Problem 102 - Chemistry and Chemical Reactivity

Question

Two acids, each approximately \(0.01 \mathrm{M}\) in concentration, are titrated separately with a strong base. The acids show the following pH values at the equivalence point: HA, \(\mathrm{pH}=9.5,\) and \(\mathrm{HB}, \mathrm{pH}=8.5\) (a) Which is the stronger acid, HA or HB? (b) Which of the conjugate bases, \(A^{-}\) or \(B^{-},\) is the stronger base?

Step-by-Step Solution

Answer

(a) HB is the stronger acid. (b) \(A^{-}\) is the stronger conjugate base.

Step 1: Understanding the Equivalence Point

During a titration at the equivalence point, the amount of acid is stoichiometrically equivalent to the amount of base added. For weak acids titrated with strong bases, the pH at the equivalence point is greater than 7, due to the basic nature of the conjugate base formed.

Step 2: Analyzing pH at Equivalence Point for HA

For acid HA, the \mathrm{pH} at the equivalence point is 9.5. This indicates it has a relatively strong conjugate base \(A^{-}\), which results in a more basic solution.

Step 3: Analyzing pH at Equivalence Point for HB

For acid HB, the \mathrm{pH} at the equivalence point is 8.5. This is lower than the pH for HA, indicating its conjugate base \(B^{-}\) is less basic, meaning HB itself is a stronger acid than HA.

Step 4: Determine the Stronger Acid

To determine which acid is stronger, compare the pH values: \(HB\) with pH 8.5 is a stronger acid than \(HA\) with pH 9.5, because a stronger acid has a weaker conjugate base resulting in a less basic solution at equivalence.

Step 5: Determine the Stronger Conjugate Base

The stronger conjugate base corresponds to the weaker acid. \(HA\) with the higher pH at equivalence point (9.5) has the stronger conjugate base \(A^{-}\), while \(B^{-}\) is weaker because it results in a lower equivalence point pH of 8.5.

Key Concepts

Equivalence Point

In titration, the equivalence point is the stage where the number of moles of acid equals the number of moles of base. This point is crucial because it indicates that all the acid has reacted with the base, forming water and a salt. At this moment, the chemical reaction reaches a balance. The pH at the equivalence point is not always 7, especially when titrating weak acids with strong bases. In such cases, the solution becomes slightly basic because the conjugate base formed from the weak acid has a higher ability to accept protons.

pH

pH is a measure of how acidic or basic a solution is. It ranges from 0 to 14, with 7 being neutral. Values below 7 indicate acidity, while values above 7 mean the solution is basic. During a titration involving weak acids, the pH at the equivalence point is often higher than 7. This is due to the presence of a conjugate base, which can make the solution more basic. Therefore, by comparing pH values at the equivalence point, we can determine the relative strengths of the acids being titrated. A higher pH at equivalence implies a stronger conjugate base and a weaker acid.

Weak Acids

Weak acids only partially dissociate in water. This means they do not release all their hydrogen ions into the solution. As a result, the pH of their solutions is relatively higher compared to strong acids, which fully dissociate. During a titration of a weak acid with a strong base, the equivalence point tends to exceed a pH of 7. Weak acids have distinct characteristics:

• They do not completely ionize in solution.
• The pH at the equivalence point is typically above 7.
• The strength of the weak acid is inversely related to the basicity of its conjugate base.

Conjugate Base

The conjugate base of a weak acid forms when the acid loses a proton. For weak acids, the conjugate base plays a significant role in determining the pH at the equivalence point. Since weak acids do not release all their hydrogen ions, their conjugate bases are more capable of accepting protons, making them relatively stronger bases. Key facts about conjugate bases include:

• The stronger the weak acid, the weaker its conjugate base.
• A higher pH at equivalence signifies a stronger conjugate base, due to its basic nature.
• The ability of a conjugate base to accept protons increases the basicity of the solution at equivalence.

Hence, understanding conjugate bases is essential for predicting the behavior of acids during titration.