Question

The unit of molar conductance of an electrolyte solution will be
This question has multiple correct options
A. \[{\text{oh}}{{\text{m}}^{ - 1}}{\text{c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\]
B. \[{\text{mho c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\]
C. \[{\text{S c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\]
D. \[{\text{oh}}{{\text{m}}^{ - 1}}{\text{c}}{{\text{m}}^{ - 1}}{\text{mo}}{{\text{l}}^{ - 1}}\]

Answer 1

Hint:Write the relationship between the molar conductance and specific conductance. Then substitute the units of various quantities in these units and determine the unit of molar conductivity.

Complete answer:
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 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.
\[
  {\Lambda _m} = \dfrac{{1000{\text{c}}{{\text{m}}^3}{\text{d}}{{\text{m}}^{ - 3}} \times {\text{S/cm}}}}{{{\text{mol/d}}{{\text{m}}^3}}} \\
  {\Lambda _m} = {\text{S c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}} \\
 \]
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 \[{\text{oh}}{{\text{m}}^{ - 1}}{\text{c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\] .

Hence, the options A, B and C represent correct options. The option D, represents an incorrect answer.

Note:
Molar conductance gives the conductance of a solution containing one mole of the electrolyte. The specific conductance is the conductance of unit volume of electrolyte solution placed between two platinum electrodes having unit cross section area.