Question

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

Answer 1

- Hint: The conductance is the property of the conductor (metallic as well as electrolytic) which facilitates the flow of electricity through it. It is equal to the reciprocal of resistance, that is,
Conductance = 1/Resistance = $\dfrac{1}{R}$
There are three kinds of conductance that we take into consideration:
1. Specific Conductance or Conductivity
2. Equivalent Conductance
3. Molar Conductance

Complete step-by-step solution -

The molar conductance of a solution is defined as the conductance of all the ions produced by ionization of 1 g-mole of an electrolyte when present in V ml of solution. It is denoted by ${{\Lambda }_{m}}$.
Therefore,
Molar conductance ${{\Lambda }_{m}}=\kappa \times V$.
where,
V is the volume in mL containing 1 g-mole of the electrolyte. If c is the concentration of the solution in g-mole per litre, then
${{\Lambda }_{m}}=\kappa \times \dfrac{1000}{M}$
The unit of molar conductance is \[oh{{m}^{-1}}c{{m}^{2}}mo{{l}^{-1}}\].
The SI unit of molar conductance
\[=siemens\text{ }per\text{ }metre\text{ }per\text{ }\left( mol\text{ }per\text{ }litre \right)\]
\[=S\text{ }{{m}^{-1}}{{\left( mol\text{ }{{L}^{-1}} \right)}^{-1}}\]
\[=S\text{ }{{m}^{-1}}L\text{ }mo{{l}^{-1}}\]
\[\left( 1\text{ }litre\text{ }=\text{ }1000\text{ }c{{m}^{3}}=\text{ }1\text{ }d{{m}^{3}}=\text{ }{{10}^{-3}}{{m}^{3}} \right)\]
\[\therefore \] Units of molar conductance (${{\Lambda }_{m}}$)
\[=S{{m}^{-1}}{{10}^{-3}}{{m}^{3}}mo{{l}^{-1}}\]
\[={{10}^{-3}}S\text{ }{{m}^{2}}mo{{l}^{-1}}\]
\[=\left( mS \right)\text{ }{{m}^{2}}mo{{l}^{-1}}\]
\[1\text{ }millisiemen\text{ }\left( mS \right)\text{ }=\text{ }{{10}^{-3}}S\].
 The general SI unit of molar conductance (${{\Lambda }_{m}}$)
\[~=\text{ }S\text{ }{{m}^{2}}mo{{l}^{-1}}\]
\[1\text{ }S\text{ }{{m}^{2}}mo{{l}^{-1}}=\text{ }{{10}^{4}}S\text{ }c{{m}^{2}}~mo{{l}^{-1}}\]
or \[1\text{ }S\text{ }c{{m}^{2}}mo{{l}^{-1}}=\text{ }{{10}^{4}}S\text{ }{{m}^{2}}~mo{{l}^{-1}}\]
The following expression is used to mathematically represent the relationship between molar conductance and specific conductance of a solution.
${{\Lambda }_{m}}=\dfrac{\kappa }{c}$
where,
             ${{\Lambda }_{m}}$= molar conductivity
             $\kappa $ = specific conductivity
             c = concentration in mole per litre.

Note: The general definition of molar conductivity is presented as the conducting power of all the ions which are produced by dissolving one mole of an electrolyte in the solution. It can also be defined as the ionic strength of a solution or the concentration of salt.