Kohlrausch’s law, also known as the law of Independent migration of Ions, tells us that the total of the limiting molar conductance of cations and anions of an electrolyte is equal to the molar conductivity of that electrolyte. This law helps us study electrochemical cells and diluted liquids and is applicable in determining weak electrolytes’ molar conductivity.

In this article, we will learn the concepts of Kohlrausch law, its applications, etc. We have to study Kohlrausch Law in Class 12 for board exams.

What is Kohlrausch’s Law?

Kohlrausch Law, also known as Kohlrausch’s Law of Independent Migration of Ions, refers to an electrolyte’s limiting molar conductivity to its constituent ions. The law was proposed by Friedrich Kohlrausch in the late 19th century and is used to calculate the limiting molar conductivity, degree of dissociation, and dissociation constant of weak electrolytes. It is also used to measure the solubility of the salt.

For example, the limiting molar conductivity, of sodium chloride is determined when the limiting molar conductivities of sodium ion and chloride ion are given.

Λ^o_NaCl = Λ^o_Na+ + Λ^o_Cl-

Statement of Kohlrausch law

Limiting molar conductivity of an Electrolyte equals the sum of the individual limiting molar conductivities of the cations and anions that make up the electrolyte.

What is Molar Conductivity?

Molar conductivity is a measure of the ability of a substance to conduct electricity in solution. It is defined as the conductivity of a solution containing one mole of the substance in question. Molar conductivity is usually denoted by the symbol Λ_m and is expressed in units of Siemens per meter squared per mole (S m² mol⁻¹).

The molar conductivity of a solution increases with the decrease in concentration. This increase in molar conductivity is because of the rise in the total volume containing one mole of the electrolyte. When the electrolyte concentration approaches zero, the molar conductivity is known as the limiting molar conductivity, Λ°_m. Kohlrausch’s Law is based on molar conductivity and is widely used to study dilute liquids and electrolyte solutions.

Formula of Kohlrausch law

Kohlrausch’s Law, also known as the Law of Independent Migration of Ions, states that at infinite dilution when dissociation is complete, each ion makes a definite contribution towards the equivalent conductance of the electrolyte. In other words, the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the individual ions. The law can be expressed as:

λ^∞_eq = λ^∞_c + λ^∞_a

where,

• λ_eq∞ is Molar Conductivity at infinite dilution
• λ_c∞ is Conductivity of the cation at infinite dilution
• λ_a∞ is Conductivity of the anion at infinite dilution

Kohlrausch’s Law is essential for calculating the limiting molar conductivity, degree of dissociation, and dissociation constant of weak electrolytes, as well as for determining the solubility of salts.

It is based on the concept that at infinite dilution when dissociation is complete, each ion makes a definite contribution towards the equivalent conductance of the electrolyte. The law is beneficial in studying dilute liquids and electrolyte solutions, as it allows for calculating the behavior of ions in such systems.

Kohlrausch’s Law of Independent Migration

Some applications of Kohlrausch’s law of independent migration of ions are:

Kohlrausch’s Law of Independent Migration of Ions can be represented graphically by plotting an electrolyte’s molar conductivity (λm) against the square root of its concentration (√c). According to Kohlrausch’s Law, the plot should be a straight line with an intercept equal to the limiting molar conductivity (λ∞m) and a slope similar to -A, where A is a constant.

The value of A depends on the type of electrolyte and the temperature at which the measurement is taken. The graph obtained by plotting λm against √c helps determine the limiting molar conductivity of weak electrolytes, which cannot be obtained by extrapolation of molar conductivity to zero concentration. The value of λ∞m can be determined from the intercept of the straight line obtained from the plot. The graph can also be used to calculate the degree of dissociation and dissociation constant of weak electrolytes.

At lower concentrations, weak electrolytes exhibit a steep increase in molar conductivity. Therefore, extrapolating molar conductivity to zero concentration will not yield Λ, the limiting molar conductivity. Consequently, we calculate the limiting molar conductivity for weak electrolytes, Λ, using the Kohlrausch law of independent ion migration.

For a weak electrolyte at a particular concentration, Kohlrausch’s law also aids in calculating the dissociation constant from the molar conductivity and limiting molar conductivity values.

