Question

The charge on cation and anion of an electrolyte is ${\nu ^ + }$ and ${\nu ^ - }$ respectively. One molecule of electrolyte furnishes ‘c’ cations and ‘a’ anions. Which expression is not correct?
A)${\lambda _M} = {\lambda _{eq}} \times ({\nu ^ + } \times c)$
B)${\lambda _M} = {\lambda _{eq}} \times ({\nu ^ - } \times a)$
C)${\lambda _M} = {\lambda _{eq}} \times {\nu ^ + }$
D)${\lambda _M} = {\lambda _{eq}} \times ({\text{total charge on cation or anion}})$

Answer 1

Recall the relationship between equivalent conductivity and molar conductivity. In general, if one molecule of an electrolyte gives ‘c’ cations and ‘a’ anions, then molar conductivity will be the multiplication of equivalent conductivity and total charge on either cations or anions present in one formula unit of the electrolyte.

Complete step by step answer:
In the question, we are given that one molecule of an electrolyte furnishes ‘c’ number of cations and ‘a’ number of anions.
Since, charge on each cation is ${\nu ^ + }$ and charge on each anion is ${\nu ^ - }$.
Therefore, total charge on cation will be: ${\nu ^ + } \times c$
And, total charge on anion will be: ${\nu ^ + } \times a$
Relationship between molar conductivity and equivalent conductivity:
molar conductivity (${\lambda _M}$) = equivalent conductivity (${\lambda _{eq}}$) $\times$ equivalent factor of the electrolyte
And, the equivalent factor of the electrolyte is generally equal to the total charge on either anions or cations present in one formula unit of the electrolyte.
Therefore, we get equation as: ${\lambda _M} = {\lambda _{eq}} \times ({\text{total charge on cation or anion}})$
Also, total charge on cation is: ${\nu ^ + } \times c$and, total charge on anion is: ${\nu ^ + } \times a$
Therefore, we can also write the equation as: ${\lambda _M} = {\lambda _{eq}} \times ({\nu ^ + } \times c)$,
Or, ${\lambda _M} = {\lambda _{eq}} \times ({\nu ^ - } \times a)$
Therefore, equations in options A, B and D are correct and in option C is incorrect.
Thus, option C is the answer.

Note: Equivalent conductivity or equivalent conductance (${\lambda _{eq}}$): It is the conductance of all the ions produced by one gram equivalent of an electrolyte in solution.
Molar conductance or conductivity (${\lambda _M}$): It is the conductance of all the ions produced by one mole of an electrolyte in solution. Conductance is the ease with which the current flows through the electrolyte. It is the reciprocal of the resistance.