Problem 21 - Chemistry: An Atoms-Focused Approach

Question

What is the pH of a buffer that is \(0.200 M\) chloroacetic acid and \(0.100 M\) sodium chloroacetate at \(25^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

Answer: The pH of the buffer solution is approximately 2.55.

Step 1: Identify the weak acid and its conjugate base

In this buffer solution, the weak acid is chloroacetic acid (abbreviated as HA) and its conjugate base is the chloroacetate ion (A-), which is formed when sodium chloroacetate dissociates in water.

Step 2: Write the chemical equilibrium for the weak acid

The chemical equilibrium for the dissociation of chloroacetic acid can be written as follows: \[ HA \rightleftharpoons H^+ + A^- \]

Step 3: Determine the \(K_a \, \)of chloroacetic acid

The acid dissociation constant, \(K_a \), for chloroacetic acid at \(25^{\circ} \mathrm{C} \) is \(1.4 \times 10^{-3}\).

Step 4: Apply the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the acid dissociation constant and the concentrations of the weak acid and its conjugate base: \[ pH = pK_a + \log \frac{[A^-]}{[HA]} \]

Step 5: Calculate the \(pK_a \, \)of chloroacetic acid

To find the \(pK_a \, \) of chloroacetic acid, take the negative logarithm of its \(K_a\): \[ pK_a = - \log(1.4 \times 10^{-3}) \] \[ pK_a ≈ 2.85 \]

Step 6: Use the concentrations given in the exercise to find the pH

Now, plug the known concentrations of the weak acid and its conjugate base as well as the \(pK_a \, \) value into the Henderson-Hasselbalch equation: \[ pH = 2.85 + \log \frac{0.100}{0.200} \] \[ pH ≈ 2.85 - 0.301 \]

Step 7: Calculate the pH of the buffer solution

After evaluating the expression in Step 6: \[ pH ≈ 2.85 - 0.301 \] \[ pH ≈ 2.55 \] The pH of the buffer solution is approximately 2.55.

Key Concepts

pH Calculation

Calculating pH is a crucial skill in understanding how acidic or basic a solution is. For buffer solutions, which resist changes in pH upon adding small amounts of acid or base, this calculation is slightly different than for non-buffer solutions. Buffer solutions typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. The pH of such a solution is influenced by the concentrations of these components as well as the acid dissociation constant, denoted as \(K_a\).

One essential tool for calculating the pH of a buffer is the Henderson-Hasselbalch equation, which neatly incorporates these factors to give you the pH directly.

• Weak acids only partially dissociate in solution, which imparts a particular pH to the buffer.
• In our example, chloroacetic acid acts as the weak acid, while sodium chloroacetate provides the conjugate base.

By carefully measuring the concentrations of these two components, we can pinpoint how the solution will react in terms of pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch Equation is a simplified way of calculating the pH of buffer solutions. It relates the pH of a solution to the acid dissociation constant \(K_a\) and the concentrations of the acid (\(HA\)) and its conjugate base (\(A^-\)).

The equation is:\[ pH = pK_a + \log \left(\frac{[A^-]}{[HA]}\right) \]
This equation is beneficial because it allows you to estimate the pH of buffer solutions with relative ease. A few essential points about the equation include:

• \(pK_a\) is the negative logarithm of the \(K_a\) of the weak acid. This helps transform the exponential nature of the \(K_a\) into a linear and more manageable scale.
• \([A^-]\) and \([HA]\) are the molar concentrations of the conjugate base and the weak acid, respectively.

When used correctly, the Henderson-Hasselbalch Equation simplifies pH calculation in systems with weak acids and their conjugate bases into just a few manageable steps.

For our specific example, the equation uses the known concentrations of chloroacetic acid (0.200 M) and sodium chloroacetate (0.100 M) to arrive at a pH of approximately 2.55.

Acid Dissociation Constant (Ka)

The acid dissociation constant, \(K_a\), is an important parameter in chemistry that quantifies the strength of a weak acid in solution. It essentially describes how well an acid donates protons to water to form hydronium ions (\(H^+\)), which directly affects the solution's pH.

This constant is vital for understanding the behavior of the weak acid because it allows chemists to predict how an acid will behave under certain conditions.

• \(K_a\) values can vary significantly between different acids. A larger \(K_a\) value indicates a stronger acid, suggesting it dissociates to a greater extent in solution.
• Conversely, a smaller \(K_a\) signifies a weaker acid, with less dissociation occurring and, therefore, a less acidic solution.

In buffer solutions, knowing the \(K_a\) helps in calculating the \(pK_a\), which is needed in the Henderson-Hasselbalch equation to find the pH. In our example, the \(K_a\) of chloroacetic acid is given as \(1.4 \times 10^{-3}\), indicating it's a weak acid.

This \(K_a\) value is transformed into \(pK_a\) by taking the negative logarithm, resulting in \(pK_a \approx 2.85\), which is then plugged into the Henderson-Hasselbalch Equation to find the buffer's pH.