Ostwald’s Dilution Law: The Key to Weak Electrolytes
In Ionic Equilibrium, dealing with Strong Electrolytes (like HCl or NaCl) is easy because they dissociate 100% in water. But what about Weak Electrolytes (like Acetic acid or Ammonium hydroxide)? They only partially dissociate.
To calculate exactly how much of a weak electrolyte breaks apart into ions, we rely on a fundamental mathematical derivation known as Ostwald's Dilution Law. Let's build the equation step-by-step.
Video Tutorial: Deriving the Law
Watch Abhishek Sengar sir from CHEMCA use the standard ICE Table method to extract the mathematical relationship between the Degree of Ionization (α) and Concentration (C).
1. Setting up the ICE Table
Let's consider a weak binary electrolyte, AB, with an initial concentration of C (moles/Liter) and a Degree of Dissociation equal to α.
- Initial (I): [AB] = C, [A+] = 0, [B-] = 0
- Change (C): [AB] loses -Cα, [A+] gains +Cα, [B-] gains +Cα
- Equilibrium (E): [AB] = C(1 - α), [A+] = Cα, [B-] = Cα
2. Writing the Equilibrium Expression
The equilibrium constant (K) for this dissociation is:
K = ([A+] × [B-]) / [AB]
Substitute our equilibrium values into the formula:
K = (Cα × Cα) / C(1 - α)
K = (C2α2) / C(1 - α)
Cancel out one 'C' from the numerator and denominator to get the exact expression:
3. The "Weak Electrolyte" Approximation
Because AB is a weak electrolyte, its degree of dissociation (α) is very, very small compared to 1 (usually less than 0.05 or 5%).
Therefore, mathematically, we can approximate the denominator: 1 - α ≈ 1.
By applying this approximation, the denominator disappears, leaving us with the final, highly usable form of Ostwald's Dilution Law:
Fig: Dropping the (1-α) term simplifies the algebra immensely, allowing us to easily calculate the degree of ionization.
4. The Concept of "Dilution"
From our final formula α = √(K / C), we can see that α is inversely proportional to the square root of the Concentration (C).
What happens if we add more water to the solution? We are diluting it, which means we are decreasing the concentration (C). According to the math, if C decreases, α MUST increase! This is the physical meaning of Ostwald's Dilution Law: Diluting a weak electrolyte forces it to ionize more.
Practice Questions for JEE & NEET
Test your conceptual understanding of the limitations of this law!
Question 1: According to Ostwald's Dilution Law, what happens to the degree of dissociation (α) of a weak acid as the volume of the solution approaches infinity (infinite dilution)?
Answer: α approaches 1 (or 100% dissociation).
Reasoning:
Concentration (C) is defined as Moles / Volume. Therefore, C is inversely proportional to Volume (V).
If we substitute this into our law: α = √(K × V).
As the volume (V) increases towards infinity, the math suggests α will keep increasing until it maxes out at 1 (since α cannot exceed 100%). At infinite dilution, even weak electrolytes behave like strong electrolytes and dissociate completely!
Question 2: A student tries to calculate the degree of dissociation of a 0.1M solution of Hydrochloric Acid (HCl) using the formula K = Cα2. Why is this mathematically and chemically incorrect?
Answer: Because Ostwald's Dilution Law is strictly valid ONLY for weak electrolytes.
Reasoning:
HCl is a Strong Acid, meaning it dissociates nearly 100% in water. Therefore, its actual α value is approximately 1.
Remember how we derived the formula? We explicitly assumed that (1 - α) ≈ 1 because α was supposed to be tiny! If α = 1, then the denominator (1 - α) becomes 0. Dividing by zero destroys the mathematical equation. You cannot use this shortcut for strong electrolytes!
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