A buffer contains 0.10 \(\mathrm{mol}\) of a weak acid and 0.20 \(\mathrm{mol}\) of its conjugate base in 1.0 \(\mathrm{L}\) of solution. Determine whether or not each addition exceeds the capacity of the buffer. a. adding 0.020 mol of \(\mathrm{NaOH}\) b. adding 0.020 \(\mathrm{mol}\) of \(\mathrm{HCl}\) c. adding 0.10 mol of \(\mathrm{NaOH}\) d. adding 0.010 \(\mathrm{mol}\) of \(\mathrm{HCl}\)

A weak acid is a compound that does not completely ionize in water, forming an equilibrium between the acid (HA) and its conjugate base (A^-). The conjugate base is the species formed after the acid donates a proton (H⁺). This pair works together in buffer solutions to resist changes in pH.

When a strong base like NaOH is added to the buffer, it reacts with the weak acid, converting HA to A^-. Conversely, when a strong acid like HCl is added, it reacts with the conjugate base, converting A^- to HA. These reactions are how buffers maintain a stable pH: the weak acid neutralizes added base and the conjugate base neutralizes added acid.

The pH of a solution is a measure of its acidity or alkalinity. For buffer solutions, the pH largely depends on the ratio of the concentration of the weak acid to its conjugate base. Using the Henderson-Hasselbalch equation, \( pH = pKa + \log\frac{\left[A^-\right]}{\left[HA\right]} \) where \( pKa \) is the acid dissociation constant, we can calculate pH.

Upon adding small amounts of a strong acid or base, the buffer works to adjust the ratio of [HA] to [A^-] to minimize the pH change. Effective buffer action requires maintaining the concentrations of HA and A^- within a certain range. If too much strong acid or base is added, it can overwhelm the buffer, leading to a significant pH shift.

The strong acids and bases are completely dissociated in water. When a strong acid like HCl is added to a buffer, it donates protons (H⁺), which react with the conjugate base present in the buffer. The reaction can be represented as \( A^- + H^+ \rightarrow HA \).

Similarly, the addition of a strong base such as NaOH introduces hydroxide ions (OH^-) that react with the weak acid of the buffer: \( HA + OH^- \rightarrow A^- + H_2O \).

This exchange allows buffers to adjust to additions of strong acids or bases without suffering drastic pH changes. However, the balance between the weak acid and its conjugate base is critical, and excessive additions can exceed the buffer's capacity to stabilize pH, leading to a phenomenon called buffer overload.