Specific Conductance, Equivalent

CONDUCTANCE, MOLAR CONDUCTANCE

In a metallic conductor of length (l) cross−section (a) and the resistance (R), the relation between them is given by

R =

where ρ is the specific resistance. It is the resistance of unit length of a conductor of unit cross−section.

The reciprocal of resistance is termed conductance (C) and the reciprocal of specific resistance is called specific conductance or conductivity (L). Hence,

The specific conductance, L =

The conductance of a given conductor, C = ..(i)

∴ L = ..(ii)

The resistance is expressed in units of ohm, the conductance has units of ohm−1 or mho.

The conductance of solutions is also governed by the same relations. From (i), if l = 1,
a = 1, the specific conductance L = C. That is,

the specific conductance (L) is the conductance of the solution enclosed between two electrodes of 1 sq. cm area and 1 cm apart.

The conductance of a solution depends upon the number of ions present and hence on the concentration. To compare the conductivity of different solutions, it is necessary to take the concentration of the solutions into consideration. It is done by using equivalent
conductance, λ.

The equivalent conductance is defined as the conductance of a solution containing 1 gm−equivalent of the dissolved electrolyte such that the entire solution is placed between two electrodes 1 cm apart. As direct determination of this quantity would need electrodes of enormous sizes, the equivalent conductance (Λ) is always evaluated through measurement of specific conductance (L) with the help of equation (ii) and putting the value in equation (iii).

Suppose the solution of the electrolyte has a concentration of c gm−eqv. per litre. Then the volume of the solution containing 1 gm−eqv would be 1000/c cubic centimeter. If this solution be imagined to be placed between two electrodes 1 cm apart (l = 1), the cross−section of the column of solution or electrodes would be 1000/c sq. cm. Hence the equivalent conductance of the solution,

Λ = …(iii)

L being the specific conductance.

An alternate unit, called molar conductance µ, is defined as the conductance of a solution containing 1 gm mole per litre, the solution being placed between two electrodes kept
1 cm apart. As before, µ = 1000 L/c’, where c’ is the molar concentration.

Transport number/ Transference number: Under a potential gradient, current is transported by the migration of ions, the positive ions moving towards the cathode and the negative ions towards the anode. The total charge released at the cathode and at the anode is of course equal but the fraction of the total current conveyed by the cations and the anions through the solution are not necessarily equal. For example, in a dil. solution of HNO3, only 16% of the current is conveyed by ions, the rest by the H+ ions. Thus, (the fraction of the current carried by cations and anions, represented by t+ and t− are called transport number or transference numbers).

i.e. t+ =

(n+ z + = n− z− as the solution being electrically neutral)

∴ t+ = and t − = ..(v)

where ni number of respective ions

zi charge of respective ions

ui speed of respective ions