Question

The measured resistance of a conductance cell was $100\Omega$ $({{M}_{KCl}}=74\cdot 5gmo{{l}^{-1}})$ and cell constant $=1\cdot 25c{{m}^{-1}}$. Calculate the molar conductance of the solution. If the answer is X, then give an answer as $X-10\cdot 5$.

Answer 1

Hint First find the specific conductance $\left( K \right)$ as it is required to find the molar conductance. Specific conductance can be found using cell constant and Resistance and both are given in the question. Cell Constant is the ratio of the distance between the electrode plates to the surface area of the plate.
Formula Used: $\text{K}\left( \text{Specific conductance} \right)=\dfrac{1}{\dfrac{a}{R}}$
Where $\dfrac{1}{a}\text{ }\to \text{ Cell Constant}$
$R\text{ }\to \text{ Resistance}$

Complete Step By Step Solution:
So, $K=\dfrac{1\cdot 25c{{m}^{-1}}}{100\Omega \left( Ohms \right)}=\text{ 0}\cdot \text{0125 }{{\Omega }^{-1}}\text{ c}{{\text{m}}^{-1}}$
The molar conductance is given as -$\lambda =\dfrac{1000K}{C}$
Here K is specific conductance and
C is concentration of the solution
Let us assume the concentration of the solution is $1M$
So, $\lambda =\dfrac{1000\times 0\cdot 0125}{1}=\dfrac{1000c{{m}^{3}}{{L}^{-1}}\times 0\cdot 0125oh{{m}^{-1}}c{{m}^{-1}}}{1mol{{L}^{-1}}}$
$\implies12\cdot 5oh{{m}^{-1}}c{{m}^{2}}mo{{l}^{-1}}$ $\left( oh{{m}^{-1}}\to \text{ Siemen}\left( S \right) \right)$
Now we have to give answer in the form $X-10\cdot 5$ so our X obtained is $12\cdot 5$
So, $\text{X}-\text{10}\cdot \text{5= 12}\cdot \text{5}-\text{10}\cdot \text{5}$
$\implies2$
Specific Conductance: It is the ability of a substance to conduct electricity. It is the reciprocal of specific resistance or resistivity. We can say that it is the conductance of one centimeter cube of a conductor.
Molar conductivity: It is defined as the conducting power of all the ions produced by dissolving one mole of an electrolyte in a solution. It is also defined as conductivity divided by its molar concentration. It is donated by lambda.
Specific Conductivity is equal to the molar conductivity multiplied by morality of the solution.

Note: The concepts of molarity, concentration, moles, conductivity, both specific and molar should be clear. The relations connecting cell constants, resistance, and the specific conductance should also be studied properly. Topics like resistivity, conductivity should be a given thorough reading, other similar concepts like normality, gram-equivalent weight should also be considered. One can go through the working, nature and properties of electrolytic solutions and the electrodes.