IB Chemistry R3.1 R3.1.3

pH Calculations & Titrations

Calculating pH for strong and weak acids/bases, titration curves, indicators, and buffers.

Reactivity 3.1 SL & HL ⏱️ ~5 min revision

pH of Strong Acids & Bases SL

Strong acids and bases fully dissociate, so the initial concentration directly gives you [H⁺] or [OH⁻].

Core Formulas

Essential pH and pOH Relationships

\[\text{pH} = -\log_{10}[\text{H}^+], \quad \text{pOH} = -\log_{10}[\text{OH}^-]\] \[[\text{H}^+] = 10^{-\text{pH}}, \quad [\text{OH}^-] = 10^{-\text{pOH}}\] \[\text{pH} + \text{pOH} = 14.00 \quad (\text{at } 298\text{ K})\]

Worked Example

pH of a Strong Acid

Problem: Calculate the pH of a \(0.10\text{ mol dm}^{-3}\text{ HCl}\) solution.

Solution: \(\text{HCl}\) is a strong monoprotic acid → \([\text{H}^+] = 0.10\text{ mol dm}^{-3}\).

\[\text{pH} = -\log_{10}(0.10) = 1.00\]
Worked Example

pH of a Diprotic Strong Base

Problem: Calculate the pH of \(0.0044\text{ mol dm}^{-3}\text{ Ca(OH)}_2\) at \(298\text{ K}\).

Solution: \(\text{Ca(OH)}_2\) releases \(2\text{ OH}^-\) ions per formula unit:

\[[\text{OH}^-] = 2 \times 0.0044 = 0.0088\text{ mol dm}^{-3}\] \[\text{pOH} = -\log_{10}(0.0088) = 2.06\] \[\text{pH} = 14.00 - 2.06 = 11.94\]

HLpH of Weak Acids (Using Ka)

Weak acids partially dissociate. Use an ICE table to find [H⁺].

HL Extension

Worked Example: pH of a Weak Acid

Problem: Calculate the pH of \(0.534\text{ mol dm}^{-3}\) formic acid (\(\text{HCOOH}\)), given \(K_{\text{a}} = 1.77 \times 10^{-4}\).

Solution: Using the small-\(x\) approximation (\([\text{H}^+] = \sqrt{K_{\text{a}} \times c}\)):

\[[\text{H}^+] = \sqrt{1.77 \times 10^{-4} \times 0.534} = \sqrt{9.45 \times 10^{-5}} = 9.72 \times 10^{-3}\text{ mol dm}^{-3}\] \[\text{pH} = -\log_{10}(9.72 \times 10^{-3}) = 2.01\]

HLpH of Weak Bases (Using Kb)

HL Extension

Worked Example: pH of a Weak Base

Problem: Calculate the pH of \(0.0325\text{ mol dm}^{-3}\text{ NH}_3\), given \(K_{\text{b}} = 1.77 \times 10^{-5}\).

Solution: \([\text{OH}^-] = \sqrt{K_{\text{b}} \times c} = \sqrt{1.77 \times 10^{-5} \times 0.0325} = 7.58 \times 10^{-4}\text{ mol dm}^{-3}\)

\[\text{pOH} = -\log_{10}(7.58 \times 10^{-4}) = 3.12 \implies \text{pH} = 14.00 - 3.12 = 10.88\]

Titration Curves

Strong Acid + Strong Base Titration

R3.1.3 pH Calculations & Titrations - IB | ChemEasy Volume of base added / cm³ pH 0 7 14 Equivalence point (pH = 7 for SA/SB)

HLAll Four Titration Curve Types

Combination Initial pH Equiv. PH Key Features
SA + SB~17Steep symmetric jump; no buffer region
WA + SB~3-4> 7Buffer region before equiv.; half-equiv: pH = pKa
SA + WB~11< 7Buffer region; half-equiv: pOH = pKb
WA + WBModerateVariesVery shallow curve; no steep section; pH meter needed

HLChoosing an Indicator

An indicator is a weak acid (HInd) whose conjugate base (Ind⁻) has a different colour. It changes colour when pH ≈ pKa of the indicator (±1).

HL Extension

Indicator Selection Rule

An indicator is suitable for a titration if its \(\text{p}K_{\text{In}} \pm 1\) range falls entirely within the vertical inflection jump of the pH curve.

  • Strong Acid + Strong Base: Jump pH 3–11 → Phenolphthalein or Methyl orange.
  • Strong Acid + Weak Base: Jump pH 3–7 → Methyl orange (\(\text{p}K_{\text{In}} \approx 3.7\)).
  • Weak Acid + Strong Base: Jump pH 7–11 → Phenolphthalein (\(\text{p}K_{\text{In}} \approx 9.3\)).
  • Weak Acid + Weak Base: No sharp vertical jump → No indicator suitable (use pH probe).

HLSalt Hydrolysis

When a salt dissolves, its ions may react with water (hydrolyse). The pH depends on the parent acid and base:

Salt Type Made From Solution pH Example
NeutralSA + SB= 7NaCl
BasicWA + SB> 7CH₃COONa
AcidicSA + WB< 7NH₄Cl

HLBuffer Solutions

A buffer resists changes in pH when small amounts of acid or base are added. Made from comparable amounts of a conjugate pair.

HL Extension

Buffer Action and Henderson-Hasselbalch

Acidic Buffer: Weak acid + conjugate salt (e.g. \(\text{CH}_3\text{COOH} / \text{CH}_3\text{COONa}\)).

Basic Buffer: Weak base + conjugate salt (e.g. \(\text{NH}_3 / \text{NH}_4\text{Cl}\)).

Henderson-Hasselbalch Equation:

\[\text{pH} = \text{p}K_{\text{a}} + \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)\]

When \([\text{A}^-] = [\text{HA}]\), \(\text{pH} = \text{p}K_{\text{a}}\) (maximum buffer capacity).

Henderson-Hasselbalch Equation

pH = pKa + log([A⁻] / [HA])

At the half-equivalence point, [A⁻] = [HA], so log(1) = 0 → pH = pKa. This is how you experimentally determine Ka from a titration curve.

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