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Lesson Video: V: Degree of Dissociation Chemistry

In this video, 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.

17:46

Video Transcript

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

Let’s consider the difference between a strong and weak acid. When hydrochloric acid, a strong acid, is dissolved in water, all of the molecules disassociate into hydrogen ions and chloride ions. So if 50 molecules of hydrochloric acid were dissolved in water, all 50 molecules would disassociate. In contrast, when hydrofluoric acid, a weak acid, is dissolved in water, only a portion of the molecules will disassociate and an equilibrium is established. If 50 molecules of hydrofluoric acid are dissolved in water, on average, only one molecule would disassociate into hydrogen ions and fluoride ions.

The extent to which an acid dissociates can be represented by the degree of dissociation. The degree of dissociation can be defined as the proportion of the substance that dissociated. It is often given the symbol 𝛼 and can be calculated by dividing the amount of dissociated substance by the total amount of substance, both dissociated and undissociated. We can use the number of molecules or the number of moles for the amounts. Let’s go ahead and calculate the degree of dissociation for each acid.

The total number of hydrochloric acid molecules was 50, and all 50 molecules dissociated. So the degree of dissociation is one. There were also 50 molecules of hydrofluoric acid, but only one molecule dissociated. So the degree of dissociation is 0.02. Notice that when calculating the degree of dissociation, the total number of ions produced is not used in the equation. The degree of dissociation may also be given as a percentage by multiplying the resulting decimal value by 100 percent.

Weak acids typically have very low degrees of dissociation. In general, as the strength of the acid increases, so does the degree of dissociation, with strong acids having a degree of dissociation of one. So the degree of dissociation can give us some insight into the strength of an acid. But the extent to which a weak acid dissociates is dependent on the concentration of the acid. So to better quantify the strength of an acid, we can calculate an acid dissociation constant. An acid dissociation, constant symbol 𝐾 a is the equilibrium constant for the dissociation of an acid in water. It is temperature dependent, but it is not dependent on the acid concentration.

For the dissociation of a generic mono product weak acid, represented here by HA, we can write this acid dissociation constant expression. The brackets indicate that we should use the concentration of each species. And as we are calculating in equilibrium constant, we should use the concentrations at equilibrium. If the acid is very weak, very few molecules will disassociate. So the concentrations of the ions at equilibrium will be low, while the concentration of the acid is high. This will result in a low acid dissociation constant. As the strength of the acid increases, the concentration of the ions will increase, and the acid dissociation constant will increase.

We now have two quantities degree of dissociation and acid dissociation constants that can help us to understand the strength of an acid. These two quantities can be related to one another. Let’s consider the following example. In this diagram, one HA picture represents one mole of HA. So initially, 10 moles of HA, a weak acid, are dissolved in water to produce 10 liters of solution. This means that the initial concentration of HA is one molar and the initial concentration of H plus and A minus is zero molar.

If the degree of dissociation of one molar HA is 0.2, then at equilibrium 20 percent of the acid will have dissociated. At equilibrium, the concentration of HA will be 0.8 molar and the concentration of H plus and A minus will be 0.2 molar. This means that the concentration of the acid decreased by 0.2 molar, while the concentration of the ions increased by 0.2 molar. Thus, the concentration’s changed by a value equal to the degree of dissociation. If we replace the changing concentration with the degree of dissociation, then the equilibrium concentration of HA in moles per liter is one minus the degree of dissociation and the equilibrium concentration for H plus and A minus in moles per liter is equal to the degree of dissociation.

We can substitute these equilibrium concentrations into the acid dissociation constant expression to determine that 𝐾 a is equal to the degree of dissociation squared divided by one minus the degree of dissociation. This expression allows us to relate the acid dissociation constant and degree of dissociation but only when the initial concentration of acid is one molar. We said earlier that the degree of association is dependent on concentration. So we need an expression that includes the initial concentration of the acid.

Let’s define the initial concentration of the acid as 𝑐 naught. We know that initially the concentrations of H plus and A minus will be zero molar. As the dissociation proceeds, the concentration of HA will decrease by the initial concentration times the degree of dissociation, while the concentration of H plus and A minus will increase by the initial concentration of the acid times the degree of dissociation. Adding the initial concentration and changing concentration gives us these equilibrium concentrations. We can substitute these equilibrium concentrations into the 𝐾 a expression. We can simplify the expression by factoring the initial concentration and by combining the degrees of dissociation.

We are left with the following expression, which allows us to relate the acid dissociation constant and degree of dissociation for any initial concentration. This is known as Oswald’s dilution law. And it can be applied to any dissociation constant, not just acid dissociation constants. For many weak acids, we can simplify Oswald’s dilution law even further. Many weak acids have a degree of dissociation that is very small. If the degree of association is very small, then one minus the degree of dissociation will be approximately equal to one. This means that for weak acids with very small degrees of dissociation, we can use the approximation 𝐾 a is approximately equal to the degree of dissociation squared times the initial concentration. Rearranged to solve for the degree of dissociation, we find that the degree of dissociation is approximately equal to the square root of the 𝐾 𝐚 divided by the initial concentration.

It’s important to recognize that this approximation only works for acids which have very small degrees of dissociation. And it’s also worth mentioning that all of these relationships are temperature dependent. With that said, we can see from the approximation that the degree of dissociation is inversely proportional to the square root of the initial concentration. This means that as the initial concentration of acid increases, the degree of dissociation will decrease, and vice versa. So if we dilute a solution, that is, we add more solvent, and decrease the concentration, the proportion of molecules that disassociate will increase.

