Buffer Solutions

Buffers

• A buffer is a solution containing a weak acid and its conjugate base (or a weak base and its conjugate acid).
• Buffers resist changes in pH upon addition of small amounts of strong acid or base.

How Buffers Work

• Buffers neutralize added strong acids and bases.
• Added $OH^-$ or $H_3O^+$ are consumed, minimizing direct pH impact.
• Added $OH^-$ is converted to the weak base, $A^-$: $HA(aq) + OH^-(aq) \rightarrow A^-(aq) + H_2O(l)$.
• Added $H<em>3O^+$ is converted to the weak acid, $HA$: $A^-(aq) + H</em>3O^+(aq) \rightarrow HA(aq) + H_2O(l)$.
• Buffers maintain a nearly constant pH.

Buffering Action

• Example with acetic acid and acetate salt:
  • Addition of $H_3O^+$ shifts equilibrium to the left.
  • Addition of $OH^-$ shifts equilibrium to the right: $OH^- + CH<em>3COOH(aq) \rightarrow H</em>2O(l) + CH_3COO^-(aq)$.

pH Calculation

• The Henderson-Hasselbalch equation calculates buffer pH:
  • $pH = pK_a + log \frac{[A^-]}{[HA]}$, where $[A^-]$ is the concentration of the conjugate base and $[HA]$ is the concentration of the weak acid.

Henderson-Hasselbalch Equation Derivation

• $K<em>a = \frac{[A^-][H</em>3O^+]}{[HA]}$
• $[H<em>3O^+] = K</em>a \frac{[HA]}{[A^-]}$
• $-log[H<em>3O^+] = -log K</em>a + log \frac{[HA]}{[A^-]}$
• $pH = pK_a + log \frac{[A^-]}{[HA]}$

pKa and pKb Relationship

• $K<em>a \times K</em>b = K_w = 1.0 \times 10^{-14}$
• $pK<em>a + pK</em>b = 14$

Basic Buffers

• For a basic buffer: $B + H_2O \rightleftharpoons HB^+ + OH^-$
• Use the Henderson-Hasselbalch equation by considering the acid reaction: $HB^+ + H<em>2O \rightleftharpoons B + H</em>3O^+$
• $pH = pK_a + log \frac{[B]}{[HB^+]}$

Buffer Capacity

• Buffer capacity is the amount of strong acid or base a buffer can handle before significant pH change.
• Limited by the amount of $HA$ and $A^-$ present.
• More moles of buffer components = higher capacity.

Buffering Effectiveness

• A good buffer neutralizes moderate amounts of added acid or base within a specific buffering range.
• Effectiveness depends on:
  1. Relative amounts of acid and base.
  2. Absolute concentrations of acid and base.

Buffering Range

• Most effective when $0.1 < \frac{\text{[base]}}{\text{[acid]}} < 10$.
• Effective pH range: $pK_a \pm 1$

Preparing a Buffer with a Specific pH

1. Choose a weak acid with a $pK_a$ close to the desired pH.
2. Use the Henderson-Hasselbalch equation to find the required $\frac{\text{[conjugate base]}}{\text{[weak acid]}}$ ratio: $\frac{[A^-]}{[HA]} = 10^{(pH - pK_a)}$.