Conductivity and Molar Conductivity

Conductivity and molar conductivity are important concepts in the field of chemistry that help us understand the ability of substances to conduct electricity in solution. These properties are particularly relevant in the study of electrolytes, which are substances that dissociate into ions when dissolved in a solvent.

Conductivity
Conductivity is a measure of how well a substance conducts electricity. It is defined as the reciprocal of resistivity and is represented by the symbol σ. Conductivity is influenced by factors such as the concentration of ions, the mobility of the ions, and the temperature of the solution. The unit of conductivity is Siemens per meter (S/m).

Molar Conductivity
Molar conductivity is the conductivity of a solution containing one mole of solute in a volume of one liter. It is represented by the symbol Λm and is measured in Siemens per meter squared per mole per liter (S·m²·mol⁻¹·L⁻¹). Molar conductivity is a useful parameter to compare the conductivity of different solutions at the same concentration.

The Relationship between Conductivity and Molar Conductivity
The molar conductivity of a solution is directly proportional to its conductivity. The relationship between these two properties can be expressed using the equation:

Λm = κ / c

where Λm is the molar conductivity, κ is the conductivity, and c is the concentration of the solution. This equation shows that molar conductivity decreases with increasing concentration, as the number of ions per unit volume decreases.

Applying the Kohlrausch Law
The Kohlrausch Law states that the molar conductivity of an electrolyte at infinite dilution is the sum of the molar conductivities of its constituent ions. This law allows us to determine the molar conductivity of individual ions in a solution by measuring the molar conductivity of the electrolyte at different concentrations.

The Kohlrausch Law equation:
Λm = Λm⁰ - (A⁺ × Λm⁺⁺) - (A⁻ × Λm⁻⁻)

where Λm is the molar conductivity of the electrolyte, Λm⁰ is the molar conductivity at infinite dilution, A⁺ and A⁻ are the concentrations of the cation and anion, and Λm⁺⁺ and Λm⁻⁻ are the molar conductivities of the cation and anion at infinite dilution, respectively.

Conclusion
Conductivity and molar conductivity are important properties that help us understand the ability of substances to conduct electricity in solution. By studying these properties, scientists can gain insights into the behavior of electrolytes and their constituent ions. The relationship between conductivity and molar conductivity, as well as the application of the Kohlrausch Law, allows for the determination of molar conductivities of individual ions in a solution.