Problem 79 - Chemistry and Chemical Reactivity

Question

You have \(0.010 \mathrm{M}\) solutions of benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\) \(\left(K_{\mathrm{a}}=6.3 \times 10^{-5}\right)\) and 4 -chlorobenzoic acid, \(\mathrm{ClC}_{6} \mathrm{H}_{4} \mathrm{CO}_{2} \mathrm{H}\) \(\left(K_{\mathrm{a}}=1.0 \times 10^{-4}\right) .\) Which solution will have the higher pH?

Step-by-Step Solution

Answer

The benzoic acid solution has the higher pH.

Step 1: Understand the Problem

We have two solutions, each consisting of a different acid. We need to determine which acid solution has a higher pH. Recall that pH is inversely related to the acid's ability to donate protons (H+), which is measured by the acid dissociation constant, \(K_{a}\). A lower \(K_{a}\) value typically indicates a weaker acid, resulting in a higher pH for its solution.

Step 2: Compare Acid Strengths Using \(K_{a}\) Values

Benzoic acid has a \(K_{a}\) of \(6.3 \times 10^{-5}\), while 4-chlorobenzoic acid has a \(K_{a}\) of \(1.0 \times 10^{-4}\). Since \(6.3 \times 10^{-5} < 1.0 \times 10^{-4}\), benzoic acid is the weaker acid compared to 4-chlorobenzoic acid.

Step 3: Determine the Relationship between \(K_{a}\) and pH

Higher \(K_{a}\) values correspond to stronger acids, which dissociate more in solution, leading to more \(H^+\) ions and thus lower pH values. Conversely, a lower \(K_{a}\) indicates less dissociation, fewer \(H^+\) ions, and a higher pH.

Step 4: Identify the Solution with the Higher pH

Since benzoic acid has a lower \(K_{a}\), it is the weaker acid, resulting in fewer hydrogen ions in solution. Therefore, the benzoic acid solution will have a higher pH compared to the 4-chlorobenzoic acid solution.

Key Concepts

pH Calculation

Calculating pH is a fundamental skill in acid-base chemistry. The pH of a solution describes its acidity or basicity on a scale of 0 to 14. It's determined by the concentration of hydrogen ions (\(H^+\)) in a solution and can be calculated using the formula:
\[pH = -\log[H^+]\]

This equation shows that pH is the negative logarithm of the hydrogen ion concentration. A high concentration of \(H^+\) ions means a low pH (more acidic), while a lower concentration means a higher pH (more basic).

• Acids produce \(H^+\) ions in water, hence lowering the pH.
• Bases reduce \(H^+\) ion concentration, increasing the pH.
• The pH scale is logarithmic, meaning each whole number change represents a tenfold change in \(H^+\) concentration.

Understanding pH involves comprehending how acids dissociate and release \(H^+\) ions, influencing the balance of the solution.

Acid Dissociation Constant (Ka)

The Acid Dissociation Constant (\(K_a\)) is a crucial parameter that measures an acid's strength. Specifically, it reflects how well an acid dissociates into \(H^+\) ions and its conjugate base in solution. A higher \(K_a\) indicates a stronger acid capable of donating more \(H^+\) ions, leading to a lower pH. The relationship is expressed as:
\[K_a = \frac{[H^+][A^-]}{[HA]}\]

Where \([HA]\) is the concentration of the acid, and \([A^-]\) is the concentration of its conjugate base.

• A strong acid has a high \(K_a\) and dissociates completely, while a weak acid has a lower \(K_a\) and partially dissociates.
• The equilibrium position of an acid-base reaction depends on the \(K_a\) value.

By comparing \(K_a\) values, you can easily determine which acid is stronger and predict the pH implications for solutions of different acids.

Comparing Acid Strength

When comparing acid strength, you primarily look at the \(K_a\) values. An acid with a higher \(K_a\) is considered stronger since it donates more \(H^+\) ions into the solution. Here's the process:

• Identify the \(K_a\) values of the acids in question. For example, benzoic acid has a \(K_a\) of \(6.3 \times 10^{-5}\), while 4-chlorobenzoic acid's \(K_a\) is \(1.0 \times 10^{-4}\).
• Compare the values: A higher \(K_a\) (\(1.0 \times 10^{-4}\)) means 4-chlorobenzoic acid is the stronger acid.
• Stronger acids produce more \(H^+\) ions, resulting in a lower pH.

Thus, the benzoic acid solution will have a higher pH because it's a weaker acid with a lower \(K_a\). This comprehension aids in anticipating the behaviors of different acids in solutions, crucial for predicting chemical reactions and balances.