Question

The conductivity of saturated solution of silver oxalate is $4.5\times {{10}^{-5}}{{\Omega }^{-1}}c{{m}^{-1}}$. If it's ${{K}_{SP}}=1.35\times {{10}^{-11}}{{M}^{3}}$. The molar conductivity of saturated solution would be
(1) $250{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}$
(2) $300{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}$
(3) $350{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}$
(4) $400{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}$

Answer 1

Hint: The answer to this question is based on the physical chemistry part that includes the concept of molar conductivity of the solution that is given by the formula, Molar conductivity = $\dfrac{K(conductivity)}{C(concentration)}$

Complete Solution : The concepts of physical chemistry that deals with the chapters of several calculations like molar conductivity, resistivity, molarity, molality etc., are familiar to us.
Now, let us see what molar conductivity is and how it is calculated.
- Molar conductivity is the conductivity of an electrolytic solution which is the ratio of conductivity to that of its molar concentration.
Thus, it is given by, Molar conductivity = $\dfrac{K(conductivity)}{C(concentration)}$ ………..(1)
- Solubility product plays an important role here and is defined as it is the type of dynamic equilibrium which exists when a chemical compound in the solid is in equilibrium with a solution of that compound.

-Now, from the given data we have, ${{K}_{sp}}=1.35\times {{10}^{-11}}{{M}^{3}}$ …….(2)
Now, the dissociation of silver oxalate is as shown below along with the solubility product,
      \[A{{g}_{2}}{{C}_{2}}{{O}_{4}}\to 2A{{g}^{+}}+{{C}_{2}}{{O}_{4}}^{2-}\]

Thus, the solubility product is given by,
 ${{K}_{sp}}={{(2s)}^{2}}\times s=1.35\times {{10}^{-11}}{{M}^{3}}$
\[\Rightarrow 4{{s}^{3}}=1.35\times {{10}^{-11}}\]
\[\Rightarrow s=\sqrt{\dfrac{1.35\times {{10}^{-11}}}{4}}=1.5\times {{10}^{-3}}M\] …………(3)
Thus, the molar concentration is \[1.5\times {{10}^{-3}}M\]
Substituting equation numbers (2) and (3) in equation (1) we get,

Molar conductivity \[=\dfrac{4.5\times {{10}^{-5}}}{1.5\times {{10}^{-3}}}=3\times {{10}^{-2}}{{\Omega }^{-1}}{{m}^{2}}mo{{l}^{-1}}\]
\[\Rightarrow \] Molar conductivity = $300{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}$
Therefore, the correct answer is option 2) $300{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}$
So, the correct answer is “Option B”.

Note: Note that molar conductivity and molar conductivity are two different terms. Conductivity simply means that the conductance of the solution per unit volume and it can also be considered as the concentration of ions per unit volume of the solution whereas molar conductivity means the conductivity of the entire solution that is having 1 mole of electrolyte dissolved in it.