Question

The molar conductance at infinite dilution for electrolytes BA and CA are $140$ and $120oh{m^{ - 1}}c{m^2}mo{l^{ - 1}}$ . If the molar conductance at infinite dilution of BX is $198oh{m^{ - 1}}c{m^2}mo{l^{ - 1}}$ , then at infinite dilution, the molar conductance of CX is ____.
A.$178$
B.$198$
C.$218$
D.$130$

Answer 1

We have to remember that at infinite dilution (excess of solvent is added), the molar conductivity (conductivity of all the ions from one mole of the electrolyte) of an electrolyte can be expressed as the sum of the contribution from its individual ions are expressed as Kohlrausch’s law. Friedrich Wilhelm Georg Kohlrausch was a German scientist and he is one of the most important physicists.

Complete answer:
We must know that the Kohlrausch’s law one of the uses is calculation of molar conductivity at infinite dilution for weak electrolytes, and also degree of association is calculated by the use of Kohlrausch’s law. Kohlrausch’s law also used to calculate the sparingly soluble salt solubility and for weak electrolytes dissociation constant is calculated.
Given, BA and CA are $140$ and $120oh{m^{ - 1}}c{m^2}mo{l^{ - 1}}$ and the molar conductance at infinite dilution of BX is $198oh{m^{ - 1}}c{m^2}mo{l^{ - 1}}$ .
From Kohlrausch’s law,
${\lambda ^0}_{CX} = {\lambda ^0}_C + {\lambda ^0}_X$
The above equation can be written as,
${\lambda ^0}_{CX} = {\lambda ^0}_{CA} + {\lambda ^0}_{BX} - {\lambda ^0}_{BA}$
Now we can substitute the known values we get,
$\Rightarrow {\lambda ^0}_{CX} = 120 + 198 - 140$
On simplification we get,
$\lambda _{CX}^0 = 178$
And hence Option A. $178$ is the correct answer.

Additional information:-
We must remember that the elasticity, thermal conduction, thermoelasticity, electrical and magnetic precision measurements are also investigated by Kohlrausch. Kohlrausch invented the bridge, which is used to measure conductivity and the Kohlrausch bridge is still used for measuring conductivity. Almost $50$ years he spent on electrochemical phenomena, magnetic and electrical instruments.

Note:
We have to remember that the Kohlrausch’s law has many applications in electrolytes. Sparingly soluble salts like $AgCl$ , $BaS{O_4}$ etc. dissolves very little in water and the solutions are considered as infinitely dilute. The determining the specific conductivity, $K$ , and the molar conductivity is calculated from the formula, ${\lambda _m}^0 = k \times \dfrac{{1000}}{{Molarity}} = k \times \dfrac{{1000}}{{so\operatorname{lub} ility}} = \dfrac{{k \times 1000}}{{\lambda _m^0}}$
-He wrote a book that contains measuring techniques and experimental setup and also contains a physical quantities table.