Problem 108 - 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: \(\mathrm{HA}, \mathrm{pH}=9.5,\) 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 base.

Step 1: Identifying the Principle

The strength of an acid is determined by how much it ionizes in solution. A stronger acid has a higher concentration of undissociated hydrogen ions \(H^{+}\). The pH at the equivalence point for each titration shows the strength of the conjugate base relative to water.

Step 2: Understanding pH at Equivalence Point

For acids being titrated with a strong base, a neutralization reaction occurs that forms water and the conjugate base. The pH at the equivalence point indicates the acidity/basicity of the solution formed by the conjugate base in water.

Step 3: Comparing Acid Strength

Since the pH values at the equivalence point are provided: a pH of 9.5 for \(\text{HA}\) and 8.5 for \(\text{HB}\). The higher the pH, the stronger the conjugate base. Thus, \(\text{A}^{-}\) is a stronger base, indicating \(\text{HA}\) is weaker as an acid compared to \(\text{HB}\). Therefore, \(\text{HB}\) is the stronger acid.

Step 4: Determining Conjugate Base Strength

The strength of a conjugate base is inversely related to the strength of the acid. Since \(\text{HB}\) is the stronger acid, \(\text{B}^{-}\) is the weaker base compared to \(\text{A}^{-}\). Hence, \(\text{A}^{-}\) is the stronger conjugate base.

Key Concepts

Understanding Acid Strength

Acid strength refers to the ability of an acid to donate protons, or hydrogen ions \( H^+ \), to a base. A strong acid fully dissociates in water, which means it completely releases its \( H^+ \) ions into the solution. In contrast, weak acids only partially dissociate, holding onto most of their hydrogen ions.
In the case of the exercise, we analyze the strength of two acids, HA and HB, by observing their pH at the equivalence point when titrated with a strong base.
The lower the pH at the equivalence point, the stronger the acid. This is because stronger acids have weaker conjugate bases, and thus shift the pH nearer to neutral when the strong base is added.
In this specific scenario, \( ext{HB} \) is shown to be the stronger acid due to its lower pH value of 8.5 at the equivalence point, compared to \( ext{HA} \) at 9.5.

Conjugate Base Dynamics

When an acid donates a hydrogen ion, the remaining part is called its conjugate base. The strength of a conjugate base is related to the strength of its parent acid.
If the acid is strong, it means it dissociates more completely, and its conjugate base is relatively weak because it holds a poor ability to accept a proton back.
In our exercise, HA and HB form the conjugate bases \( ext{A}^- \) and \( ext{B}^- \) respectively. Since HB is the stronger acid, \( ext{B}^- \) is the weaker conjugate base. This principle arises because a strong acid loses its proton readily and does not favor regaining it, thus \( ext{B}^- \) is less inclined to reform HB.

Exploring the Equivalence Point

The equivalence point in an acid-base titration occurs when the amount of acid exactly neutralizes the amount of base, or vice versa.
At this point, all the acid has reacted with the base to form water and the conjugate base of the acid. The pH at the equivalence point gives insight into the basicity of the conjugate base.
If the equivalence point pH is above 7, the conjugate base is basic, as seen in our exercise with HA and HB. For HA with a pH of 9.5, its conjugate base \( ext{A}^- \) reflects stronger basicity compared to HB's pH of 8.5, where \( ext{B}^- \) is a weaker base.

Decoding pH

pH is a measure of the acidity or basicity of a solution. It is calculated as the negative logarithm of the hydrogen ion concentration: \[ \text{pH} = -\log[H^+] \]
A lower pH corresponds to a higher concentration of hydrogen ions and indicates an acidic solution. Conversely, a higher pH suggests a basic solution.
During a titration, monitoring pH changes helps identify the equivalence point and characterizes the nature (acidic or basic) of the solution after neutralization.
In our exercise, the pH values at the equivalence point serve to compare acid strengths and the basicity of their conjugate bases.

Understanding Neutralization Reactions

A neutralization reaction in chemistry happens when an acid and a base react to form water and a salt. The essential process involves the combination of hydrogen ions \( H^+ \) from the acid with hydroxide ions \( OH^- \) from the base to create water \( H_2O \).
In the titration of HA and HB, the strong base fully reacts with the acids, leading to the formation of water, making the solution technically more neutral. However, the presence of the conjugate base affects the overall pH, leading to slight basic values at the equivalence point.
This explains why despite the term 'neutralization', the pH may not be exactly 7, especially when weak acids are titrated with strong bases. In our exercise, this principle helps reveal the basicity of \( ext{A}^- \) and \( ext{B}^- \), and thereby the relative weakness in acidity of HA compared to HB.