Problem 3 - Chemistry An Atoms First Approach

Question

Mixing together solutions of acetic acid and sodium hydroxide can make a buffered solution. Explain. How does the amount of each solution added change the effectiveness of the buffer?

Step-by-Step Solution

Answer

Mixing acetic acid (a weak acid) and sodium hydroxide (a strong base) forms a buffered solution containing both the weak acid and its conjugate base, sodium acetate. Buffer effectiveness is determined by the Henderson-Hasselbalch equation: \( pH = pK_a + \log \frac{[A^-]}{[HA]} \), comparing the concentrations of these two components. The buffer's capacity to resist pH changes is higher when the base/acid concentrations ratio is close to 1 and when the overall concentrations are high. Changing the amounts of acetic acid and sodium hydroxide added to the solution will affect this ratio and, consequently, the buffer's effectiveness.

Step 1: Introduction to pH and Buffer

A buffer solution is a mixture of a weak acid and its conjugate base, or a weak base and its conjugate acid. It helps to resist changes in pH when small amounts of an acid or a base are added. In our case, mixing acetic acid (a weak acid) and sodium hydroxide (a strong base) will yield a buffered solution.

Step 2: Formation of the Buffer

The reaction between acetic acid (CH3COOH) and sodium hydroxide (NaOH) can be represented as follows: \( CH_3COOH + NaOH \rightarrow CH_3COONa + H_2O \) Sodium acetate (CH3COONa) is the salt formed, and it represents the conjugate base of acetic acid, while water is another product. In a buffered solution, both the weak acid (acetic acid in this case) and its conjugate base (sodium acetate) will be present in appreciable amounts.

Step 3: Henderson-Hasselbalch Equation

The effectiveness of a buffer is determined by its ability to resist changes in pH. This can be explained using the Henderson-Hasselbalch equation: \( pH = pK_a + \log \frac{[A^-]}{[HA]} \) where pH is the solution's pH, pKa is the acid dissociation constant of the weak acid, [A-] is the concentration of the conjugate base (here, the acetate ion from sodium acetate), and [HA] is the concentration of the weak acid (acetic acid in this case).

Step 4: Change in Buffer Effectiveness

The effectiveness of the buffer depends on the ratio of the concentrations of the conjugate base and the weak acid, \(\frac{[A^-]}{[HA]}\). As we add different amounts of acetic acid and sodium hydroxide solutions, the concentrations of the acetate ion and acetic acid in the solution will change. Consequently, the buffer capacity, which reflects the solution's ability to resist changes in pH, will also change. A buffer solution will be more effective when the ratio of base/acid concentrations is close to 1, and when the overall concentrations of both components are high. Adding more of one component without the other may cause a decrease in the buffer's ability to resist pH changes, as it disturbs the equilibrium.