Buffers

Overview

A buffer is a solution that resists changes in pH when small amounts of acid or base are added. Buffers contain a weak acid and its conjugate base (or weak base and conjugate acid) in similar concentrations.

Buffer Components

Acidic Buffer

• Weak acid (HA) + Conjugate base (A⁻)
• pH < 7
• Example: CH₃COOH / CH₃COO⁻

Basic Buffer

• Weak base (B) + Conjugate acid (BH⁺)
• pH > 7
• Example: NH₃ / NH₄⁺

How Buffers Work

Adding Acid (H⁺)

$$\text{H}^+ + \text{A}^- \rightarrow \text{HA}$$

Conjugate base neutralizes added acid.

Adding Base (OH⁻)

$$\text{OH}^- + \text{HA} \rightarrow \text{A}^- + \text{H}_2\text{O}$$

Weak acid neutralizes added base.

Henderson-Hasselbalch Equation

For Acidic Buffers

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

For Basic Buffers

$$\text{pOH} = \text{p}K_b + \log\left(\frac{[\text{BH}^+]}{[\text{B}]}\right)$$

Or:

$$\text{pH} = \text{p}K_a + \log\left(\frac{[\text{B}]}{[\text{BH}^+]}\right)$$

(where pKa is for the conjugate acid BH⁺)

Buffer Preparation

Method 1: Mix Weak Acid and Salt

Example: Acetic acid + Sodium acetate

Method 2: Partial Neutralization

Add strong base to weak acid (or strong acid to weak base)

• Some weak acid converts to conjugate base

Example Calculations

Example 1: Finding pH

A buffer contains 0.20 M acetic acid and 0.15 M sodium acetate. $K_a = 1.8 \times 10^{-5}$

$$\text{p}K_a = -\log(1.8 \times 10^{-5}) = 4.74$$ $$\text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$ $$\text{pH} = 4.74 + \log\left(\frac{0.15}{0.20}\right)$$ $$\text{pH} = 4.74 + \log(0.75) = 4.74 + (-0.12) = 4.62$$

Example 2: Preparing a Buffer

Prepare a pH 5.00 buffer using acetic acid (pKa = 4.74).

$$\text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$ $$5.00 = 4.74 + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$ $$0.26 = \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$ $$\frac{[\text{A}^-]}{[\text{HA}]} = 10^{0.26} = 1.82$$

Need ratio of acetate to acetic acid = 1.82:1

Example 3: Adding Acid to Buffer

0.50 L buffer: 0.10 M HA, 0.10 M A⁻ Add 0.010 mol HCl. Find new pH. (pKa = 4.74)

Initial moles:

$$\text{HA} = 0.10 \times 0.50 = 0.050 \text{ mol}$$ $$\text{A}^- = 0.10 \times 0.50 = 0.050 \text{ mol}$$

After adding H⁺:

$$\text{A}^- + \text{H}^+ \rightarrow \text{HA}$$ $$\text{A}^-: 0.050 - 0.010 = 0.040 \text{ mol}$$ $$\text{HA}: 0.050 + 0.010 = 0.060 \text{ mol}$$

New pH:

$$\text{pH} = 4.74 + \log\left(\frac{0.040}{0.060}\right)$$ $$\text{pH} = 4.74 + \log(0.667) = 4.74 - 0.18 = 4.56$$

pH changed only from 4.74 to 4.56!

Buffer Capacity

The amount of acid or base a buffer can neutralize before significant pH change.

Factors Affecting Capacity

1. Higher concentrations → Greater capacity
2. Ratio closer to 1:1 → Greater capacity
3. More moles of components → Greater capacity

Maximum Buffer Capacity

Occurs when [HA] = [A⁻] (ratio = 1, pH = pKa)

Effective Buffer Range

$$\text{pH} = \text{p}K_a \pm 1$$

Buffer is most effective when pH is within 1 unit of pKa.

[A⁻]/[HA]	pH - pKa
10:1	+1
1:1	0
1:10	-1

Biological Buffers

Blood Buffer System (pH 7.4)

$$\text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^- \quad \text{p}K_a = 6.4$$

$\text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3$ provides additional regulation.

Phosphate Buffer (intracellular)

$$\text{H}_2\text{PO}_4^- \rightleftharpoons \text{H}^+ + \text{HPO}_4^{2-} \quad \text{p}K_a = 7.2$$

Protein Buffers

Amino acid side chains can accept or donate H⁺.

Common Buffer Systems

Buffer	pKa	Useful pH Range
Phosphoric/Phosphate	2.1	1.1 - 3.1
Acetic/Acetate	4.74	3.7 - 5.7
Carbonic/Bicarbonate	6.4	5.4 - 7.4
Phosphate (H₂PO₄⁻)	7.2	6.2 - 8.2
Tris	8.1	7.1 - 9.1
Ammonia/Ammonium	9.25	8.3 - 10.3

Summary

Key Equations

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

Buffer Requirements

1. Weak acid/base + conjugate
2. Similar concentrations (within 10:1)
3. pH within pKa ± 1

Buffer Capacity Increases With

• Higher total concentration
• Ratio closer to 1:1
• pH closer to pKa