α = Λ/Em°

where,

• α is Dissociation Constant
• Λ is Molar Conductivity
• Em° is Limiting Molar Conductivity

Application of Kohlrausch’s Law

Some of the critical uses of Kohlrausch’s Law include:

• Calculation of the dissociation constant of an electrolyte: Kohlrausch’s Law can be used to determine the dissociation constant of an electrolyte by studying the molar conductivity at infinite dilution.

• Calculating the limiting molar conductivity of a weak electrolyte: The law allows for estimating the limiting molar conductivity of weak electrolytes, which is essential for understanding their behavior in dilute solutions.

• Determination of the degree of dissociation of weak electrolytes: Kohlrausch’s Law can be used to determine the degree of dissociation of weak electrolytes by studying their molar conductivity at different concentrations.

• Calculation of the solubility of sparingly soluble salts: The law can be used to calculate the solubility of sparingly soluble salts by determining their limiting molar conductivity.

• Determination of the transport number of ions in an electrolyte: Kohlrausch’s Law can be used to calculate the transport number of ions in an electrolyte, which is an essential parameter in electrochemical systems.

• Determination of the ionic strength of a solution: Kohlrausch’s Law can be used to determine the ionic strength of a solution, which is a crucial parameter in electrochemical systems.

Read More,

• Equivalent Conductance Formula
• Electrochemical Cells
• Primary and Secondary Cells

Kohlrausch Law Class 12 – Solved Problems

Q1. The equivalent conductance of a strong electrolyte increases on dilution due to

1. An increase in the number of ions and the ionic mobility of the solution
2. Complete dilution of the electrolyte at standard dilution
3. An increase in the ionic mobility of solution
4. None of Above

Option (3) is Correct

Explanation:

Equivalent conductance of a strong electrolyte increases on dilution due to an increase in the ionic mobility of the solution.

Q2. Calculate the limiting molar conductivity of sodium sulphate(Na₂SO₄). If the limiting molar conductivity of Na⁺ is 50.1 S.cm²/mol and 1/2 SO₄^2- is 80.0 S.cm²/mol.

Solution:

Given,

• λ^∞_Na+ = 50.1 S.cm²/mol
• 1/2 λ^∞_SO42− = 80.0 S.cm²/mol

According to Kohlrausch’s Law of Independent Migration

λ^∞(Na₂SO₄) = 2λ^∞_Na+ + 2×(1/2λ^∞_SO42−)

λ^∞(Na₂SO₄) = 2 (50.1)+2×80

=> λ^∞(Na₂SO₄) = 260.2 S.cm²/mol

So, the limiting molar conductivity of sodium sulphate is 260.2 S.cm²/mol.

Q3. The molar conductance of a solution ____ with dilution while its specific conductance ___ with dilution.

1. Decreases, Increases
2. Increases, Decreases
3. Decreases, Decreases
4. Increases, Increases

Option (1) is Correct

Explanation:

Molar conductance of a solution increases with dilution while its specific conductance decreases with dilution.

Kohlrausch’s Law – FAQs

1. Define Kohlrausch Law

Kohlrausch law, named after Friedrich Kohlrausch, describes the conductivity of electrolyte solutions and states that each ion in a solution contributes independently to the overall conductivity.

2. What is Mathematical Expression of Kohlrausch Law?

The mathematical expression of Kohlrausch Law is:

Λ_m = λ₊c₊ + λ₋c₋

3. What is Infinite Dilution in Electrochemistry?

Infinite dilution refers to the state when the concentration of an electrolyte becomes extremely low, approaching zero. In this condition, ions are widely separated, allowing for precise measurement of ion conductivities.

4. What is Kohlrausch Law and its Applications?

Kohlrausch’s law helps predict and understand the conductivity of electrolyte solutions. Its applications include determining molar conductivities and ion mobility and studying the dissociation of electrolytes in various concentrations.

5. Who Discovered Law of Independent Migration of Ions?

The law of independent migration of ions was discovered by Friedrich Kohlrausch in the late 19th century, contributing significantly to our understanding of electrolyte behavior.