Question

Resistance of 0.2M solution of an electrolyte is 50$\Omega $. The specific conductance of the solution is $1.4S{{m}^{-1}}$. The resistance of 0.5M solution of the same electrolyte is 280$\Omega $. The molar conductivity of 0.5M solution of the electrolyte in $S{{m}^{2}}mo{{l}^{-1}}$ is:
A) $5\times {{10}^{3}}$
B) $5\times {{10}^{2}}$
C) $5\times {{10}^{-4}}$
D) $5\times {{10}^{-3}}$

Answer 1

Hint: According to thermodynamics in chemistry, calculation of thermal resistivity leads to the required answer where the formula is given by $R=\dfrac{l}{k\times A}$. Thus the answer to this solution includes calculation of molar conductivity by its formula.

Complete step by step answer:
According to the data given we have,
Resistance R=0.2M and specific conductance k=$1.4S{{m}^{-1}}$
Therefore, according to the formula $R=\dfrac{l}{k\times A}$,
Substituting the above values,
$50=\dfrac{1}{1.4}\times \dfrac{l}{A}$ $\Rightarrow \dfrac{l}{A}=70{{m}^{-1}}$
$\Rightarrow \dfrac{l}{A}=70{{m}^{-1}}$ …….(1)
Similarly, for same electrolyte having different concentration i.e.,0.5M solution having R= 280$\Omega $, applying the above formula we get,
$R=\dfrac{1}{k}\times \dfrac{l}{A}$ Substituting equation (1) in above formula we get,
$\begin{align}
& 280=\dfrac{1}{k}\times 70 \\
& k=\dfrac{1}{4}S{{m}^{-1}} \\
\end{align}$
Now, molar conductance is given by the formula,
${{\Lambda }_{m}}=\dfrac{k}{1000\times m}$
where, ${{\Lambda }_{m}}$= molar conductivity
k= specific conductance calculated
m= molarity of the solution
By substituting the calculated specific conductance and the molarity of solution that is 0.5M, we get \[{{\Lambda }_{m}}=\dfrac{1/4}{1000\times 0.5}=\dfrac{1}{2000}\]
\[\Rightarrow {{\Lambda }_{m}}=5\times {{10}^{-4}}S{{m}^{2}}mo{{l}^{-1}}\]

Thus, option C) is the correct answer.

Additional information:
Molar conductivity depends on several factors such as temperature, distance between the electrodes and concentration of electrolytes in the solution. The molar conductivity depends inversely on dilution of solution also. On increasing the dilution that is on making the solution more dilute, the molar conductivity increases because of increased ionic dissociation.
Thermal resistance is a heat property and a measurement of a temperature difference wherein a material resists a heat flow. This property is necessary in several electrical applications and in various instruments as well.

Note: Thermal resistance is the reciprocal of thermal conductance. While calculating the thermal resistance care is to be taken that it is not substituted by formula of thermal resistivity. The units are to be the same throughout solving equations.