Lesson Explainer: Degree of Dissociation Chemistry

In this explainer, we will learn how to define and calculate the degree of dissociation of a weak acid and use it to derive Ostwald’s law of dilution.

In general, the dissociation of a substance involves the separation of the substance into individual components. We can consider the degree of dissociation in the same way we think about the percentage yield.

Imagine a reversible reaction where a substance dissociates into two pieces.

The degree of dissociation is similar to the percentage of substance that has dissociated.

The degree of dissociation is defined as the proportion of the substance that is dissociated, and it is usually expressed as a decimal. The degree of dissociation is often given the symbol (alpha).

When expressing amounts in moles, we can express the degree of dissociation in the following way.

The table below shows how we could analyze the simple systems we have already looked at. It is straightforward to calculate the amount of undissociated substance. The amount of dissociated substance can be determined by counting complete sets of products of dissociation. When we calculate the degree of dissociation, it is essential that we use the total amount of substance (dissociated and undissociated) when we perform the division.

Degrees of dissociation are always in the range of 0 to 1. When performing calculations, care is needed to not count the number of individual pieces. Only the number of units of dissociated substance should be measured regardless of how many pieces the substance dissociates into. We need to count sets of pieces, not the pieces themselves.

Degrees of dissociation greater than 0 and less than 1 are the most interesting. If something completely dissociates, or does not dissociate at all, then we do not need to consider the degree of dissociation at all.

We can apply degrees of dissociation to many different types of chemical systems. Here, we will focus on weak acids.

A weak acid is, by definition, an acid that dissociates incompletely in water. The degree of dissociation is an important characteristic of weak acids. A stronger weak acid will have a higher degree of dissociation than a weaker weak acid.

When a weak acid dissolves in water, some acid will also dissociate:

Once the system has reached equilibrium, there will be fixed concentration of hydrogen ions (and therefore a fixed pH):

This equation is the same equation we use when discussing the acid dissociation constant, .

We can express the acid dissociation constant of a weak acid in terms of the concentrations of the products ( and ions) and the reactants :

We can derive a relationship between an acid dissociation constant and the degree of dissociation using this equation.

To start, let’s look at the dissociation equation again:

If we start with 1 mol of , we will produce mol of and mol of . Let’s go through the initial, change, equilibrium (ICE) table step by step to see how we arrive at this result.

In this scenario, we start with having a concentration of 1 M.

As we are dealing with a weak acid, we know that it will dissociate partially. This will produce some and ions, but there will still be some left. The amount of ions and ions produced will depend on the strength of the acid.

The proportion of that will dissociate is the degree of dissociation, . Therefore, the concentration of will decrease by M. Also, the dissociation will increase the concentration of ions and ions by M:

We can then calculate the final concentrations in terms of the degree of dissociation:

We can now write in terms of at a concentration of 1 M for :

However, there is something wrong here: this equation for applies only when the concentration is exactly 1 M. We can, however, derive an equation for for a general concentration, , in place of 1 M. Starting as before, we calculate it as follows:

When we put these terms into our expression for , this is what we get:

The result is known as Ostwald’s dilution law, and it applies to any dissociation constant, not just acid dissociation constants.

For many weak acids, the degree of dissociation is close enough to 0; this allows us to use a helpful approximation. If is very small, is very close to 1.

This means that we can derive an approximate relationship between degrees of dissociation and acid dissociation constants: and if is very small,

For acids that are weak enough, the degree of dissociation is proportional to the square root of its acid dissociation constant and inversely proportional to the square root of its concentration. As the concentration goes down, the degree of dissociation goes up, and the larger the acid dissociation constant, the greater the degree of dissociation.

The basic consequence of this is that, as we dilute a solution, we reduce the solute concentration by adding more solvent, and so the degree of dissociation of the solute goes up.

Example 1: Identifying the Factor That Increases the Degree of Dissociation of a Weak Acid in a Set of Factors

Which of the following factors would increase the degree of dissociation of a weak acid?

1. Increasing dilution
2. Decreasing volume
3. Decreasing dilution
4. Increasing acid concentration

Answer

The degree of dissociation of an acid is the proportion of acid molecules that have dissociated in a given solution. The degree of dissociation will depend on the acid and factors such as the strength of internal bonds or how much energy is released when it dissociates.

A weak acid is an acid that, when mixed with water, will only dissociate a little. Therefore, only a fraction of acid molecules will dissociate, and the rest will be dissolved as whole molecules.

The acid dissociation constant is a fixed property of a weak acid (for a given temperature). Acid dissociation constants are related to degrees of dissociation by Ostwald’s dilution law, which can be expressed in this simple form for a weak acid: Here, is the degree of dissociation of the weak acid at equilibrium, is the acid dissociation constant, and is the total concentration of the weak acid (including dissociated and undissociated forms).

All four of the potential answers relate in some way to the concentration of the acid. Increasing dilution will decrease the acid concentration, while decreasing volume and decreasing dilution will increase the acid concentration.

If we increase the concentration of the weak acid, the degree of dissociation will decrease as Ostwald’s dilution law suggests:

The only factor that will produce the opposite effect is “Increasing dilution.” This will reduce the concentration of the weak acid and increase the degree of dissociation.

The answer is option A, increasing dilution.

The graph below shows the relationship between the concentration and the degree of dissociation for ethanoic acid .

We can zoom in on the interesting area: below 0.1 M.

Here, we can see that the degree of dissociation remains very low until the concentration falls below about 0.01 M.

The relationship between the concentration and the degree of dissociation is of particular importance when dealing with electrolytes.

If we have a weak electrolyte (like a solution of ethanoic acid), we might expect that if we double the concentration, the electrical conductivity will double as well. As the ion concentration increases, so does the electrical conductivity.

However, the electrical conductivity will be less than double its prior value.

The same occurs if we halve the concentration. The electrical conductivity will be a little above half its prior value. This is because, as the concentration increases, the degree of dissociation goes down, and as the concentration decreases, the degree of dissociation goes up.

This graph shows how the concentration of dissociated ethanoic acid changes with the total concentration.

The dissociation of acids is affected by temperature and other conditions, so values of and can change for reasons other than concentration changes.