Acids, Bases and Buffers

• Acid: proton ($\text{H}^+$) donor
• Base: proton acceptor
• Conjugate acid-base pair: differ by one proton

$\text{HA} + \text{B} \rightleftharpoons \text{A}^- + \text{BH}^+$

HA and A⁻ are a conjugate pair; B and BH⁺ are a conjugate pair.

$\text{pH} = -\log_{10}[\text{H}^+]$ $[\text{H}^+] = 10^{-\text{pH}}$

Strong Acids (Fully Ionised)

For a strong monobasic acid like HCl: $[\text{H}^+] = [\text{acid}]$

Example: pH of 0.10 mol/dm³ HCl: $\text{pH} = -\log(0.10) = 1.0$

For H₂SO₄ (strong dibasic): $[\text{H}^+] = 2 \times [\text{acid}]$

Strong Bases

Use $K_w$: $K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}$ at 25°C

$[\text{H}^+] = \frac{K_w}{[\text{OH}^-]}$

Example: pH of 0.10 mol/dm³ NaOH: $[\text{OH}^-] = 0.10$ $[\text{H}^+] = \frac{1.0 \times 10^{-14}}{0.10} = 1.0 \times 10^{-13}$ $\text{pH} = -\log(1.0 \times 10^{-13}) = 13.0$

$K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14} \text{ mol}^2\text{ dm}^{-6} \text{ at } 25°\text{C}$

• In pure water: $[\text{H}^+] = [\text{OH}^-] = 1.0 \times 10^{-7}$, so pH = 7
• $K_w$ increases with temperature (dissociation of water is endothermic)
• At higher temperatures, pH of pure water < 7, but water is still neutral ($[\text{H}^+] = [\text{OH}^-]$)

A weak acid partially ionises: $\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$

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

Assumptions

1. Since ionisation is small, $[\text{HA}]_{\text{equilibrium}} \approx [\text{HA}]_{\text{initial}}$
2. $[\text{H}^+] = [\text{A}^-]$ (each HA produces one H⁺ and one A⁻)

Therefore: $K_a \approx \frac{[\text{H}^+]^2}{[\text{HA}]}$ $[\text{H}^+] = \sqrt{K_a \times [\text{HA}]}$

Example

Question: Calculate the pH of 0.10 mol/dm³ ethanoic acid ($K_a = 1.8 \times 10^{-5}$).

$[\text{H}^+] = \sqrt{1.8 \times 10^{-5} \times 0.10} = \sqrt{1.8 \times 10^{-6}} = 1.34 \times 10^{-3}$ $\text{pH} = -\log(1.34 \times 10^{-3}) = 2.87$

$pK_a$

$pK_a = -\log K_a$ $K_a = 10^{-pK_a}$

Smaller $pK_a$ = stronger acid.

A buffer resists changes in pH when small amounts of acid or base are added.

How Buffers Work

An acidic buffer contains:

• A weak acid (HA) — provides reservoir of undissociated molecules
• Its conjugate base (A⁻) — usually from a sodium salt

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

• Adding acid: Extra H⁺ reacts with A⁻ → HA. Equilibrium shifts left. pH barely changes.
• Adding base: Extra OH⁻ reacts with HA → A⁻ + H₂O. H⁺ is replaced from equilibrium. pH barely changes.

Henderson-Hasselbalch Equation

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

Example

Question: Calculate the pH of a buffer made from 0.20 mol/dm³ ethanoic acid and 0.30 mol/dm³ sodium ethanoate. ($pK_a = 4.74$)

$\text{pH} = 4.74 + \log\left(\frac{0.30}{0.20}\right) = 4.74 + \log(1.5) = 4.74 + 0.18 = 4.92$

Blood as a Buffer

Blood is buffered at pH 7.4 by the carbonic acid–hydrogencarbonate system: $\text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^-$

Strong Acid + Strong Base

• Start at low pH (~1)
• Sharp vertical section at equivalence point (pH ~7)
• Suitable indicators: any with range across 3–11

Weak Acid + Strong Base

• Start at higher pH (~3)
• Buffer region with gentle slope before equivalence
• Equivalence point above pH 7 (~8.5–10)
• Use phenolphthalein (range 8.2–10)
• Half-equivalence point: pH = $pK_a$

Strong Acid + Weak Base

• Equivalence point below pH 7 (~4–5)
• Use methyl orange (range 3.1–4.4)

Weak Acid + Weak Base

• No sharp equivalence point
• No suitable indicator — use a pH meter

• Strong acid pH: straightforward $-\log[\text{H}^+]$
• Weak acid pH: use $K_a$ formula with the square root
• Buffers: use Henderson-Hasselbalch; be careful about moles vs concentrations
• At the half-equivalence point: $[\text{HA}] = [\text{A}^-]$, so pH = $pK_a$
• Always check: is the acid strong or weak? This determines the approach

• Strong acids: fully ionise; $[\text{H}^+] = [\text{acid}]$
• Weak acids: partially ionise; use $K_a = \frac{[\text{H}^+]^2}{[\text{HA}]}$
• $K_w = [\text{H}^+][\text{OH}^-] = 10^{-14}$ at 25°C
• Buffers resist pH changes; pH = $pK_a + \log([\text{A}^-]/[\text{HA}])$
• Titration curves depend on acid/base strength; choose indicator to match equivalence pH