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 Λ_{ ‹v›} = (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.»—It is in these conclusions—in particular that the proportion of ionized electrolyte ‹may be determined experimentally›, and that frequently a ‹large proportion is found to be ionized at finite concentrations›,—that the ‹modern theory of ionization differs from the older theory of Clausius›. The former is an elaboration of the latter, and some opponents[83] of the modern theory still uphold the latter as offering an adequate explanation of the phenomena of conductivity. All facts, then, in particular, which confirm the validity of the ‹conception of the degree of ionization›, as introduced by Arrhenius, [p052] must be considered as criteria favoring his theory, specifically. The development of chemistry in the last twenty years is replete with such evidence and we shall meet it in many connections throughout our work.