Problem 28 - 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, \(\mathrm{ClCH}_{2} \mathrm{CO}_{2} \mathrm{H}, \mathrm{p} K_{\mathrm{a}}=2.87\)

Step-by-Step Solution

Answer

Chloroacetic acid is the stronger acid.

Step 1: Understand Acid Strength

The strength of an acid is determined by its dissociation constant, \( K_a \). A larger \( K_a \) value means a stronger acid, as it dissociates more in solution.

Step 2: Convert pKa to Ka for Chloroacetic Acid

Given \( \mathrm{p}K_a = 2.87 \) for chloroacetic acid, convert it to \( K_a \) using the formula: \( K_a = 10^{-\mathrm{p}K_a} \).\[ K_a = 10^{-2.87} \approx 1.35 \times 10^{-3} \]

Step 3: Compare Ka Values

Compare the \( K_a \) values of both acids. - Acetic acid: \( K_a = 1.8 \times 10^{-5} \)- Chloroacetic acid: \( K_a = 1.35 \times 10^{-3} \)

Step 4: Determine the Stronger Acid

Since \( 1.35 \times 10^{-3} \) (chloroacetic acid's \( K_a \)) is greater than \( 1.8 \times 10^{-5} \) (acetic acid's \( K_a \)), chloroacetic acid is the stronger acid.

Key Concepts

Dissociation Constant

The dissociation constant, often represented as \( K_a \), plays a crucial role when discussing acid strength. It helps us understand how well an acid dissociates in water. Essentially, \( K_a \) is a measure of the ionization of the acid in solution. The higher the \( K_a \) value, the more the acid ionizes, and consequently, the stronger the acid.

• Acids with higher \( K_a \) values dissociate more completely in water.
• This leads to a greater production of hydronium ions \( (H_3O^+) \), indicating stronger acidity.

To put it simply, if you have two acids, comparing their \( K_a \) values tells you which one is stronger. A higher \( K_a \) suggests a more complete dissociation, making it a stronger acid. When determining acid strength, always remember: stronger acids have larger dissociation constants.

pKa to Ka Conversion

The dissociation constant \( K_a \) can also be expressed in a logarithmic form known as \( \text{p}K_a \). This form is often more manageable because it deals with smaller numbers. However, when comparing acid strength, we need the \( K_a \) values. That's where conversion comes into play.The relationship between \( \text{p}K_a \) and \( K_a \) is given by the formula: \[ K_a = 10^{-\text{p}K_a} \]This transformation is vital for accurately assessing and comparing the strengths of different acids. For example, if chloroacetic acid has a \( \text{p}K_a \) of 2.87, we calculate \( K_a \) as follows:

• First, apply the formula: \( K_a = 10^{-2.87} \)
• Adjusting the numbers gives us \( K_a \approx 1.35 \times 10^{-3} \)

This conversion allows us to directly compare dissociation constants and determine which acid is stronger.

Comparison of Ka Values

Once we've determined the \( K_a \) values of different acids, the next step is to compare these values to identify the stronger acid. This process is straightforward but crucial to understanding acid strength.Here’s how it works:

• Acetic acid has a \( K_a \) of \( 1.8 \times 10^{-5} \).
• Chloroacetic acid, after conversion, has a \( K_a \) of \( 1.35 \times 10^{-3} \).

When comparing \( K_a \) values:

• The larger the \( K_a \), the stronger the acid.
• Here, \( 1.35 \times 10^{-3} \) is significantly larger than \( 1.8 \times 10^{-5} \).
• Thus, chloroacetic acid is the stronger acid between the two.

This method is a reliable way to gauge acid strength, and being able to perform these comparisons enhances your understanding of chemical properties.