The relationship between degree of dissociation and concentration is of particular importance when dealing with electrolytes. In general, the electrical conductivity of an electrolyte is proportional to the ion concentration. So we might expect that doubling the concentration of a weak electrolyte will double the electrical conductivity.

Ethanoic acid is a weak electrolyte. If the concentration of ethanoic acid is doubled, then the degree of dissociation will decrease. This means that the proportion of molecules that disassociate will decrease, and the concentration of hydrogen ions and acetate ions in solution will be less than double the original amount. So doubling the electrolyte concentration does not double the ion concentration. Therefore, the electrical conductivity will be less than double the original amount.

Likewise, if we halve the concentration, the degree of dissociation will increase, and the concentration of the ions will be slightly greater than one-half their original value. So the electrical conductivity will also be slightly greater than one-half its prior value.

Before we summarize what we’ve learned about degree of dissociation, let’s take a look at some questions.

A 0.3 molar solution of benzoic acid was found to be 1.47 percent dissociated. What is the value of 𝐾 𝐚 to two decimal places for this acid? Assume one minus 𝛼 is approximately equal to one.

Benzoic acid is a weak acid. When it is dissolved in water, only a portion of the molecules will dissociate into benzoate ions and hydrogen ions. We are told that 1.47 percent of the acid was found to be dissociated. This means that if we dissolved 100 moles of benzoic acid in water, at equilibrium 1.47 moles will have dissociated into ions, while the remaining 98.53 moles are undissociated. The proportion of the substance that is dissociated is called the degree of dissociation. It is usually represented by the symbol 𝛼 and is typically given as a decimal. We were given the percentage of dissociation. We can convert the percentage of dissociation to a decimal by dividing by 100 percent. So the degree of dissociation of the benzoic acid given in the question is 0.0147.

We want to use the degree of dissociation to calculate the value of 𝐾 𝐚. 𝐾 𝐚 is the acid dissociation constant, an equilibrium constant for the dissociation of an acid in water. The acid dissociation constant and the degree of dissociation can be related using Oswald’s dilution law. In this expression, 𝑐 naught represents the initial concentration of the acid. The question tells us that the concentration is 0.3 molar. We know the degree of dissociation and the concentration. So we could put those values into the expression and solve for 𝐾 𝐚. But the question tells us to assume that one minus 𝛼 is approximately equal to one.

If the denominator of the expression is approximately equal to one, we can rewrite the expression as 𝐾 𝐚 is approximately equal to 𝛼 squared times 𝑐 naught. We can substitute the degree of dissociation and concentration into the expression and perform the calculation to determine the acid dissociation constant. Rounding our answer to two decimal places, we have determined that the value of 𝐾 𝐚 for benzoic acid is 6.48 times 10 to the negative fifth molar or moles per liter.

Which of the following factors would increase the degree of dissociation of a weak acid? (A) Increasing dilution, (B) decreasing volume, (C) decreasing dilution, (D) increasing acid concentration.

When a weak acid is mixed with water, only a portion of the molecules dissociate into ions. We can represent the extent to which the molecules dissociate with the degree of dissociation. Degree of dissociation, typically given the symbol 𝛼, is the proportion of the substance that is dissociated. The degree of dissociation is dependent on a number of factors, including the strength of the acid, temperature, and concentration. The strength of an acid can be quantified using an acid dissociation constant, or 𝐾 a. The degree of dissociation, 𝐾 𝐚, and the initial concentration of the acid, represented by 𝑐 naught, can be related to one another using Oswald’s dilution law.

For weak acids with very low degrees of dissociation, one minus 𝛼 can be approximated to one. And Oswald’s dilution law can be simplified to 𝐾 𝐚 is approximately equal to 𝛼 squared times 𝑐 naught. This can be rearranged to solve for the degree of dissociation. Here, we can see that the degree of dissociation is inversely proportional to the square root of the acid concentration. Thus, increasing the concentration will decrease the degree of dissociation, and decreasing the concentration will increase the degree of dissociation. We want to determine which factor would cause the degree of dissociation to increase. So we need to determine which factor would cause the concentration to decrease.

Answer choice (A), increasing dilution means that we are adding more solvent to the solution. Increasing the amount of solvent will cause the concentration to decrease. A decrease in concentration corresponds with an increase in the degree of dissociation. Let’s look at answer choice (B). Decreasing the volume of the solvent will increase the concentration, so the degree of dissociation will decrease. Answer choice (C) is the opposite of answer choice (A). Decreasing dilution will cause an increase in the concentration, so the degree of dissociation will decrease. Lastly, we know that increasing the acid concentration will cause a decrease in the degree of dissociation. So the factor that would increase the degree of dissociation of a weak acid is answer choice (A), increasing dilution.

Now let’s summarize what we’ve learned. Degree of dissociation is the proportion of a substance that has dissociated. It can be calculated by dividing the amount of substance dissociated by the total amount of substance, where the amount may be given as a number of molecules or a number of moles. The degree of dissociation can be related to the acid dissociation constant via Ostwald’s dilution law, where 𝐾 𝐚 is the acid dissociation constant, 𝛼 is the degree of dissociation, and 𝑐 naught is the initial concentration of the acid.

For weak acids with very low degrees of dissociation, one minus 𝛼 is approximately equal to one. So we can use the approximations 𝐾 𝐚 is approximately equal to 𝛼 squared times 𝑐 naught or 𝛼 is approximately equal to the square root of 𝐾 𝐚 divided by 𝑐 naught. The degree of dissociation is inversely proportional to the square root of the acid concentration. So increasing the concentration of the acid will decrease the degree of dissociation, and vice versa.

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