# Ostwald's Dilution Law of Acids and Bases

Instructor: Justin Wiens

Justin teaches college chemistry and has Bachelor and Doctorate degrees in chemistry.

This lesson is about the Ostwald Dilution Law, which is an application of the expression for an electrolyte's equilibrium constant. This law only works for weak electrolytes, including weak acids and weak bases.

## Introduction to Equilibrium

Chemical reactions can always proceed in two different directions: forward and backward. Whenever we process a reaction, we call the starting materials reactants, and the ending materials products. The relative amounts of reactants and products depends on the relative rates of the forward and backward reactions.

For a generic molecule, AB, dissociating into the A+ and B- ions, or the reverse reaction of the ions coming together, we can write the following chemical equations:

AB → A+ + B-

AB ← A+ + B-

When the rates of a forward and backward chemical reaction are equal, we have reached equilibrium. At equilibrium, the amounts of reactants and products are constant, but the reactants consistently form products, and vice versa.

One way of expressing the relative amounts of products versus reactants is the equilibrium constant, Keq . The equilibrium constant for our AB molecule is written as:

In this equation, the quantities in brackets are the concentrations of the ions and the AB molecule, usually in molarity.

### Ostwald's Dilution Law: What is It?

Ostwald's Dilution Law tells us that the equilibrium constant, and the initial concentration of an electrolyte (prior to dissociation or association), can be used to calculate the extent of this dissociation or association for the electrolyte.

### Ostwald's Dilution Law: Derivation of the Equation

Let's take the example of a weak acid dissociation, to derive the dilution law. We'll start with an equation for the acid dissociation constant:

Because a weak acid is a weak electrolyte, we know that it will dissociate to a small extent. How much, you ask? We're not exactly sure, so let's call that small amount x. The variable x is the fraction of weak acid molecules that dissociate. Therefore, the amount of acid molecules that do not dissociate is just 1 - x. The equilibrium expression then looks like the following:

If we ask, ''How many acid molecules out of 100 will dissociate?'', the answer is found in this equation. We just need to solve for x. Since we expect x to be small, relative to the number 1 in the denominator of the equation, the following is true:

To find x, we simply rearrange the final equality and take the square root:

### Applying the Dilution Law

Let's try an example problem with Ostwald's Dilution Law.

#### Problem

A weak base with an initial concentration in water of 0.44 M, has an equilibrium association constant Kb of 2.4 x 10-5 . What percent of the base molecules will become protonated?

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