Question

Define molar conductance of a solution. State its unit. How is it related to the specific conductance of the solution?

Answer 1

Conductance of solution refers to the ease with which electricity flows through the solution. Solutions conduct electricity due to the movement of ions. Conductance is the reciprocal of resistance.

Complete step by step answer:
There are three types of conductance that we usually use. They are Specific conductance, Molar conductance and Equivalent conductance.
Molar conductance is defined as the conductance of all the ions produced by one mole of electrolyte in a given solution. It is denoted by ${\Lambda _m}$.
Molar conductance can be written as,
Molar conductance ,${\Lambda _m}$ = Conductance of $1{m^3}$ of the solution $\times$ volume of the solution in ${m^3}$ containing one mole of the electrolyte.
Specific conductance is defined as conductance of one metre cube of the solution. It is denoted by $\kappa$. Specific conductance is also called conductivity of the solution. It is the reciprocal of resistivity. It can be written as,
Specific conductance, $\kappa = \dfrac{1}{\rho } = \left( {\dfrac{l}{a}} \right)\left( {\dfrac{1}{R}} \right) = \left( {\dfrac{l}{a}} \right) \times G$
Where $\rho$ is resistivity, l is length of electrode, a is area between the electrodes, R is resistance and G is conductance of solution.
SI unit of conductance is Siemen(S). Conductance is also expressed using $oh{m^{ - 1}}$.Unit of length is m and unit of area is ${m^2}$. Hence the unit of specific conductance will be $S{m^{ - 1}}$ or $oh{m^{ - 1}}{m^{ - 1}}$. SI unit is $S{m^{ - 1}}$.
Let us look into the equation of molar conductance. We know that conductance of $1{m^3}$ of the solution is called specific conductance. Hence the equation for molar conductance can be rewritten as,
Molar conductance ,${\Lambda _m}$= specific conductance $\times$ volume of the solution in ${m^3}$ containing one mole of the electrolyte.
Let c be the concentration of the electrolyte solution. Then the volume of the solution in ${m^3}$ containing one mole of the electrolyte will be $\left( {\dfrac{1}{c}} \right)$. Hence,
Molar conductance ,${\Lambda _m}$ = specific conductance $\times$ $\left( {\dfrac{1}{c}} \right)$
Molar conductance ,${\Lambda _m}$ = $\kappa$ $\times$ $\left( {\dfrac{1}{c}} \right)$
Hence the relation between molar conductance and specific conductance is,
${\Lambda _m} = \dfrac{\kappa }{c}$
The SI unit of concentration is $mol{m^{ - 3}}$ . Hence the SI unit of molar conductance is $S{m^2}mo{l^{ - 1}}$.

Note: While doing the problems related to conductivity, we should be careful about the units. Usually volume expresses in litre. The volume in litre should be converted into ${m^3}$ using $1L = {10^{ - 3}}{m^3}$ before substituting into the equation.