Question

The conductance of 0.1 M NaCl was measured in a conductivity cell having cell constant $\text{10 c}{{\text{m}}^{\text{-1}}}$ to be 22 mS. The molar conductivity of 0.1 M NaCl in appropriate units is
(A)- 22 mS cm/M
(B)- 22 mS M/cm
(C)- 2200 mS cm/M
(D)- 2200 mS/ (M cm)

Answer 1

Hint: The molar conductivity is related to the conductivity of the molar concentration of the electrolyte solution in the cell, which determines the conducting power of the ions of one moles of sodium chloride on dissolving in the solution.

Complete step by step answer:
In the given conductivity cell with 0.1M sodium chloride solution, with the conductance and the cell constant equal to 22 mS and $\text{10 c}{{\text{m}}^{\text{-1}}}$ respectively.
Then, the molar conductivity of the given solution is the conductance of volume of one mole of NaCl solution in the cell, having two electrodes of square unit area and 1 cm apart. That is, the conductivity (specific conductance) of the electrolyte solution by its molar concentration, where the specific conductance is the conductance of unit volume of cell given by:
$\text{Specific}\,\text{conductance =}\,\text{Conductance }\!\!\times\!\!\text{ Cell}\,\text{constant}$ with the SI unit equal to Siemen/metre.
So, substituting the values of conductance and cell constant in the above equation, we get, Specific conductance = $\text{22 mS }\!\!\times\!\!\text{ 10 c}{{\text{m}}^{\text{-1}}}=220\,\text{mS/cm}$.
Then, the molar conductivity of the 0.1M solution will be $\text{=}\dfrac{\text{specific}\,\text{conductance}}{\text{molar}\,\text{concentration}}=\dfrac{\text{220}\,\text{mS/cm}}{\text{0}\text{.1}\,\text{M}}=2200\,\,mS\,/Mcm$

Therefore, the molar conductivity of 0.1 M NaCl in appropriate units is option (D)- 2200 mS/ (M cm).

Note: The molar conductivity contributes to the determination of the ionic strength of the given solution. It varies for the weak or strong electrolyte on dilution, that is, with the decrease in the concentration, as more dissociation of the ions is produced. It is also used because the specific conductance of different electrolytes changes with the same solvent and temperature.