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Question: The conductivity of \({\text{0}}{\text{.20 M}}\) solution of \({\text{KCl}}\) at \({\text{298 K}}\) ...

The conductivity of 0.20 M{\text{0}}{\text{.20 M}} solution of KCl{\text{KCl}} at 298 K{\text{298 K}} is 0.025 S cm−1{\text{0}}{\text{.025 S c}}{{\text{m}}^{ - 1}}. Calculate its molar conductivity.

Explanation

Solution

The conductance of a unit cube material is known as conductivity. The units of conductivity are S cm−1{\text{S c}}{{\text{m}}^{ - 1}} or S m−1{\text{S }}{{\text{m}}^{ - 1}}. The ratio of conductivity to the molar concentration of the dissolved electrolyte is known as its molar conductivity. The units of molar conductivity are S cm2 mol−1{\text{S c}}{{\text{m}}^2}{\text{ mo}}{{\text{l}}^{ - 1}} or S m2 mol−1{\text{S }}{{\text{m}}^2}{\text{ mo}}{{\text{l}}^{ - 1}}.

Formula used: Λ=kC\Lambda = \dfrac{k}{C}

Complete step by step answer:
Calculate the molar conductivity of the solution of KCl{\text{KCl}} using the equation as follows:
Λ=kC\Lambda = \dfrac{k}{C}
Where Λ\Lambda is the molar conductivity of the solution,
k is the conductivity of the solution,
C is the molar concentration of the solution.
The number of moles of a solute per litre of solution is known as the molarity of the solution. Thus, the molarity of the solution is 0.20 M=0.20 mol L−1{\text{0}}{\text{.20 M}} = 0.20{\text{ mol }}{{\text{L}}^{ - 1}}.
But 1 L=103 cm3{\text{1 L}} = {10^3}{\text{ c}}{{\text{m}}^3}. Thus, the molarity of the solution is 0.20×103 mol cm−30.20 \times {10^3}{\text{ mol c}}{{\text{m}}^{ - 3}}.
Substitute 0.025 S cm−1{\text{0}}{\text{.025 S c}}{{\text{m}}^{ - 1}} for the conductivity of the solution, 0.20×103 mol cm−30.20 \times {10^3}{\text{ mol c}}{{\text{m}}^{ - 3}} for the molarity of the solution. Thus,
Λ=0.025 S cm−10.20×103 mol cm−3\Lambda = \dfrac{{{\text{0}}{\text{.025 S c}}{{\text{m}}^{ - 1}}}}{{0.20 \times {{10}^3}{\text{ mol c}}{{\text{m}}^{ - 3}}}}
Λ=1.25×10−4 S cm2 mol−1\Lambda = 1.25 \times {10^{ - 4}}{\text{ S c}}{{\text{m}}^2}{\text{ mo}}{{\text{l}}^{ - 1}}
Thus, the molar conductivity of 0.20 M{\text{0}}{\text{.20 M}} solution of KCl{\text{KCl}} at 298 K{\text{298 K}} is 1.25×10−4 S cm2 mol−11.25 \times {10^{ - 4}}{\text{ S c}}{{\text{m}}^2}{\text{ mo}}{{\text{l}}^{ - 1}}.

Note: The conducting power of all the ions that are produced by dissolving one mole of any electrolyte in the solution is known as the molar conductivity of the solution.
As the temperature of the solution increases, the molar conductivity of the solution increases. This is because as the temperature increases the interaction and the mobility of the ions in the solution increases.
The molar conductivity of both strong and weak electrolytes increases as the dilution increases. This is because dilution increases the degree of dissociation and the total number of ions that carry current increases.