pH Titration Curves

Introduction

A pH titration curve makes the changing chemical composition visible. Before equivalence, the original analyte and its reaction products determine pH. Near equivalence, a small titrant addition can cause a large pH change. After equivalence, excess titrant often dominates. The curve's shape tells an analyst which indicator might work and what acid–base model belongs in each calculation region.

Core explanation

For a strong acid such as HCl titrated with strong base NaOH, initial pH is controlled by the acid concentration. Before equivalence, subtract OH⁻ moles from initial H⁺ moles and divide the remaining H⁺ by total solution volume. At equivalence, in an ideal dilute system at 25 °C with neutral salt and water, pH is approximately 7. After equivalence, calculate excess OH⁻ concentration from excess base moles and total volume, find pOH, then use pH + pOH = 14 at 25 °C. This simple model ignores activity corrections relevant at higher ionic strength.

For a weak acid HA titrated by strong base, the starting pH is higher than that of an equally concentrated strong acid because HA partially dissociates. Before equivalence, added OH⁻ converts HA to A⁻. The mixture of HA and A⁻ is a buffer, so pH often changes gradually. At half-equivalence, n(HA) and n(A⁻) are approximately equal, giving pH ≈ pKₐ under the Henderson–Hasselbalch conditions. At equivalence, HA has been converted mainly to A⁻; its hydrolysis makes pH above 7 for an ordinary weak acid. After equivalence, excess strong base dominates.

The equivalence volume is set by initial analyte moles and reaction stoichiometry, not by acid strength. If 25.00 mL of 0.1000 mol L⁻¹ monoprotic HCl and 25.00 mL of 0.1000 mol L⁻¹ monoprotic acetic acid are separately titrated with 0.1000 mol L⁻¹ NaOH, each needs 25.00 mL for equivalence. Their pH curves differ substantially. A weak base titrated with strong acid produces the corresponding acidic equivalence region due to its conjugate acid.

The volume axis always reflects delivered titrant; the solution volume in a pH calculation is initial analyte volume plus added titrant volume, unless sampling removes appreciable liquid. The vertical jump sharpness depends on concentration and acid/base strength.

Step-by-step reasoning

1. Write initial analyte amount and choose representative titrant volumes. 2. Before equivalence, calculate remaining strong species or weak-acid buffer composition. 3. At equivalence, identify which conjugate ion remains and whether it hydrolyses. 4. After equivalence, calculate excess strong titrant concentration with total volume. 5. Plot the regions and choose an endpoint method from the steep segment.

Visual explanation

On one pH-versus-base-volume graph, draw two rising curves that cross the same equivalence volume. The strong-acid curve begins at lower pH and passes near pH 7 at equivalence. The weak-acid curve begins higher, has a broad buffer region, marks pH = pKₐ at half-equivalence and passes above pH 7 at equivalence. Both climb into the excess-base region afterward.

Real-world analogy

Adding base to strong acid is like pouring water into an empty bucket of acid equivalents: until the bucket is nearly filled, excess acid controls the condition. A weak-acid buffer is more like a shock absorber that changes composition while resisting a large pH shift. At equivalence the shock absorber is used up, so further additions cause a sharper response.

Real-world example

An analyst examining acetic acid in vinegar can collect pH readings after each small base addition. The curve's half-equivalence region provides an estimate of the acid's pKₐ, while the inflection near equivalence estimates its amount. If the sample includes multiple acids, the observed curve may be broader or less easily interpreted as one ideal monoprotic system.

Why?

Why is weak-acid/strong-base equivalence basic? The main solute at equivalence is the weak acid's conjugate base A⁻. It reacts with water, A⁻ + H₂O ⇌ HA + OH⁻, producing some hydroxide. The pH therefore usually exceeds 7 under ordinary dilute aqueous conditions at 25 °C.

Common misconception

“Both curves have the same equivalence pH because equal moles react” confuses stoichiometric equivalence with solution equilibrium after reaction. Another error is using the initial volume alone when calculating excess acid or base concentration; added titrant changes total volume.

Worked example

Titrate 25.00 mL of 0.1000 mol L⁻¹ HCl with 0.1000 mol L⁻¹ NaOH. Initial H⁺ is 0.002500 mol. After 20.00 mL base, 0.002000 mol OH⁻ has reacted, leaving 0.000500 mol H⁺ in 0.04500 L. Thus [H⁺] ≈ 0.01111 mol L⁻¹ and pH ≈ 1.95. Equivalence occurs at 25.00 mL, not at the 20.00 mL point. The calculation illustrates the before-equivalence strong-acid region.

Quick check

1. Do equal initial moles of a monoprotic strong acid and weak acid require different base moles for complete neutralisation? Answer: No. If both donate one titratable proton per molecule, equal analyte moles require equal base moles. Their pH curve shapes and equivalence pH differ, not their stoichiometric titrant amounts.

Exam focus

Identify the chemical regime before applying a formula: excess strong acid/base, buffer, weak conjugate species at equivalence, or excess titrant. Show total volume in concentration calculations. State the 25 °C idealisation when asserting neutral pH 7 at strong-acid/strong-base equivalence.

Advanced insight

The maximum slope of a pH curve can be used to estimate equivalence, but sampled data and electrode lag can shift an apparent numerical peak. First- or second-derivative methods require adequately spaced readings and careful treatment of noise. A smooth theoretical curve does not guarantee a perfectly located experimental equivalence volume.

Summary

Titration curves plot pH against titrant volume and reveal reaction regions. Strong-acid/strong-base equivalence is near neutral under standard dilute conditions; weak-acid/strong-base equivalence is basic because the conjugate base hydrolyses. A weak acid produces a buffer region and half-equivalence pH near pKₐ, while stoichiometry fixes equivalence volume.

Practice questions

1. Why is pH approximately pKₐ at half-equivalence for a simple weak acid titration? Answer: About half of HA has become A⁻, making their concentrations approximately equal. In Henderson–Hasselbalch, log([A⁻]/[HA]) is then approximately zero.

2. What is the total solution volume after 18.0 mL titrant is added to 25.0 mL analyte? Answer: Assuming additive volumes, 43.0 mL, or 0.0430 L, is used to calculate concentrations at that point.

3. What species controls pH well beyond equivalence in strong-base titration of a weak acid? Answer: Excess OH⁻ from the added strong base usually dominates; the weak conjugate base contribution is comparatively small.