Problem 32 - Chemistry and Chemical Reactivity

Question

Which is the stronger of the following two acids? (a) acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}, K_{\mathrm{a}}=1.8 \times 10^{-5}\) (b) chloroacetic acid, \(\mathrm{ClCH}_{2} \mathrm{CO}_{2} \mathrm{H}, \mathrm{p} K_{a}=2.85\)

Step-by-Step Solution

Answer

Chloroacetic acid is the stronger acid.

Step 1: Understand the Concept

Acid strength is often compared using the acid dissociation constant \( K_a \) or its logarithmic counterpart, \( \mathrm{p}K_a \). The smaller the \( \mathrm{p}K_a \) value, the stronger the acid.

Step 2: Evaluate Given Values

We have two acids, each with different acid strength indicators: Acetic acid with \( K_a = 1.8 \times 10^{-5} \) and chloroacetic acid with \( \mathrm{p}K_a = 2.85 \). We need to express both acids in the same terms. Since acetic acid is given in \( K_a \), convert chloroacetic acid's \( \mathrm{p}K_a \) to \( K_a \).

Step 3: Convert \( \mathrm{p}K_a \) to \( K_a \) for Chloroacetic Acid

Convert the \( \mathrm{p}K_a \) value of chloroacetic acid to \( K_a \) using the formula: \[ K_a = 10^{-\mathrm{p}K_a} \] Substitute \( \mathrm{p}K_a = 2.85 \):\[ K_a = 10^{-2.85} \approx 1.41 \times 10^{-3} \]

Step 4: Compare \( K_a \) Values

Now compare the \( K_a \) values: - Acetic acid \( K_a = 1.8 \times 10^{-5} \)- Chloroacetic acid \( K_a = 1.41 \times 10^{-3} \)The larger \( K_a \) value indicates a stronger acid strength. Here, chloroacetic acid has a larger \( K_a \) than acetic acid.

Key Concepts

Acid Dissociation Constant (Ka)

The acid dissociation constant, often represented by the symbol \( K_a \), is a vital parameter in understanding acid strength. \( K_a \) describes the extent to which an acid dissociates in water. A higher \( K_a \) value indicates a greater degree of dissociation, which implies the acid is stronger. This means the acid is more capable of donating a proton (\( H^+ \)) to the surrounding solution. As a result:

• Stronger acids dissociate more completely in water.
• They tend to have larger \( K_a \) values.

Acids vary in their strength, and comparing their \( K_a \) values can directly show which acid is stronger. For example, comparing acetic acid with \( K_a = 1.8 \times 10^{-5} \) and chloroacetic acid with \( K_a = 1.41 \times 10^{-3} \), chloroacetic acid is clearly stronger. This is because its \( K_a \) value is much larger, indicating it dissociates more in solution.

pKa Value

The \( \mathrm{p}K_a \) value provides another method to express the strength of an acid. The \( \mathrm{p}K_a \) is the negative logarithm of the acid dissociation constant, expressed mathematically as:\[\mathrm{p}K_a = -\log_{10}(K_a)\]This means that lower \( \mathrm{p}K_a \) values correspond to stronger acids. It's crucial because:

• A small \( \mathrm{p}K_a \) value points to a high \( K_a \), signifying a strong acid.
• Easy comparison of acidity strengths without dealing with very small \( K_a \) values.

When given chloroacetic acid's \( \mathrm{p}K_a = 2.85 \), converting it to \( K_a \) as demonstrated allows easier comparison with acetic acid's \( K_a \). These conversions help categorize the acid strength effectively, aiding in identifying the stronger acid.

Comparison of Acidity

Comparing the acidity of different acids involves evaluating either their \( K_a \) or \( \mathrm{p}K_a \) values to understand which acid is stronger.

• A higher \( K_a \) means stronger acidity because the acid releases protons more freely.
• Conversely, a lower \( \mathrm{p}K_a \) means stronger acidity as it indicates a larger \( K_a \).

For example, considering acids like acetic acid and chloroacetic acid, conversion between \( \mathrm{p}K_a \) and \( K_a \) is often necessary to carry out a direct comparison of their strengths. When converted, chloroacetic acid's \( K_a \) is notably greater than acetic acid's, demonstrating that chloroacetic acid is the stronger acid. Such comparisons help predict and understand chemical reactivities and behaviors in solutions.