Buffers Knowledge-Based Study

Study notes

1. A buffer solution is an aqueous solution that resists significant changes in pH upon the addition of small amounts of strong acid or strong base, or upon dilution.

   To function effectively, a buffer must contain two key components simultaneously:

   • A weak conjugate acid-base pair consisting of either a weak acid and its conjugate base (e.g., $\text{CH}_3\text{COOH}$ and $\text{CH}_3\text{COO}^-$).
   • A weak base and its conjugate acid (e.g., $\text{NH}_3$ and $\text{NH}_4^+$).

   A mixture of a strong acid and its conjugate base, such as $\text{HCl}$ and $\text{NaCl}$, cannot act as a buffer because $\text{Cl}^-$ is an extremely weak base with negligible affinity for protons in aqueous solution.

   Consider an acidic buffer containing equimolar amounts of a weak acid, $\text{HA}$, and its conjugate base, $\text{A}^-$:

   • When a small amount of strong acid ($\text{H}_3\text{O}^+$) is added: The conjugate base neutralizes the added hydronium ions according to the reaction:
     $\text{A}^-(aq) + \text{H}_3\text{O}^+(aq) \rightarrow \text{HA}(aq) + \text{H}_2\text{O}(l)$
     Because the strong acid is converted into the weak acid $\text{HA}$, the hydronium ion concentration increases only slightly.
   • When a small amount of strong base ($\text{OH}^-$) is added: The weak acid neutralizes the hydroxide ions according to the reaction:
     $\text{HA}(aq) + \text{OH}^-(aq) \rightarrow \text{A}^-(aq) + \text{H}_2\text{O}(l)$
     Because hydroxide reacts to produce the weak conjugate base $\text{A}^-$, the hydroxide concentration increases only slightly.

   The pH of a buffer solution can be derived from the equilibrium expression of the weak acid:

   $$K_a = \frac{[\text{H}_3\text{O}^+][\text{A}^-]}{[\text{HA}]}$$

   Taking the negative logarithm of both sides yields the Henderson-Hasselbalch equation:

   $$\text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$

   Key consequences of this relationship include:

   • When $[\text{A}^-] = [\text{HA}]$, the ratio is 1, and since $\log(1) = 0$, the buffer pH equals the $\text{p}K_a$ of the weak acid.
   • A buffer functions most effectively within the range of $\text{pH} = \text{p}K_a \pm 1$, where neither component is depleted too rapidly.

   Two main parameters define the performance of a buffer:

   • Buffer Range: The usable pH interval over which the buffer resists pH changes, typically spanning $\text{p}K_a \pm 1$. Outside this range, the ratio of conjugate base to conjugate acid exceeds 10:1 or falls below 1:10, severely reducing protective action.
   • Buffer Capacity: The amount of strong acid or base that can be absorbed before the pH changes significantly. Buffer capacity depends directly on the absolute concentrations of the buffer components; solutions with higher concentrations of $\text{HA}$ and $\text{A}^-$ have a greater buffer capacity, even if their pH values are identical.