Acid-Base Titration Curves

Introduction

An acid-base titration adds a measured solution to a sample while monitoring pH or a suitable endpoint signal. Its curve records how the mixture changes before, at, and after stoichiometric equivalence. Reading the curve requires both reaction stoichiometry and equilibrium chemistry; the steepness and equivalence pH depend on the strengths of the reacting acid and base.

Core explanation

Place titrant volume on the horizontal axis and measured pH on the vertical axis. The initial pH describes the analyte before addition. As titrant reacts, the solution composition evolves. For a strong acid titrated with strong base, excess strong acid controls pH before equivalence; after equivalence, excess strong base controls it. Near the equivalence point, a small volume can cause a large pH change because neither excess reagent remains substantial.

For a weak acid titrated with strong base, the early additions create its conjugate base. The mixture enters a buffer region and the pH rises comparatively gradually. At half-equivalence, half the original weak acid has become conjugate base, so pH is approximately pKa under standard assumptions. At equivalence the sample chiefly contains conjugate base, which hydrolyzes water; its pH is commonly above 7 at 25 °C. A weak base titrated by strong acid gives a corresponding acidic conjugate species and an equivalence pH commonly below 7.

Equivalence is defined by moles and balanced-reaction coefficients, not by the observed pH being 7. For a monoprotic acid and monobasic titrant, n(OH⁻ added) = initial n(acid) at equivalence. A polyprotic acid may display multiple equivalence regions if its dissociation steps are sufficiently separated. The measured endpoint is the signal used to stop the experiment, such as a color transition. It should be selected to fall close to the equivalence volume; it is not conceptually identical to equivalence.

Always account for the changing total volume when finding concentrations from remaining moles. At equivalence, identify the salt ions and assess whether either hydrolyzes. A sketch can show qualitative regions but does not by itself establish a precise concentration or Ka. Actual curves depend on concentration, temperature, acid/base strength, and instrument resolution. Titration calculations often proceed piecewise because different species control pH in different volume regions.

Step-by-step reasoning

1. Balance the neutralization reaction and calculate equivalence volume. 2. Mark initial, pre-equivalence, equivalence, and post-equivalence regions. 3. Identify controlling species and relevant equilibrium in each region. 4. Use total volume and an appropriate pH calculation for the chosen point.

Visual explanation

Sketch an S-shaped pH curve for adding base to acid. Mark the steep central section and label its stoichiometric midpoint as equivalence; mark a separate endpoint signal nearby.

Real-world analogy

A delivery route changes behavior when a warehouse's outstanding orders have all been filled. Before that point each delivery removes a deficit; afterward deliveries accumulate as surplus. Equivalence is the zero-deficit crossing.

Real-world example

Water-quality laboratories can titrate an acidic sample with standardized base to estimate its acid content. Recording pH across additions reveals more than a single final color, including buffering regions.

Why?

Why can equivalence pH differ from 7? The salt produced at equivalence may contain a conjugate acid or base that reacts with water, changing hydronium and hydroxide levels.

Common misconception

“The center of every titration jump is pH 7.” That is characteristic of a simple strong acid-strong base pair at 25 °C, not all titrations.

Worked example

A 25.0 mL sample of monoprotic acid requires 20.0 mL of 0.100 M NaOH to reach equivalence. Added hydroxide is 0.0200 L × 0.100 mol/L = 0.00200 mol. Thus the original acid concentration was 0.00200 mol/0.0250 L = 0.0800 M. This stoichiometric result does not require the acid's Ka. Determining the equivalence pH would require its strength and the final solution volume.

Quick check

1. Does an indicator endpoint always coincide exactly with equivalence? Answer: No. The observed transition should be close to, but may differ from, the stoichiometric equivalence point.

Exam focus

Separate equivalence volume from equivalence pH. Determine moles using the balanced equation, then choose the appropriate acid-base equilibrium for the region being tested.

Advanced insight

The derivative of pH with respect to titrant volume can help locate a steep equivalence region instrumentally. For very dilute or weak systems, the jump can be less sharp and endpoint selection becomes harder.

Summary

A titration curve links measured pH with added titrant volume. Stoichiometry fixes equivalence, while excess strong reagent, buffer equilibria, or salt hydrolysis determine pH in different regions.

Practice questions

1. What does the horizontal axis usually show? Answer: Volume of titrant added. 2. What defines equivalence for a 1:1 neutralization? Answer: Equal reacting mole amounts of acid and base. 3. Why inspect the salt at equivalence? Answer: Its conjugate ion may hydrolyze, making equivalence pH differ from neutral.