148 CONDUCTIVITY OF ELECTROLYTES. chap.
where k is the specific conductivity of the normal solution. If hydrochloric acid were completely dissociated in normal
solution, then at 18° /would be ^^^^±^^"^) = ^^, or,
roughly, 0*380 ampere per volt; of this the first part is conditioned by the mobility of the hydrogen ion, and the second part by that of the chlorine ion. That part of the current strength due to the migration of the hydrogen ion is /h = Vx 0314 amperes. Now, a gram-ion carries with it 96,500 coulombs, and between A and B there is 1 c.c. of normal solution, and therefore, assuming complete dis- sociation, 0*001 gram-ion. This quantity of hydrogen ion carries a charge of 96*5 coulombs. Since the current strength due to the hydrogen ions is /« = 0*314 x V amperes (coulombs per second), the time —
= seconds
0-314 X V V
must elapse before all the hydrogen ipns between A and B have passed through the plane B, If F = 1 volt, the hydro- gen ions require about 307 seconds to pass through 1 cm. ; their velocity is, therefore, 0*00325 cm. per second.
Under the same external conditions, the velocity of the chlorine ions is 0*000678 cm. per second, and that of the other ions is of the same order of magnitude.
The assumption that the hydrochloric acid is completely dissociated has no influence on the result of the calculation. Since the velocity of the ions is proportional to the mobility and to the fall of potential per unit length, and thijs seldom reaches the value of 1 volt per centimetre, it is usually found that the velocity of the ions, and of the electricity with which they are charged, is extremely small, scarcely amounting to 0*01 mm. per second. The following numbers give the absolute velocities, U and V, of the most commonly occurring cations and anions at 18°, under the influence of a fall of potential of 1 volt per centimetre : —
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