Concise Physical Chemistry

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

THE HITTORF CELL 211

13.6 FARADAY’S LAWS

In the early nineteenth century, Faraday stated the laws:

1. The mass of any substance deposited or dissolved at an electrode is pro-
   portional to the quantity of electricity passed through the solution.


2. One equivalent weight of any substance deposited or dissolved at an elec-
   trode requires 96,485 coulombs of electricity.

(The modern value of 96,485 coulombs has been substituted for Faraday’s original

value which differed slightly.) If the quantity 96,485 coulombs is divided by the

charge on the electron (measured about a century later), one obtains the Avogadro

number. The explanation of this is that each ion carries an integral number of electrons

(negative) or lacks an integral number of electrons (positive). In honor of one of the

early geniuses of physical chemistry, the quantity 96,485 coulombs is defined as the

faraday,F.

13.7 MOBILITY AND CONDUCTANCE

If we look at transport numbers, mobility, and ionic conductance, it should be evident

that a fast-moving ion carries more of the total charge transported than a slow one.

Also, transport numbers are the fraction of electrical charge carried by each ion, so

they must add up to 1. In an aqueous solution of a univalent salt,t++t−= 1 .0 and

the sum of the molar (or molal) ionic conductances is◦=λ◦++λ◦−. The fraction

of current carried by an ion can be given by either the transport numbers or the ratio

of ionic conductivityλ◦±to the total molar conductivity◦, each at infinite dilution:

t+=

λ◦+

◦

, t−=

λ◦−

◦

In an electrolyte of faster and slower ions, the faster ion carries a greater proportion

of the total charge transfer than the slower ion in proportion to their relative speeds.

Therefore the ratio of transport numbers is the same as the ratio of ionic mobilities:

t+

t−

=

u+

u−

13.8 THE HITTORF CELL

Transport numbers can be determined directly by measuring the change in concen-

tration brought about by transference in a compartmentalized cell called aHittorf

cell(Fig. 13.5). A Hittorf cell consists of three compartments: an anode compart-

ment, a cathode compartment, and a central compartment between them. A potential

is imposed on a solution in the cell containing, for example, Ag+ions, which are