Question

The conductance of 0.1M KCl (conductivity $ = {\text{X}} =
{\text{Oh}}{{\text{m}}^{ - 1}}$) is Y. If the conductance of $0.1{\text{ M}}$ ${\text{NaOH}}$ filled in the same cell is ${\text{Z Oh}}{{\text{m}}^{ - 1}}$, the molar conductance of ${\text{NaOH}}$ will be:
(A) ${10^3}\dfrac{{{\text{XZ}}}}{{\text{Y}}}$
(B) ${10^4}\dfrac{{{\text{XZ}}}}{{\text{Y}}}$
(C) $10\dfrac{{{\text{XZ}}}}{{\text{Y}}}$
(D) $0.1\dfrac{{{\text{XZ}}}}{{\text{Y}}}$

Answer 1

Hint: To solve this we must first calculate the cell constant. The cell constant is the ratio of conductivity of a solution to the conductance of the solution.After finding out the cell constant using the formula we can go for calculating the molar conductance.

Complete step by step solution:
We know that the cell constant is the ratio of conductivity of a solution to the conductance of the solution.
Thus,
Cell constant $ = \dfrac{{{\text{Conductivity}}}}{{{\text{Conductance}}}}$
We are given that the conductivity is X and the conductance is Y. Thus,
Cell constant $ = \dfrac{{\text{X}}}{{\text{Y}}}$
Now we have to calculate the molar conductance of the $0.1{\text{ M}}$ ${\text{NaOH}}$ solution.
We know the relationship between molar conductance and conductivity is given by the equation as follows:
${\lambda _m} = \dfrac{{K \times 1000}}{M}$ …… (1)
Where ${\lambda _m}$ is the molar conductance,
$K$ is the conductivity,
$M$ is the molarity.
We know the relationship between conductivity, cell constant and conductance is as follows:
Conductivity $ = {\text{Cell constant}} \times {\text{Conductance}}$
Thus, equation (1) becomes as follows:
${\lambda _m} = \dfrac{{{\text{Cell constant}} \times {\text{Conductance}} \times 1000}}{M}$
Substitute $\dfrac{{\text{X}}}{{\text{Y}}}$ for the cell constant, Z for the conductance, $0.1{\text{ M}}$ for the molarity and solve for the molar conductance as follows:
$\Rightarrow {\lambda _m} = \dfrac{{\dfrac{{\text{X}}}{{\text{Y}}} \times {\text{Z}} \times 1000}}{{0.1}}$
$\Rightarrow {\lambda _m} = \dfrac{{{\text{XZ}}}}{{\text{Y}}} \times {\text{1}}{{\text{0}}^4}$
Thus, the molar conductance of ${\text{NaOH}}$ will be ${10^4}\dfrac{{{\text{XZ}}}}{{\text{Y}}}$.

Thus, the correct option is (B) ${10^4}\dfrac{{{\text{XZ}}}}{{\text{Y}}}$.

Note: The conductance of a conductor always depends on the temperature, concentration of the electrolyte used. As the temperature of the conductor increases the concentration of the electrolyte increases. As the concentration of the electrolyte increases, the conductance of the conductor increases.