Question

The molar conductivity of a \[{\text{0}}{\text{.5 mol/d}}{{\text{m}}^{\text{3}}}\] solution of \[{\text{AgN}}{{\text{O}}_{\text{3}}}\] with electrolytic conductivity of \[5.76 \times 10 - 3{\text{Sc}}{{\text{m}}^{{\text{ - 1}}}}{\text{ }}\]at 298 K is:
A) \[{\text{0}}{\text{.086 Sc}}{{\text{m}}^{\text{2}}}{\text{/mol}}\]
B) \[{\text{028}}{\text{.8 Sc}}{{\text{m}}^{\text{2}}}{\text{/mol}}\]
C) \[{\text{2}}{\text{.88 Sc}}{{\text{m}}^{\text{2}}}{\text{/mol}}\]
D) \[{\text{11}}{\text{.52 Sc}}{{\text{m}}^{\text{2}}}{\text{/mol}}\]

Answer 1

Hint: Molar conductivity is the conductance power of all ions of 1 mole of an electrolyte in a specific volume of solution. We can calculate the molar conductivity using an equation related to specific conductance and molar concentration.

Formula Used: \[{\Lambda _{\text{m}}} = \dfrac{{{\text{K}} \times {\text{1000}}}}{{\text{M}}}\]

Complete step by step answer:
We have given the molar concentration of \[{\text{AgN}}{{\text{O}}_{\text{3}}}\] the solution and its electrolytic conductivity.
Molar concentration of \[{\text{AgN}}{{\text{O}}_{\text{3}}}\] = \[{\text{0}}{\text{.5 mol/d}}{{\text{m}}^{\text{3}}}\]
Electrolytic conductivity = \[5.76 \times 10^{ - 3}{\text{Sc}}{{\text{m}}^{{\text{ - 1}}}}{\text{ }}\]
Now, we can calculate the molar conductivity using an equation related to specific conductance and molar concentration as follows:
\[{\Lambda _{\text{m}}} = \dfrac{{{\text{K}} \times {\text{1000}}}}{{\text{M}}}\]
Here,
\[{\Lambda _{\text{m}}}\] = molar conductivity
\[{\text{K}}\] = specific conductance
M= molar concentration.
Now, we can substitute \[5.76 \times 10^{ - 3}{\text{Sc}}{{\text{m}}^{{\text{ - 1}}}}{\text{ }}\] for specific conductance, \[{\text{0}}{\text{.5 mol/d}}{{\text{m}}^{\text{3}}}\] for molar concentration and can calculate molar conductivity.
\[{\Lambda _{\text{m}}} = \dfrac{{5.76 \times 10^{- 3}{\text{Sc}}{{\text{m}}^{{\text{ - 1}}}}{\text{ }} \times {\text{1000}}}}{{{\text{0}}{\text{.5 mol/d}}{{\text{m}}^{\text{3}}}}}\]
\[{\Lambda _{\text{m}}} = {\text{11}}{\text{.52 Sc}}{{\text{m}}^{\text{2}}}{\text{/mol}}\]
Thus, the molar conductivity of the given \[{\text{AgN}}{{\text{O}}_{\text{3}}}\] solution is \[{\text{11}}{\text{.52 Sc}}{{\text{m}}^{\text{2}}}{\text{/mol}}\].

Hence, the correct option is an option (D) \[{\text{11}}{\text{.52 Sc}}{{\text{m}}^{\text{2}}}{\text{/mol}}\].

Additional Information: In electrolytic conduction, ions move towards the oppositely charged electrode. A measure of conductance of ions of 1 mole of electrolyte is known as molar conductance. More the number of ions in the solution greater is the molar conductance.

Note: Molar conductivity depends on the concentration of the electrolytic solution. It is inversely proportional to the concentration of the solution. Molar conductivity is used to determine the efficiency of an electrolyte to conduct the electricity in a solution. The conductivity of solution increases with dilution because on dilution the degree of ionisation of an electrolyte increases and more ions are produced in the solution.