _Sitz. preuss. Akad. Wiss._, 1901, 42, p. 1026). Such
relations suggest that the frictional resistance to the motion of an ion
is due to the ordinary viscosity of the liquid, and that the ion is
analogous to a body of some size urged through a viscous medium rather
than to a particle of molecular dimensions finding its way through a
crowd of molecules of similar magnitude. From this point of view W. K.
Bousfield has calculated the sizes of ions on the assumption that
Stokes's theory of the motion of a small sphere through a viscous medium
might be applied (_Zeits. phys. Chem._, 1905, 53, p. 257; _Phil. Trans._
A, 1906, 206, p. 101). The radius of the potassium or chlorine ion with
its envelope of water appears to be about 1.2 X 10^-8 centimetres.
For the bibliography of electrolytic conduction see ELECTROLYSIS. The
books which deal more especially with the particular subject of the
present article are _Das Leitvermogen der Elektrolyte_, by F.
Kohlrausch and L. Holborn (Leipzig, 1898), and _The Theory of Solution
and Electrolysis_, by W. C. D. Whetham (Cambridge, 1902).
(W. C. D. W.)