Provide the graph of $\Lambda_{m}$ versus $c^{1/2}$ for aqueous solutions of strong and weak electrolytes,and clarify their differences and uses.

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(N/A) The graph of $\Lambda_{m}$ versus $c^{1/2}$ for aqueous solutions of strong and weak electrolytes is shown below:
Feature Strong Electrolyte (e.g.,$KCl$) Weak Electrolyte (e.g.,$CH_{3}COOH$)
Graph Nature Linear graph. Non-linear (curved) graph.
Kohlrausch Equation Follows $\Lambda_{m} = \Lambda_{m}^{o} - A c^{1/2}$. Does not follow this linear relation.
Determination of $\Lambda_{m}^{o}$ Can be obtained by extrapolating the graph to zero concentration (intercept). Cannot be obtained by extrapolation as the curve becomes parallel to the y-axis at low concentrations.

Uses:
$1$. For strong electrolytes,the graph allows the determination of molar conductivity at infinite dilution $(\Lambda_{m}^{o})$ using the intercept.
$2$. For weak electrolytes,$\Lambda_{m}^{o}$ cannot be determined graphically; it is calculated using Kohlrausch's Law of independent migration of ions.

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