Buffer Solution Notes

Buffer Solutions

Definition

• A buffer solution is an aqueous solution of a weak acid and its conjugate base, or a weak base and its conjugate acid.
• It resists changes in pH upon addition of small amounts of acid or base.
• Used to maintain a nearly constant pH in chemical applications.

Chemistry of Buffer Solutions

• Equilibrium between a weak acid (HA) and its conjugate base (A-): $HA \leftrightarrow H^+ + A^-$
• Adding $H^+$ shifts equilibrium left (Le Chatelier's principle).
• Adding $OH^-$ shifts equilibrium right, consuming $H^+$ and moderating pH change.

Henderson-Hasselbalch Equation

• $K_a = \frac{[H^+][A^-]}{[HA]}$
• $[H^+] = K_a \times \frac{[HA]}{[A^-]}$
• $pH = -\log[H^+] = -\log K_a + \log \frac{[A^-]}{[HA]}$
• $pH = pK<em>a + \log \frac{[A^-]}{[HA]}$ or $pH = pK</em>a + \log \frac{\text{[conjugate base or salt]}}{\text{[acid]}}$

Making a Buffer Solution

• Use the Henderson-Hasselbalch equation: $pH = pK_a + \log \frac{[A^-]}{[HA]}$
• pH depends on: the $pK_a$ of the weak acid and the ratio of the concentrations of the acid and salt.
• pH does not depend on the actual concentration of the buffer, but on the ratio of the two parts.

Calculating pH of a Buffer

• Example: 0.20M $CH<em>3COOH$ and 0.30M $CH</em>3COONa$ solution, $K_a = 1.8 \times 10^{-5}$, pH = 4.9
• 0.20M $CH_3COOH$ solution, pH = 2.72

Buffer Capacity

• Measure of a buffer's efficiency in resisting pH changes.
• Indicates the amount of acid or base that can be added before the buffer loses its ability to resist the change in pH.
• Depends on: how close the pH is to the $pK_a$ (within 1-2 pH units) and the total concentration of the buffer.

Concentration Effect

• A buffer of 0.001M $CH<em>3COOH$ and 0.001M $CH</em>3COONa$ has the same pH as a buffer made with 0.1M $CH<em>3COOH$ and 0.1M $CH</em>3COONa$. However, the 0.1M buffer has a larger buffer capacity.

Applications of Buffers

• Useful in chemical manufacturing and biochemical processes due to resistance to pH changes.
• Ideal buffer: $pK_a$ equals desired pH for maximum buffer capacity.
• Enzymes require precise pH; buffers prevent denaturation.
• Carbonic acid ($H<em>2CO</em>3$) and bicarbonate ($HCO_3^−$) buffer in blood plasma (pH 7.35-7.45).
• Used in fermentation, dyeing fabrics, chemical analysis, and pH meter calibration.
• Biological samples in research often use buffers like PBS (pH 7.4).

Example

• 100ml buffer solution containing 0.2 mol $K<em>2HPO</em>4$ and 0.1 mol $KH<em>2PO</em>4$, $K_a = 6.2 \times 10^{-8}$
• pH after adding 20.0 ml of 0.035M NaOH: 7.51
• pH after adding 20.0 ml of 0.035M HCl: 7.50