Question

A 0.1M solution of a monobasic acid has a specific resistance of $\,'r'\,ohm - cm\,$ . Its molar conductivity is:
A.$\,\dfrac{{10}}{r}\,$
B.$\,10r\,$
C.$\dfrac{{{{10}^4}}}{r}$
D.$\dfrac{{{{10}^4}}}{{2r}}$

Answer 1

Hint: Conductance is the indicator of a material's ability to make electricity (electrons) pass through it smoother.Molar conductivity is a term used in electrolysis to measure the electrolytic conductance. It is a measure invented to overcome the limitations of specific conductivity, however there is a relationship between molar conductivity and specific conductivity.
Formula used:
${\Lambda _m} = \dfrac{{\kappa \times 1000}}{M}$
Where, ${\Lambda _m} = $ molar conductivity
$\kappa = $ specific conductance
$M = $ Molarity
$\kappa = \dfrac{1}{\rho }$
Where, $\kappa = $ specific conductance and $\rho = $ specific resistance

Complete answer:
Let us first understand what is molar conductivity;
Molar conductivity is the conductance property of an electrolyte solution containing one mole, or it is a function of the solution's ionic strength or salt concentration.Consequently, it is not a constant. In other words, molar conductivity can also be described as the conducting strength of all the ions that are produced while dissolving one mole of electrolyte in a solution.
Now, let us solve this question;
Let’s first analyse the given data;
$M = 0.1M$
$\kappa = r\,\Omega cm$
As we saw above, $\kappa = \dfrac{1}{\rho }$
Therefore, $\kappa = \dfrac{1}{r}$
(Since resistivity and resistance are directly proportional)
Also, the molar conductivity is given by ${\Lambda _m} = \dfrac{{\kappa \times 1000}}{M}$
Now, substituting in the equation of molar conductivity we get;
${\Lambda _m} = \dfrac{{\dfrac{1}{r} \times 1000}}{{0.1M}}$
On solving we get the value of molar conductivity as
$ = \dfrac{{{{10}^4}}}{r}$
Therefore, it is clear that option C is the correct answer for this question.

Additional information: With a decrease in concentration or dilution, the molar conductivity of both weak and solid electrolytes increases.We recognise that the conductivity provided by a single mole of ions is molar conductivity.We are still discussing the same unit mole of ions even after dilution.The additional dilution, however, results in the dissociation of further electrolytes into ions and the amount of activated ions in the solution also increases efficiently.More conductivity is imparted by these activated ions.

Note:
Various electrolytic solutions have varying concentrations and thus contain various ion numbers.Specific conductance is not an acceptable quantity to evaluate the conductance of different electrolytic solutions because of this. That is why molar conductivity was introduced and applied for this purpose instead. Specific conductance is otherwise known as conductivity and specific resistance is otherwise known as resistivity.