Concise Physical Chemistry

c13 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

212 COULOMETRY AND CONDUCTIVITY

Anode Ag+ Cathode

Ag+

Ag+

FIGURE 13.5 A three-compartment Hittorf cell.

deposited (electroplated) on the cathode. We can understand the use of the cell by

taking two extreme hypothetical cases:

1. If there were no transference of charge by Ag+moving into the cathode com-
   partment from the central compartment, the concentration would be reduced
   by one equivalent (gram atomic weight) per Faraday passed through the cell.


2. If silver ions carriedallthe charge through the Hittorf apparatus, all the Ag+
   ions lost at the cathode would be replaced by Ag+ions migrating into the
   cathode compartment from the central compartment. The concentration of
   Ag+ions would be unchanged.

In fact, the actual concentration in the cathode compartment is altered by less

than one equivalent per coulomb but more than zero. The number of equivalents

per coulomb transferred into the cathode compartment is the transference number

of Ag+. One can determine the transport numbers of both ions for example, Ag+

and NO− 3 , along with their mobilities by a simple experiment (but one that requires

precise analytical technique).

The conductance of a solution is the amount of charge in coulombs passing through

it between electrodes at a given potential difference in volts per unit length of the

resistor in units of V m−^1. From our idea that current flows through a solution of

electrolyte due to passage of ions and from Faraday’s proof that each ion carries an

integral multiple of the unit charge e−, the controlling factor must be the mobility

with which ions move through the solvent, water in the case at hand. In fact the

equivalent ionic conductance at infinite dilutionλ◦and the ionic mobility are directly

proportional:

λ◦+=Fu◦+

and

λ◦−=Fu◦−

Taking values for Ag+(aq) and NO− 3 (aq) (Example 13.3), we have

u◦+=

λ◦+

F

=

62. 6 × 10 −^4

96 , 485

= 64. 9 × 10 −^8 m^2 V−^1 s−^1