Question

Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with concentration ?

Answer 1

Conductivity (k) The inverse of resistivity $\left(\rho \right)$, is called conductivity.

$k=\frac{1}{\rho }=\frac{1}{R}\times \frac{1}{A}$

$=G\times \frac{1}{A}$

[G = conductance, 1 = length, A = cross-section area R = resistance]

If l = 1 cm and $A=1c{m}^2,thenk=G,$

So, conductivity of an electrolytic solution may be defined as the conductance of a solutino of 1 cm length with area of cross - section equal to $1c{m}^2$. Its unit is $oh{m}^{-1}c{m}^{-1}orSc{m}^{-1}$

Molar conductivity $\left({\lambda }_m\right)$ Molar conductivity of a solution at a given concentration is the conductance of the volume (V) of solution containing one mole of electrolyte kept between two electrodes with area of cross section A and at a distance of unit length.

${\lambda }_m=\frac{kA}{l}=k$

Since, I = 1 and $A=V;{\lambda }_m=kV$

Its unit is $oh{m}^{-1}c{m}^{2}mo{l}^{-1}$ or $Sc{m}^{2}mo{l}^{-1}$

Variation of conductivity and molar conductivity with concentration

Conductivity always decreases with decrease in concentration both, for weak and strong electrolytes. This is so because the number of ions per unit volume that carry the current in a solution decrease in concentration. This is because the total volume, V of solution containing one mole of electrolyte also increases.

It has been found that decreases in k on dilution of a solution is more than compensated by increased in its volume

Molar conductivity versus $C^{12}$ for acetic acid (weak electrolyte) and potassium chloride (strong electrolyte) in aqueous solutions.