Question

For which of the following compound, the formula ${{\alpha = }}\dfrac{{{{{\lambda }}_{\text{v}}}}}{{{{{\lambda }}_\infty }}}{{\;}}$ does not hold good?
A) ${\text{C}}{{\text{H}}_{\text{3}}}{\text{COOH}}$
B) ${\text{HCl}}$
C) ${\text{HCl}}{{\text{O}}_{\text{4}}}$
D) ${\text{C}}{{\text{H}}_{\text{3}}}{\text{N}}{{\text{H}}_{\text{2}}}$

Answer 1

The given formula ${{\alpha = }}\dfrac{{{{{\lambda }}_{\text{v}}}}}{{{{{\lambda }}_\infty }}}{{\;}}$ holds good only for weak electrolytes. Weak electrolytes are solutions which do not dissociate completely in aqueous solution. In other words, they partly ionise in water.

Complete step by step solution:
According to Law of Dilution also known as Ostwald’s dilution law, the degree of dissociation, ${{\alpha }}$ is given as below:
${{\alpha = }}\dfrac{{{{{\lambda }}_{\text{v}}}}}{{{{{\lambda }}_\infty }}}{{\;}}$
where ${{{\lambda }}_{\text{v}}}$ is the molar conductivity at volume ‘$v$’,
${{{\lambda }}_\infty }$ is the molar conductivity at an infinite solution. It is also known as the limiting molar conductivity which has been extrapolated to zero concentration.
This equation holds good only for weak electrolytes. Weak electrolytes are the chemical solutions which only partly ionizes in solution.
In the given options, acetic acid (${\text{C}}{{\text{H}}_{\text{3}}}{\text{COOH}}$) and methyl amine (${\text{C}}{{\text{H}}_{\text{3}}}{\text{N}}{{\text{H}}_{\text{2}}}$) are weak electrolytes. While hydrochloric acid ( ${\text{HCl}}$ ) and perchloric acid (${\text{HCl}}{{\text{O}}_{\text{4}}}$) are strong electrolytes undergoing complete dissociation in aqueous solution.
Hence the given formula ${{\alpha = }}\dfrac{{{{{\lambda }}_{\text{v}}}}}{{{{{\lambda }}_\infty }}}{{\;}}$ does not hold good for strong electrolytes such as ${\text{HCl}}$ and ${\text{HCl}}{{\text{O}}_{\text{4}}}$.
So, the correct options are (B) and (C).

Note:
In case of strong electrolytes they obey Debye Huckel theory. The fundamental principle behind this theory is that the oppositely charged ions experience electrostatic attraction. This equation is valid for the dilution solution. In case of high concentration, the modified form Onsager equation is employed.