| Concentration of Acid. | Observed Conductivity.[A] | Ratios I. | Ratios II. |
|---|---|---|---|
| 4-molar | 0.17 | 1 | 1. |
| 2-molar | 0.22 | 1.30 | 1.30 |
| 1-molar | 0.26 | 1.53 | 1.18 |
| 0.5-molar | 0.30 | 1.76 | 1.15 |
| 0.25-molar | 0.31 | 1.83 | 1.04 |
| 0.125-molar | 0.32 | 1.88[B] | 1.03 |
[A] This is an artificial scale (see text) of conductivities, and does not represent reciprocal ohms, the standard units of conductivity.
[B] In the exact data on the conductivities of 4-molar and 1/8-molar HCl (Kohlrausch and Holborn, Leitvermögen der Elektrolyte (1898) p. 160), the ratio 348 / 181.5, or 1.92, is found, in place of 1.88 as observed.
We should expect, further, that the increase in conductivity, being dependent on the increased dissociation of a finite quantity of electrolyte, should tend towards a limit, a maximum conductivity being reached when (practically) all the acid is ionized. As a matter of experience, the conductivity of a given quantity of an acid or other ionogen does tend toward a limit. In the experiment just made, the conductivity of the acid increases very rapidly at first, as the 4-molar acid is diluted by water; but the increase in conductivity with the succeeding dilutions grows smaller and smaller and the conductivity is plainly approaching [p050] a limit (see the ratios I and II in the table). For hydrochloric acid at 18°, the limit for one mole[81] (36.5 grams HCl) at infinite dilution, as deduced from the curve of conductivities at finite dilutions, is 384 reciprocal ohms.[82]
Degree of Ionization of an Electrolyte.
The method of calculation of α in a specific case may be illustrated as follows: the resistance of a cube of 1 cm. edge of a solution of hydrochloric acid, which contains 1.825 grams hydrogen chloride in a liter, is found to be 55.55 ohms at 18°. Its conductivity then is 1 / 55.55 reciprocal ohms. Now, 1.825 grams of hydrogen chloride is 1.825 / 36.5 or 1 / 20 gram-equivalent of the acid; a whole gram-equivalent of the acid would be contained in 20 liters or 20,000 c.c. Then Λv = (1 / 55.55) × 20,000, or 360 reciprocal ohms. If we use the value at infinite dilution given above, α = 360 / 384, or 93.75%. That is, 93.75% of the hydrochloric acid is present in the ionized condition in such a solution, and 6.25% is not ionized.
By making the assumption that at infinite dilution electrolytes are completely ionized, and by taking the ratio which the equivalent conductivity of a given solution of an electrolyte bears to the maximum limit-value (calculated for the conductivity at infinite dilution) to be the degree of ionization of the electrolyte, as just explained, the theory of Arrhenius has thus made it appear possible to determine experimentally the proportion of ionized electrolyte present.
It is a significant fact that the equivalent conductivity of hydrochloric acid is close to its limit even at finite dilutions, and that the same relation holds for the strong acids and the strong bases, in general, and for most salts. But the equivalent conductivity of weak acids, like acetic acid, and of weak bases, like ammonium hydroxide, in finite dilutions is still far removed from the limits which may be calculated for infinite dilutions. Arrhenius was led then to the further important conclusion that, in the case of the first electrolytes mentioned, a very large proportion of the electrolyte must exist in the ionized form at finite concentrations, their equivalent conductivities having almost reached the limit characteristic of infinite dilution.
Clausius's Theory of Ionization and the Modern Theory.
Clausius[84] also assumed dissociated molecules or ions to be the real carriers of electricity in the passage of a current through the solution of an electrolyte, but he assumed only a minute quantity of these molecular fragments or ions to be free at any moment, their existence being supposed to be transitory and dependent in particular on exchanges of atoms between molecules. As a result of the oscillations of the atoms composing a molecule, oscillations comparable with the motions of molecules assumed in the kinetic theory of gases, molecules were considered by Clausius occasionally to reach such a condition of instability, that they dissociated into smaller particles; since the atoms were supposed to be held in a molecule by attractions of electrical charges on the atoms (theory of Berzelius), the fragments of the molecule would carry the charges, positive and negative respectively, which they possessed in the molecule. Such a breaking up or dissociation of molecules was, further, supposed to occur with particular ease during the collisions of molecules, the electrical attractions and repulsions of the charged atoms favoring, at such moments, an exchange of atoms. During the exchange, the atoms were considered to be free molecules, charged with electricity—essentially ions,—capable of moving under the influence of electrical forces and of thus carrying a current. Finally, such ions were supposed, in part, to escape recombination, and to remain free, until each ion either collided and combined with an ion of opposite charge, or collided with a molecule and displaced an atom of the same charge from that molecule, a new ion being thus liberated. The theory, as usually interpreted, assumed the existence of only a very small quantity of such free ions, that being all that was supposed to be required to explain the facts known at the time it was advanced.