Kohlrausch Law in Chemistry: Concept, Formula, and Uses

The formula for Kohlrausch's law is:
Λ°_m = ν₊λ°₊ + ν_-λ°_-
Where:

• Λ°_m is the limiting molar conductivity of the electrolyte.
• λ°₊ and λ°_- are the limiting molar conductivities of the individual cation and anion, respectively.
• ν₊ and ν_- are the number of cations and anions produced per formula unit of the electrolyte upon dissociation.

Kohlrausch's law has several important applications, including:

• Calculating the limiting molar conductivity (Λ°_m) of weak electrolytes, which cannot be determined experimentally.
• Determining the degree of dissociation (α) of a weak electrolyte at a given concentration.
• Calculating the solubility of sparingly soluble salts like AgCl or BaSO₄.
• Finding the dissociation constant (K_a) for weak acids.

Weak electrolytes, such as acetic acid (CH₃COOH), do not dissociate completely in solution at any concentration. Therefore, their limiting molar conductivity cannot be found by extrapolating a graph to zero concentration. Kohlrausch's law provides an indirect method to calculate this value by using the known ionic conductivities of strong electrolytes, overcoming a major experimental limitation.

To find the limiting molar conductivity of acetic acid (a weak electrolyte), you need the Λ°_m values of three strong electrolytes: HCl, NaCl, and CH₃COONa. The calculation is performed as follows:
Λ°_m(CH₃COOH) = [Λ°_{m(CH₃COONa)} + Λ°_m(HCl)] - Λ°_m(NaCl)
This works because the ionic conductivities of Na⁺ and Cl⁻ ions are effectively subtracted, leaving only the sum of the conductivities for H⁺ and CH₃COO⁻ ions.

Limiting molar conductivity (Λ°_m) represents the molar conductivity of an electrolyte when its concentration approaches zero (infinite dilution). At this point, the inter-ionic forces of attraction are negligible, allowing each ion to move independently and contribute its maximum value to the total conductivity.

For a sparingly soluble salt like AgCl, its saturated solution is considered to be at infinite dilution due to the very low concentration of ions. Kohlrausch's law is used to calculate the salt's Λ°_m from the ionic conductivities of Ag⁺ and Cl⁻. The solubility (S), which is equal to the molar concentration, can then be found using the formula:
S = (κ × 1000) / Λ°_m, where κ is the specific conductivity of the saturated solution.

The key difference lies in how their molar conductivity changes with dilution:

• Strong Electrolytes: Show a small, gradual increase in molar conductivity as dilution increases. This is because dilution reduces the inter-ionic forces, allowing ions to move more freely.
• Weak Electrolytes: Show a sharp and significant increase in molar conductivity upon dilution. This is because dilution shifts the equilibrium to favour more dissociation, drastically increasing the number of ions in the solution.

Yes, both factors are crucial. An ion's individual contribution (limiting ionic conductivity) depends on its charge and mobility. Higher charges lead to stronger interaction with the electric field, increasing conductivity. Ionic mobility is influenced by the ion's size; however, it is the hydrated radius (size of the ion with its surrounding water molecules) that matters. Smaller hydrated ions, like H⁺, are more mobile and have exceptionally high conductivity.

Yes, the principle of independent migration of ions, which is the basis of Kohlrausch's law, is strictly valid only at infinite dilution. This is because at any finite concentration, ions are close enough to exert forces of attraction and repulsion on each other. These inter-ionic forces hinder the free movement of ions, meaning they no longer migrate independently, and the total conductivity is less than the theoretical sum of their individual contributions.