Kohlrausch's Law

Kohlrausch's Law

Kohlrausch's Law

In 1974, Kohlrausch formulated the law of independent migration of ions based on the experimental data of conductivities aof various electrolytes and stated that-
The equivalent conductivity of an electrolyte at infinite dilution (螞o) is the sum of the ionic conductivities of their cations and anions.
o = 位+ + 位
where- 位+ and 位 are cationic and anionic conductivities at infinite dilution respectively.
Kohlrausch's Law can also be states in terms of molar conductivities as-
The limiting molar conductivity of n electrolyte is the sum of individual contributions of limiting molar conductivities of its constituent ions.
Thus, molar equivalent conductivity of an electrolyte-
μo = n+μo+ + nμo
where, n+ and n are the coefficients of positive and negative ions formed during the dissociation of electrolytes and μo+ and μo are limiting molar conductivities of cations and anions respectively.

Applications of Kohlrausch's Law

Useful in
calculating equivalent conductivity at infinite dilution.
Calculation of degree of dissociation of an electrolyte.
Calculation of solubility of sparingly soluble salt,
Calculation of ionic product of water.

Q. Calculate the limiting molar conductivity of CH3COOH. The molar conductivities of CH3COONa, HCl and NaCl at infinite dilution are 90.1 S.cm2.mol-1, 426.16 S.cm2.mol-1 and 126.45 S.cm2.mol-1 respectively.

CH3COONa = 90.1 S.cm2.mol-1
HCl=426.16 S.cm2.mol-1
NaCl=126.45 S.cm2.mol-1
According to Kohlrausch law-
CH3COOH = 位CH3COONa + 位HCl – 位NaCl
or, 位CH3COOH = 90.1 + 426.16 – 126.45
or, 位CH3COOH = 390.71 S.cm2.mol-1
So, the limiting molar conductivity of CH3COOH is, 390.71S.cm2.mol-1.

Q. From the given molar conductivities at infinite dilution, calculate λm for NH4OH.
λm for Ba(OH)2 = 457.6 ohm-1 cm2mol-1
λm for Ba(Cl)2 = 240.6 ohm-1 cm2mol-1
λm for NH4Cl = 129.8 ohm-1 cm2mol-1

Answer: 238.3 ohm-1 cm2mol-1