What is Kohlrausch's Law?

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Grade Level:

Class 12

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Definition

What is it?

Kohlrausch's Law helps us find the conductivity of a solution at infinite dilution, especially for weak electrolytes. It states that at infinite dilution, each ion contributes a definite amount to the total molar conductivity of the electrolyte, regardless of the nature of the other ion it's paired with.

Simple Example

Quick Example

Imagine you have a big pot of dal, and you add a pinch of salt. The salt makes the dal taste saltier. If you keep adding water (diluting it infinitely), the 'saltiness' contributed by each salt particle (ion) will eventually be its maximum, unaffected by how watery the dal is. Kohlrausch's Law is like finding that maximum individual saltiness.

Worked Example

Step-by-Step

Let's find the molar conductivity at infinite dilution for acetic acid (CH3COOH), a weak electrolyte, using Kohlrausch's Law. We are given the following molar conductivities at infinite dilution:
Lambda_infinity(HCl) = 426 S cm^2 mol^-1
Lambda_infinity(CH3COONa) = 91 S cm^2 mol^-1
Lambda_infinity(NaCl) = 126 S cm^2 mol^-1

Step 1: Write the equation for the desired molar conductivity.
Lambda_infinity(CH3COOH) = Lambda_infinity(CH3COO-) + Lambda_infinity(H+)

Step 2: Express the desired components using the given strong electrolytes.
We can get CH3COO- from CH3COONa and H+ from HCl. To remove Na+ and Cl- ions, we subtract NaCl.
Lambda_infinity(CH3COOH) = Lambda_infinity(CH3COONa) + Lambda_infinity(HCl) - Lambda_infinity(NaCl)

Step 3: Substitute the given values into the equation.
Lambda_infinity(CH3COOH) = 91 + 426 - 126

Step 4: Perform the calculation.
Lambda_infinity(CH3COOH) = 517 - 126

Step 5: Calculate the final value.
Lambda_infinity(CH3COOH) = 391 S cm^2 mol^-1

Answer: The molar conductivity at infinite dilution for acetic acid is 391 S cm^2 mol^-1.

Why It Matters

Understanding Kohlrausch's Law is key for engineers developing better batteries for EVs, as it helps characterize electrolyte performance. It's also vital in medicine for understanding how ions move in biological systems, and in environmental science for monitoring water quality. Knowing this helps build advanced sensors and energy solutions.

Common Mistakes

MISTAKE: Confusing molar conductivity at infinite dilution with molar conductivity at a finite concentration. | CORRECTION: Kohlrausch's Law specifically applies to infinite dilution, where inter-ionic interactions are negligible and ions move independently.

MISTAKE: Incorrectly adding or subtracting the molar conductivities of strong electrolytes to find that of a weak electrolyte. | CORRECTION: Remember the principle: sum the molar conductivities of the ions that make up the weak electrolyte, and subtract the molar conductivities of the 'extra' ions.

MISTAKE: Not considering the number of ions produced by a salt (e.g., for MgCl2). | CORRECTION: For salts like MgCl2, where 1 Mg2+ and 2 Cl- ions are produced, the molar conductivity at infinite dilution would be Lambda_infinity(Mg2+) + 2 * Lambda_infinity(Cl-). Always account for stoichiometry.

Practice Questions

Try It Yourself

QUESTION: What does Kohlrausch's Law state about the contribution of individual ions to total molar conductivity at infinite dilution? | ANSWER: Each ion contributes a definite amount to the total molar conductivity, independent of the other ion.

QUESTION: If Lambda_infinity(Na+) is 50.1 S cm^2 mol^-1 and Lambda_infinity(Cl-) is 76.3 S cm^2 mol^-1, what is Lambda_infinity(NaCl)? | ANSWER: Lambda_infinity(NaCl) = 50.1 + 76.3 = 126.4 S cm^2 mol^-1.

QUESTION: Given Lambda_infinity(BaCl2) = 280 S cm^2 mol^-1, Lambda_infinity(HCl) = 426 S cm^2 mol^-1, and Lambda_infinity(Ba(OH)2) = 520 S cm^2 mol^-1. Calculate Lambda_infinity(H2O). (Hint: H2O can be thought of as H+ and OH-). | ANSWER: Lambda_infinity(H2O) = Lambda_infinity(HCl) + (1/2) * Lambda_infinity(Ba(OH)2) - (1/2) * Lambda_infinity(BaCl2) = 426 + (1/2)*520 - (1/2)*280 = 426 + 260 - 140 = 546 S cm^2 mol^-1.

MCQ

Quick Quiz

Which of the following is NOT a condition for Kohlrausch's Law to be applicable?

Infinite dilution

Strong electrolyte

Weak electrolyte

Independent migration of ions

The Correct Answer Is:

Kohlrausch's Law is primarily useful for finding the molar conductivity of weak electrolytes at infinite dilution, as strong electrolytes already show independent migration at infinite dilution. Both weak and strong electrolytes follow the law at infinite dilution, but its practical application is mainly for weak ones. Independent migration is a key principle.

Real World Connection

In the Real World

In India, companies developing new battery technologies for electric scooters or inverters use principles like Kohlrausch's Law. By understanding how different ions contribute to conductivity, they can design better electrolyte solutions that allow batteries to charge faster and last longer. This helps power our daily lives, from mobile phones to electric rickshaws.

Key Vocabulary

Key Terms

Molar Conductivity: The conductivity of a solution containing one mole of electrolyte. | Infinite Dilution: A state where the concentration of an electrolyte is so low that ions are far apart and do not interact. | Electrolyte: A substance that conducts electricity when dissolved in a solvent. | Weak Electrolyte: An electrolyte that does not fully dissociate into ions in a solution. | Strong Electrolyte: An electrolyte that completely dissociates into ions in a solution.

What's Next

What to Learn Next

Now that you understand Kohlrausch's Law, you're ready to explore how conductivity changes with concentration for both strong and weak electrolytes. This will help you understand degree of dissociation for weak electrolytes and how it impacts their behavior in real-world applications.