The Kohlrausch's Law of Independent Migration of Ions

Kohlrausch's Law states that the limiting molar conductivity of an electrolyte is obtained by adding the limiting molar conductivities of the cation and anion of the electrolyte. This law is based on the assumption that each ion moves independently and contributes to the overall conductivity of the electrolyte.

Conductivity Measurements and Ionization Constant

Conductivity measurements can be used to determine the ionization constant of a weak electrolyte like acetic acid. When a weak electrolyte is dissolved in water, it partially ionizes into ions. The degree of ionization can be quantitatively determined by measuring the conductivity of the solution at different concentrations.

By measuring the conductivity of acetic acid solutions of varying concentrations, the molar conductivity can be calculated using the equation:

Molar conductivity (Λ) = Conductivity (κ) / Concentration (C)

The molar conductivity can then be plotted against the square root of the concentration, known as the Debye-Hückel-Onsager equation, which gives a linear relationship. From this plot, the intercept on the y-axis gives the limiting molar conductivity (Λ°) of the weak electrolyte.

The ionization constant (Ka) of acetic acid can be determined using the equation:

Ka = (Λ°)^2 / C

where C is the concentration of the weak electrolyte. By substituting the values of Λ° and C obtained from the conductivity measurements, the ionization constant can be calculated. Therefore, conductivity measurements provide a convenient method to determine the ionization constant of weak electrolytes.

Change of Conductivity and Molar Conductivity with Dilution

When a solution is diluted, both the conductivity and molar conductivity of the solution change. This can be explained by the following factors:

1. Decrease in Ionic Concentration: As the solution is diluted, the number of ions per unit volume decreases. Therefore, the conductivity of the solution decreases because there are fewer ions available to carry the electric current.

2. Increase in Solvent Mobility: Dilution increases the mobility of the solvent molecules, allowing them to move more freely. This enables a better collision between ions and solvent molecules, leading to increased ionization and increased conductivity.

3. Change in Ion-Ion Interactions: Dilution reduces the ion-ion interactions in a solution, leading to a decrease in the effective size of ions. This decrease in ion size results in an increase in the molar conductivity of the solution.

In summary, dilution of a solution leads to a decrease in conductivity due to the decrease in ionic concentration, but an increase in molar conductivity due to the decrease in ion-ion interactions and increased solvent mobility.