Question

Assertion
According to Kohlrausch’s law, the molar conductance of a strong electrolyte at infinite dilution is
sum of molar conductivities of its ions.
Reason
The current carried by cation and anion is always equal.
A. Both assertion and reason are correct and reasons is the correct explanation for assertion
B. Both assertion and reason are correct but reason is not correct explanation for assertion
C. Assertion is correct but reasons are incorrect.
D. Assertion is incorrect but reason is correct.

Answer 1

Kohlrausch’s law of independent migration of ions states that:
At infinite dilution, each ions migrate independently of its co-ions and make its own contribution to
total molar conductivity of an electrolyte irrespective of the nature of other ion with which it is
associated.
Current carried by any ion is dependent on the mobility of that ion.

Complete step by step answer:
The given assertion is correct
Because according to kohlrausch’s law molar conductivity of an strong electrolyte is the sum of
molar conductivities of the cation and molar conductivities of anion each multiplies with number of
ions present in the formula unit of an electrolyte.
That is ${\lambda _0} = {\text{ }}{\lambda ^0}_ + + {\text{ }}{\lambda ^0}_ -$
Where,
${\lambda _0}$= the molar conductivity of strong electrolyte at zero concentration.
${\lambda ^0}_ +$= the molar conductivity of cation at zero concentration
${\lambda ^0}_ -$= the molar conductivity of anion at zero concentration
For example, If we consider the strong electrolyte i.e. hydrochloric acid$\left( {HCl} \right)$, then
According to Kohlrausch’s law
Molar conductivity of hydrochloric acid ${\lambda _0}$= molar conductivity of ${H^ + }$ions i.e.
${\lambda _0}$ $\left( {{H^ + }} \right)$ + molar conductivity of $C{l^ - }$ions i.e. ${\lambda _0}$ $\left( {C{l^ - }} \right)$
Therefore the assertion is correct.
Now let’s see about reason,
Current carried by cation and anion is depend their mobility of ions and mobility of ions changes
with change in the size of that ion. Size of cation and anion is different cation has smaller size than
anion and hence both moves with different speed. Cation moves faster than anions hence current
carried by cation is more than that of anion.
Therefore the given reason is incorrect.
Hence assertion is correct and reason is incorrect
The correct option is C.

Note:
Some important application of kohlrausch law of independent migration of ions are
Kohlrausch law helps in the determination of limiting molar conductivities of any electrolyte. Weak
electrolyte have lower molar conductivity and lower degree of dissociation at higher concentration
than strong electrolyte.