Electrolysis : The Migration Of Ions

The unequal speeds of different ions moving through an electrolyte in the same potential gradient causes changes of concentration of salt (not ions separately) around the electrodes. These changes, noticed by Gmelin in 1838 and by Daniell and Miller in 1843, were first fully investigated and related to the ionic speeds by Hittorf (1853).

In

Fig: Migration of ions

the black and white circles represent the cations and anions, in the upper row a before electrolysis and in the lower row b after. The black circles move to the left with a speed u and the white circles to the right with a speed v which is, in the case considered, twice as great as u. The vertical line XY divides the original arrangement into two equal parts.

Before electrolysis there are eight black and white ions on each side. After electrolysis, when six equivalents of salt have been decomposed and the unpaired ions deposited, there are four undecomposed equivalents of salt on the left and six on the right, so that four equivalents of salt have been lost on the left and two on the right. The losses in neutral salt molecules around the electrodes are in the ratio of the speeds of the ions migrating away from the electrodes.

The fractions of the total current carried by the cation and anion, respectively, are one third and two thirds, or, generally

u/(u+v) and v/(u+v)

or, since the total current Λ_∞ is the sum of l_c and l_a:

l_c/ Λ_∞ = u/(u+v) and l_a/ Λ_∞ = v/(u+v)

The fraction of the total current carried by one ion is called the transport number of that ion, n. It is not a constant depending only on that ion, as the mobility is, but varies from salt to salt, according to the mobility of the other ion. If we refer n to the anion, then:

l_a/l_c = n/(1-n)

and from n and Λ_∞ = l_c + l_a we can calculate l_a and l_c separately.

Mobilities in Aqueous Solution at 18°

Cations l_c	Anions l_a
	Cl'	65.3
	Br'	67.3
	I'	66.1
	NO₃	61.6
	OH'	174
	CH₃COO'	35
	½SO₄''	67.9
	½CO₃''	60

The large mobilities of the hydrogen and hydroxide ions should be noted.

The value of Λ_∞ for a weak acid, such as acetic acid, is found by adding 315.6, the mobility of the hydrogen ion, to the mobility of the anion, e.g., 35 for the acetate ion, CH₃COO',

Λ_∞ for acetic acid = 315.6 + 35 = 350.6.

The specific conductivity, k, of saturated silver chloride solution at 18° is, after suitable correction by subtraction for the conductivity of the water used, 1.24 x 10^-6 ohm^-1 cm^-1, and since the solution is very dilute it may be considered completely ionised. Now Λ = k/c, and in this case Λ may be taken as Λ_∞ = 54.0 + 65.3 = 119.3; c = 1.24 x 10/1.193 x 10² = 1.04 x 10^-8 equiv. per cm³.

Protein crystallography
Chemistry guide
Electrolysis
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