Question: In infinite dilutions, the equivalent conductance of \[B{a^{2 + }}\] and \[C{l^ - }\] are \[127\] an...

Question

In infinite dilutions, the equivalent conductance of $B{a^{2 + }}$ and $C{l^ - }$ are $127$ and $76oh{m^{ - 1}}c{m^2}mo{l^{ - 1}}$ . The equivalent conductivity of $BaC{l_2}$ at infinite dilution is:
A. $101.5$
B. $139.5$
C. $203$
D. $279.5$

Answer 1

Solution

In the case of infinite solutions, it is explained by the term which the solution consists of too much solvent. And there does not occur any change in the concentration of the solution by adding more solvent. Which means, the concentration will be constant in indefinite solutions. And it can be explained on the basis of Kohlraush’s law.

Complete answer:
The equivalent conductivity of $BaC{l_2}$ at infinite dilution is not equal to $101.5$ . Hence, option (A) is incorrect.
The equivalent conductance is explained as the conducting power or the strength of all the ions which creates per one gram of electrolyte.
According to the question, the equivalent conductance of $B{a^{2 + }}$ and $C{l^ - }$ are $127$ and $76oh{m^{ - 1}}c{m^2}mo{l^{ - 1}}$ .
The molar conductivity of the barium chloride is the sum of molar conductivity of barium as well as chlorine ions. That is,
${\lambda _m}\infty \,for\,BaC{l_2} = {\lambda _m}{\infty _{(B{a^{2 + }})}} + 2{\lambda _m}{\infty _{(C{l^ - })}}$
And the equivalent conductivity of $BaC{l_2}$ at infinite dilution can be find out by using the equation,
${\lambda _m}\infty \,for\,BaC{l_2} = \dfrac{1}{2}{\lambda _m}{\infty _{(B{a^{2 + }})}} + 2{\lambda _m}{\infty _{(C{l^ - })}}$
Substitute the values of equivalent conductance of $B{a^{2 + }}$ and $C{l^ - }$ in above equation, then the equivalent conductivity of $BaC{l_2}$ at infinite dilution $= \dfrac{{127}}{2} + 76$
$= 139.5oh{m^{ - 1}}c{m^2}e{q^{ - 1}}$ .Hence, the option (B) is correct.
The equivalent conductivity of barium chloride is not equal to $203$ . Hence, option (C) is incorrect.
The equivalent conductivity of $BaC{l_2}$ is not equal to $279.5$ . Hence, the option (D) is incorrect.

Hence, the option (B) is correct.

Note:
We need to know that according to Kohlraush’s law, at infinite dilution, the equivalent conductivity of an electrolyte is the sum of the conductance of cations and anions and it will not depend on the migration of ions. When the electrolyte is at infinite dilution, the equivalent conductance of that electrolyte becomes constant. During the dilution process, the molar conductivity and molar conductivity will be increased.