Kohlrausch's law

Kohlrausch's Law in Chemistry: Definition, Applications, and Importance

Chemistry, particularly physical chemistry, deals with the study of electrolytes and their behavior in solutions. One of the fundamental principles that help understand ionic conductivity in solutions is Kohlrausch’s Law. This law plays a critical role in determining the limiting molar conductivity of weak and strong electrolytes and has significant applications in electrochemistry. In this article, we will explore the statement, formula, derivation, and applications of Kohlrausch’s Law in detail.

What is Kohlrausch’s Law?

Kohlrausch's Law, also known as the Law of Independent Migration of Ions, was proposed by Friedrich Kohlrausch in 1875. The law states that:

“At infinite dilution, the molar conductivity of an electrolyte is equal to the sum of the individual contributions of the cation and anion.”

In simple terms, each ion in a solution contributes to the total conductivity independently of other ions when the solution is extremely dilute.

Mathematical Expression

The law is mathematically expressed as:

Λ_m° = λ°₊ + λ°₋

Where:

• Λ_m° is the molar conductivity at infinite dilution.
• λ°₊ is the limiting molar conductivity of the cation.
• λ°₋ is the limiting molar conductivity of the anion.

This law applies both to strong and weak electrolytes, although it is especially important for weak electrolytes where direct measurement of Λ_m° is not possible.

Concept of Infinite Dilution

At infinite dilution, the ions are so far apart from each other that there is no interaction between them. Under such conditions, each ion moves independently and contributes to the conductivity of the solution based on its own mobility.

Example Calculation Using Kohlrausch’s Law

Suppose we want to calculate the Λ_m° for acetic acid (CH₃COOH), a weak electrolyte. We use the following data:

• Λ_m° (CH₃COONa) = 91.0 S cm² mol⁻¹
• Λ_m° (HCl) = 426.0 S cm² mol⁻¹
• Λ_m° (NaCl) = 126.4 S cm² mol⁻¹

Using the formula:

Λ_m°(CH₃COOH) = Λ_m°(CH₃COONa) + Λ_m°(HCl) − Λ_m°(NaCl)

= 91.0 + 426.0 − 126.4 = 390.6 S cm² mol⁻¹

Thus, the limiting molar conductivity of acetic acid is 390.6 S cm² mol⁻¹.

Applications of Kohlrausch’s Law

1. Determination of Λ_m° for Weak Electrolytes

Weak electrolytes do not ionize completely in solution, making it difficult to directly measure their molar conductivity. Using Kohlrausch’s Law, we can calculate their Λ_m° using values of strong electrolytes.

2. Calculation of Degree of Dissociation (α)

Once the limiting molar conductivity (Λ_m°) and observed conductivity (Λ_m) are known, the degree of dissociation can be calculated as:

α = Λ_m / Λ_m°

3. Determination of Dissociation Constant (K_a)

The dissociation constant of weak acids or bases can be determined using:

K_a = (C × α²) / (1 − α)

Where C is the concentration of the solution.

4. Verification of Ion Conductance

It helps in determining the molar conductance of individual ions like H⁺, OH⁻, Na⁺, Cl⁻, etc., which are used in various analytical calculations.

5. Determining Solubility of Sparingly Soluble Salts

Kohlrausch’s Law can be used to find the solubility of salts like AgCl, BaSO₄, etc., by calculating their limiting conductivity and then using the relation:

Λ_m = κ / C

Limitations of Kohlrausch’s Law

Although extremely useful, Kohlrausch's Law has some limitations:

• It is valid only at infinite dilution, which is an ideal condition not practically achievable.
• Does not apply to concentrated solutions where ion–ion interactions are significant.

Importance in Electrochemistry

Kohlrausch’s Law is a cornerstone in electrochemistry. It simplifies the study of ionic movement and helps in understanding the fundamental nature of electrolytic solutions. It is especially helpful in analytical chemistry, environmental testing, pharmaceutical analysis, and educational laboratories.

Conclusion

Kohlrausch’s Law of Independent Migration of Ions is a powerful tool for chemists. It provides deep insights into the behavior of ions in solution and is crucial for determining the conductivity properties of electrolytes. From calculating the dissociation of weak acids to analyzing solubility, this law has wide-ranging applications. Despite its limitations, it remains a fundamental concept in physical and analytical chemistry that every chemistry student should understand.

