What is Ostwald's Law?

Ostwald's dilution law describes the relationship between the dissociation of a weak electrolyte and its concentration in a solution. This law specifically pertains to weak electrolytes because strong electrolytes almost fully dissociate in solution, thus their dissociation isn't significantly impacted by dilution. According to the provided reference, Ostwald's law states:

“The degree of dissociation of a weak electrolyte is inversely proportional to the square root of molar concentration or directly proportional to the square root of volume holding one mole of the solute for a weak electrolyte.”

Understanding the Key Concepts

Let's break down what this means:

• Degree of Dissociation (α): This represents the fraction of the electrolyte molecules that have dissociated into ions in a solution. A higher α means more dissociation.
• Weak Electrolyte: These are substances that only partially ionize in solution (e.g., weak acids like acetic acid or weak bases like ammonia).
• Molar Concentration (C): This is the amount of the electrolyte present in moles per liter of the solution.
• Volume (V): The volume of the solution.

The Core Idea

The law essentially implies:

• Dilution and Dissociation: When you dilute a solution of a weak electrolyte (i.e., increase the volume), its degree of dissociation (α) increases. This is because the ions have more space and less tendency to recombine.
• Concentration and Dissociation: Conversely, if you increase the concentration of the electrolyte, the degree of dissociation decreases. Higher concentration leads to more frequent collisions of ions, favoring recombination.

Mathematical Representation

Ostwald’s law can be expressed mathematically using the following relationship for a weak acid HA:

HA ⇌ H⁺ + A^-

The equilibrium constant for this dissociation is:

K_a = [H⁺][A^-] / [HA]

If α is the degree of dissociation, then:

K_a = (Cα)(Cα) / C(1-α)
K_a = Cα² / (1-α)

For very weak electrolytes where α is small, we can approximate (1-α) ≈ 1. Therefore:

K_a ≈ Cα²

Rearranging for α gives us:

α ≈ √(K_a / C)

This equation shows that the degree of dissociation (α) is inversely proportional to the square root of the concentration (C), confirming the relationship from the reference.

Alternatively, since concentration (C) is inversely proportional to volume (V), we can also see that α is directly proportional to the square root of the volume (V).

Practical Insights

• Weak Acid/Base Behavior: Ostwald's dilution law explains why the pH change for a weak acid or base isn't as drastic as a strong acid or base when diluting or concentrating the solution.
• Buffer Solutions: This law provides the basis for how buffer solutions work and resist drastic pH changes.

Example

Consider a weak acid such as acetic acid. When diluted, its degree of dissociation will increase. A more diluted solution of acetic acid will have more H+ ions compared to a more concentrated solution, although the concentration of H+ ions will still be much less than a strong acid at the same concentration.

Summary Table