The equivalent conductance at infinite dilution of $\text{HCl }$ and $\text{NaCl}$ are 426.15 and 126.15 $\text{mhoc}{{\text{m}}^{2}}\text{g e}{{\text{q}}^{-1}}$ respectively. It can be said that the mobility of:
A. ${{\text{H}}^{+}}$ ions is much more than that of $\text{C}{{\text{l}}^{-}}$ ions.
B. $\text{C}{{\text{l}}^{-}}$ ions is much more than that of ${{\text{H}}^{+}}$ ions.
C. ${{\text{H}}^{+}}$ ions is much more than that of $\text{N}{{\text{a}}^{+}}$ ions.
D. $\text{N}{{\text{a}}^{+}}$ ions is much more than that of${{\text{H}}^{+}}$ ions.

Answer Verified Verified
Hint: The equivalent conductance tells us about the conductance of ions that is produced by the 1 gram equivalent of a substance. Strong electrolyte completely dissociates in the solution whereas weak electrolytes don't.

Complete step by step answer:
- It is given in the question, that the molar conductance of $\text{HCl }$ and $\text{NaCl}$ are 426.15 and 126.15 $\text{mhoc}{{\text{m}}^{2}}\text{g e}{{\text{q}}^{-1}}$ respectively which means hydrochloric acid has the higher value than sodium chloride.
- Here, we know that hydrochloric acid is a strong acid and strong electrolyte also. Which means it will completely dissociate into its respective ions.
- Due to the complete dissociation, ions separate from each other and the concentration of ions increases. The increase in the concentration of the ions increases the conductivity and hence, the value of equivalent conductance also increases.
- Here, between $\text{HCl }$and $\text{NaCl}$, the $\text{C}{{\text{l}}^{1-}}$ is a common ion so we will neglect the mobility of chlorine ion.
- So, between ${{\text{H}}^{+}}$ and $\text{N}{{\text{a}}^{+}}$, ${{\text{H}}^{+}}$ ions have a higher value of equivalent conductance.
- It indicates the higher mobility of ${{\text{H}}^{+}}$ions than the sodium ions.
Therefore, option C is the correct answer.

Note: The theory of electrolytic dissociation was given by Arrhenius which states that if the electrolyte is completely dissociated then the value of molar conductance at infinite dilution will be higher.