Problem 29 - Chemistry The Molecular Nature of Matter

Question

Aspirin is acetylsalicylic acid, a monoprotic acid whose \(K_{\mathrm{a}}\) value is \(3.3 \times 10^{-4} .\) Does a solution of the sodium salt of aspirin in water test acidic, basic, or neutral? Explain.

Step-by-Step Solution

Answer

The solution of the sodium salt of aspirin in water will test basic due to the hydrolysis of the conjugate base, which produces hydroxide ions.

Step 1: Understanding the Concept

Recognize that the sodium salt of acetylsalicylic acid (aspirin) is a salt formed from the neutralization of the acetylsalicylic acid with sodium hydroxide. Since acetylsalicylic acid is a weak acid and sodium hydroxide is a strong base, the resulting solution will likely be basic due to the presence of the conjugate base of the acetylsalicylic acid after it donates a proton.

Step 2: Recognizing Salt Hydrolysis

Understand that when the sodium salt of acetylsalicylic acid dissolves in water, it will undergo hydrolysis. The anion (conjugate base of acetylsalicylic acid) will react with water to produce hydroxide ions (OH-), making the solution basic.

Step 3: Considering the Strength of the Acid

Since acetylsalicylic acid is a weak acid with a relatively low Ka value, its conjugate base is strong enough to hydrolyze water to a significant extent. This hydrolysis shifts the equilibrium towards the production of hydroxide ions.

Step 4: Conclusion

Based on the hydrolysis of the conjugate base producing hydroxide ions, the solution of the sodium salt of aspirin in water will test as basic.

Key Concepts

Salt Hydrolysis

Salt hydrolysis is a chemical process that involves the reaction of a salt with water to form an acid or a base. When a salt formed from a weak acid and a strong base dissolves in water, the anions from the salt can remove hydrogen ions from water molecules, creating hydroxide ions \(OH^-\). This generates a basic solution due to the increased concentration of hydroxide ions.

For instance, when the sodium salt of acetylsalicylic acid is dissolved in water, it dissociates into sodium \(Na^+\) and the conjugate base of the acid. The conjugate base then undergoes hydrolysis, reacting with the water to produce \(OH^-\), which is responsible for the basic nature of the solution. Understanding salt hydrolysis is key to predicting the pH of a salt solution and its behavior in various chemical reactions.

Ka Value

The \(K_{\mathrm{a}}\) value, or acid dissociation constant, is a quantitative measure of the strength of an acid in solution. It represents the equilibrium constant for the dissociation of the acid into its conjugate base and a proton \(H^+\). The larger the \(K_{\mathrm{a}}\) value, the stronger the acid and the more completely it donates protons in water.

For acetylsalicylic acid, with a \(K_{\mathrm{a}}\) value of \(3.3 \times 10^{-4}\), we can infer that it’s a weak acid as it partially dissociates in solution. Thus, its conjugate base will be relatively strong and capable of affecting the pH of the solution through the process of hydrolysis. Knowing the \(K_{\mathrm{a}}\) value helps us predict the behavior of the acid's conjugate base once the salt is dissolved in water.

Conjugate Base

The conjugate base is what remains of an acid molecule after it donates a proton. It is a vital component in the context of acid-base chemistry because it has the potential to gain a proton during chemical reactions, which is an essential aspect of the hydrolysis process.

In our example, the conjugate base of acetylsalicylic acid is the anion formed when aspirin donates a hydrogen ion. Since acetylsalicylic acid is a weak acid, we deduce that its conjugate base is strong enough to react with water, accepting a proton and forming hydroxide ions, in turn influencing the pH of the solution. This relationship between acids and their conjugate bases is fundamental for understanding salt hydrolysis and its effects on the solution’s acidity or basicity.

Hydrolysis Equilibrium

Hydrolysis equilibrium refers to the state in which the rates of the forward and reverse hydrolysis reactions are equal, and the concentrations of the reactants and products remain constant over time. It is denoted by an equilibrium constant for hydrolysis, similar to the \(K_{\mathrm{a}}\) value for acids.

When the conjugate base of the weak acetylsalicylic acid undergoes hydrolysis, it interacts with water, producing acetylsalicylic acid and the hydroxide ion. As the hydroxide ion concentration increases, the solution becomes more basic. At hydrolysis equilibrium, the proportion of the acid and base formed is determined by the strengths of the original acid and base from which the salt was formed. Recognizing this equilibrium is crucial to understanding why a solution of the sodium salt of aspirin in water will exhibit basic characteristics.