Keywords: Kohlrausch's law, molar conductivity, infinite dilution, degree of dissociation, conductivity in chemistry, physical chemistry, weak electrolyte, strong electrolyte

20 IIT-Level Questions on Kohlrausch's Law with Answers

1. What is Kohlrausch’s Law of Independent Migration of Ions?

It states that at infinite dilution, each ion contributes independently to the total molar conductivity of an electrolyte.

2. State the mathematical expression of Kohlrausch’s Law.

Λ_m^∞ = λ^∞₊ + λ^∞_-

3. Why is Kohlrausch’s law important?

It helps in determining the molar conductivity of weak electrolytes at infinite dilution which cannot be measured directly.

4. What is the unit of molar conductivity?

S·cm²·mol⁻¹

5. How does Λ_m vary with dilution for strong electrolytes?

It increases slightly with dilution due to reduced interionic attraction.

6. Can Kohlrausch’s Law be used to calculate degree of dissociation?

Yes, by using α = Λ_m / Λ_m^∞

7. What happens to molar conductivity of a weak electrolyte on dilution?

It increases significantly as the electrolyte dissociates more upon dilution.

8. Give an example of a weak electrolyte.

CH₃COOH (Acetic acid)

9. Why can’t we measure Λ_m^∞ of weak electrolytes directly?

Because weak electrolytes do not completely dissociate even at infinite dilution.

10. How is Λ_m^∞ of acetic acid determined?

By using Kohlrausch’s law: Λ_m^∞(CH₃COOH) = Λ_m^∞(CH₃COONa) + Λ_m^∞(HCl) - Λ_m^∞(NaCl)

11. What are the values of λ^∞_Na⁺ and λ^∞_Cl⁻?

λ^∞_Na⁺ = 50.1, λ^∞_Cl⁻ = 76.3 S·cm²·mol⁻¹

12. Why does Λ_m of strong electrolytes not increase drastically with dilution?

Because they are almost fully dissociated even at moderate concentrations.

13. What is the physical meaning of λ^∞_ion?

It represents the contribution of an individual ion to molar conductivity at infinite dilution.

14. What does "infinite dilution" mean?

A hypothetical condition where ions are so far apart that they do not interact with each other.

15. Can Λ_m^∞ values be negative?

No, they are always positive since conductivity cannot be negative.

16. What is the effect of temperature on molar conductivity?

It increases with temperature due to enhanced mobility of ions.

17. How is equivalent conductivity related to molar conductivity?

Λ_eq = Λ_m / n, where n is the number of equivalents per mole.

18. What does high molar conductivity indicate?

High ion mobility and/or high degree of dissociation.

19. What is the Λ_m^∞ value of HCl?

426 S·cm²·mol⁻¹

20. Can Kohlrausch's law be used for predicting solubility of salts?

Yes, indirectly through conductivity measurements and dissociation studies.

Numerical Problems on Kohlrausch's Law

1️⃣ Calculate the molar conductivity at infinite dilution of CH₃COOH using the data:
Λ⁰(CH₃COONa) = 91 S·cm²/mol,
Λ⁰(HCl) = 426 S·cm²/mol,
Λ⁰(NaCl) = 126 S·cm²/mol.

Λ⁰(CH₃COOH) = Λ⁰(CH₃COONa) + Λ⁰(HCl) - Λ⁰(NaCl)
= 91 + 426 - 126 = 391 S·cm²/mol

2️⃣ If the molar conductivity of a solution of a weak acid is 78 S·cm²/mol and the molar conductivity at infinite dilution is 390 S·cm²/mol, calculate its degree of dissociation.

α = Λ / Λ⁰ = 78 / 390 = 0.2 or 20%
The acid is 20% dissociated at the given concentration.

3️⃣ Calculate the number of ions in 0.1 mole of NaCl using Avogadro’s number.

Each mole of NaCl gives 2 ions: Na⁺ and Cl⁻.
Number of ions = 0.1 mol × 2 × 6.022×10²³
= 1.204 × 10²³ ions

4️⃣ The molar conductivity of a 0.01 M solution of NH₄OH is 9.33 S·cm²/mol. If Λ⁰(NH₄OH) = 271.5 S·cm²/mol, calculate its degree of dissociation and dissociation constant.

α = 9.33 / 271.5 ≈ 0.0344
K = α² × C = (0.0344)² × 0.01 = 1.18 × 10⁻⁵