Question

What is molar conductivity? How is it related to the concentration of electrolyte?

Answer 1

Hint: Molar conductance gives the conductance of a solution containing a definite amount of the electrolyte. This definite amount is in terms of moles. With increase in dilution, the molar conductivity increases.

Complete answer:
If you measure the conductance of one mole of a solution, you will obtain molar conductivity.
Write the expression for the molar conductance of an electrolyte solution as shown below:
\[{\Lambda _m} = \dfrac{{1000 \times \kappa }}{C}\]
Here, \[{\Lambda _m}\] represents the molar conductance of an electrolyte solution, \[\kappa \] represents the specific conductance of that electrolyte solution and C represents the concentration of electrolyte.
The specific conductance is the conductance of unit volume of electrolyte solution placed between two platinum electrodes having unit cross section area.
The unit of the specific conductance \[\kappa \] is \[{\text{S/cm}}\] or siemens per centimeter. The unit of concentration is moles per litre or \[{\text{mol/d}}{{\text{m}}^3}\] .
Substitute units in equation (1) and find out the unit of the molar conductance.
\[
  {\Lambda _m} = \dfrac{{1000{\text{c}}{{\text{m}}^3}{\text{d}}{{\text{m}}^{ - 3}} \times {\text{S/cm}}}}{{{\text{mol/d}}{{\text{m}}^3}}} \\
  {\Lambda _m} = {\text{S c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}} \\
 \]
From the expression \[{\Lambda _m} = \dfrac{{1000 \times \kappa }}{C}\] you can say that the molar conductivity is inversely proportional to the concentration. With increase in the concentration, the molar conductivity decreases. Molar conductivity is directly proportional to dilution. With increase in dilution, the molar conductivity increases.

Note:
The unit siemens is also known as mho or \[{\text{oh}}{{\text{m}}^{ - 1}}\].
Hence, you can also write the units of molar conductance as either \[{\text{mho c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\] or \[{\text{oh}}{{\text{m}}^{ - 1}}{\text{c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\] .