## Kohlrausch’s Law Chemistry Notes

**Kohlrausch’s Law :**

On the basis of various observations Kohlrausch proposed a law of independent transport of ions. According to this law, “The limiting molar conductivity of an electrolyte can be expressed as sum of different contribution of its cation and anion.”

OR

“The value of molar conductivity is different for different electrolytes because each ion of electrolyte contributes certainly amount molar conductivity at infinite dilution of solution. This contribution does not depend on nature of other ion of electrolyte. This contribution of an individual ion is called molar ionic conductivity.”

**Mathematical Representation of Kohlrausch’s Law :**

Mathematically, for calculation of molar conductivity at infinite dilution of electrolytic solution, the number of cations present in its unit formula is multiplied by molar conductivity of cation and number of anion is multiplied by molar conductivity of anion. Then, both are added.

**Applications of Kohlrausch’s Low :**

There are following applications of this law:

- With the help of this law, molar conductivity of weak electrolyte at inlinite dikition (\(\Lambda_{m}^{\infty}\))can be calculated.
- For example : If we want to determine molar conductivity of acetic acid at infinite dilution then it can be determined with the help of strong electrolytes such as NaCl, HCl and CH
_{3}COONa, which is as follows:

With the help of above equation, we can determine the molar conductivity of CH,COOH at infinite dilution.

Degree of Dissociation of Weak Electrolyte can also be determined by this law.

We know that,

- where, α = Degree of dissociation.
- \(\Lambda_{m}^{c}\) = Molar conductivity at concentration ‘C’
- \(\Lambda_{m}^{\infty}\) = Molar conductivity at infinite dilution

Dissociation Constant of Weak Electrolyte can also be determined by this law.

- K = \(\frac{C \alpha^{2}}{(1-\alpha)}\)
- Where, K -Dissociation constant
- α = Degree of dissociation
- C = Concentration

→ The Solubility of Partially soluble salts like AgCl, BaSO_{4}. PbSO_{4}, etc., can also be calculated by this law. Its formula is given as below:

\(\Lambda_{m}^{\infty}=\frac{\kappa \times 1000}{\text { Solubility }}\)

Where, k = Specific conductivity

\(\Lambda_{m}^{\infty}\) = Molar conductivity at infinite dilution

Ionic Product of Water can also be calculated with the help of this law.

The values of ionic molar conductivity of H^{+} and OH^{–} at infinite dilution are 349.8 ohm^{-1}cm^{2} mol^{-1} and 198.5 ohm^{-1}cm^{2}mol^{-1} respectively. So,

→ Calculation of Transport Number of lons-The ratio of molar conductivity of ion at infinite dilution and molar conductivity of that electrolyte (in which that ion is present) at infinite dilution is called transport number of the ions. We know that,

This law of independent transport of Kohlrausch is applicable to all strong and weak electrolytes uniformly.