Electrochemistry

Electrolytic Conductance

The conductance of electricity by ions present in solutions is called electrolytic conductance or ionic conductance. Conductivity of electrolytic solution depends on following factors:

Nature of electrolyte
Size of ions produced and their solvation
Nature of solvent and its viscosity
Concentration of electrolyte
Temperature (conductance increases with increase in temperature)

Measurement of Conductivity of Ionic Solutions

We can use a Wheatstone bridge to measure an unknown resistance. But for doing so for an ionic solution presents two challenges. First problem is the change in composition of solution when direct current passes (DC) through the solution. Second problem is that we cannot connect an ionic solution to the bridge the way we connect a metallic conductor. The first problem is solved by using an alternating current (AC) source of power. The second problem is solved by using a specially designed vessel which is called conductivity cell.

A conductivity cell is composed of two platinum electrodes which are coated with platinum black. The electrodes have area of cross section equal to A and are separated by distance ‘l’. Hence, the solution confined between the two electrodes is a column of length l and area of cross section A. The resistance for this column of solution is given by following equation.

`R=ρl/A=l/(κA)`

The quantity `l/A` is called cell constant and is denoted by the symbol G^*.

`G^*=l/A=Rκ`

The setup for measurement of resistance is composed of two resistances R₃ and R₄, a variable resistance R₁ and the conductivity cell (resistance R₂. P is a suitable detector and the bridge is balanced when no current passes through the detector. In this condition,

Unknown resistance `R_2=(R_1R_4)/(R_3)`

Using the values of cell constant and resistance of solution in the cell, we can find the conductivity of the solution by using following equation.

`κ=text(cell constant)/R=(G_*)/R`

Molar Conductivity: Molar conductivity is the conductivity of the solution divided by molar concentration of the solution. It is given by following equation.

`λ_m=κ/c`

If the unit of conductivity is S m^-1 and the unit of concentration is mol m^-3 then unit of λ_m is S m^{2 mol^-1}

Variation of Conductivity and Molar Conductivity with Concentration

Conductivity always decreases with decrease in concentration of both, weak and strong electrolytes. This happens because the number of ions per unit volume decreases on dilution.

Molar conductivity of a solution increases with a decrease in concentration. This happens because the total volume V of solution containing one mole of electrolyte also increases. When concentration approaches zero, the molar conductivity is known as limiting molar conductivity. It is represented by the symbol λ^°_m

Kohlrausch Law of Independent Migration of Ions: This law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte. Following is an example:

Λ^°_(NaCl) = Λ^°_Na⁺+Λ^°_Cl^-