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# The conductivity of$0\cdot 1\text{N}$$\text{NaOH}$solution is$0\cdot 022\text{ S c}{{\text{m}}^{-1}}$. To this solution an equal volume of $0\cdot 1\text{N}$HCl solution is added which results into decrease of the conductivity of solution to$0\cdot 0055\text{ S c}{{\text{m}}^{-1}}$. The equivalence of conductivity of $\text{NaCl}$solution is$\text{S c}{{\text{m}}^{2}}$ equi ${{\text{v}}^{-1}}$is:A. $0\cdot 055$B. $0\cdot 11$C. 110D. 50

Last updated date: 14th Sep 2024
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Hint: Conductance: The conductance is the property of the conductor (metallic as well as electrolytic) which facilitates flow of electricity through it.
Equivalence Conductivity: It is defined as the conductance of all the ions produced by one gram equivalent of an electrolyte in a given solution. It is denoted by$\vartriangle$ .

Formula used:
${{\vartriangle }_{\text{e}}}=\text{K}\times \dfrac{1000}{\text{C}}$ or$\text{K}\times \dfrac{1000}{\text{N}}$
Where K= conductivity
N= normality

In the statement given that normality of solution 0.1N whose conductance is $0\cdot 022\text{ S c}{{\text{m}}^{-1}}$& when $0\cdot 1\text{N}$ is added to solution, the conductance becomes equal to.
Equivalent conductance$=\text{K}\times \dfrac{1000}{\text{N}}$
Where $\text{K}=0\cdot 055$
N$=0\cdot 1$
And NaOH and HCl give two electrons after reaction. So that equivalence conductance becomes double
Therefore,$\vartriangle =2\times \dfrac{\text{K}\times \text{1000}}{\text{N}}$
$\vartriangle =2\times \dfrac{0\cdot 055\times 1000}{0\cdot 1}$
On solving the equation we get equivalence conductance is$110\text{ S}-\text{c}{{\text{m}}^{2}}\text{ equi}{{\text{v}}^{-1}}$.

So, the correct answer is “Option C”.

Molar conductance:- Molar conductance is defined as the capacity of the dissociate ions to conduct electricity when the solution is diluted. It is denoted by lambda$\left( \text{ }\!\!\lambda\!\!\text{ } \right)$and its unit is given by $\text{S c}{{\text{m}}^{2}}\text{ mo}{{\text{l}}^{-1}}$.
$\vartriangle \text{m}=\text{K/C}$