Principles of Titrimetry

Introduction

A titration determines the amount of an analyte by reacting it with a known amount of another substance. The analyst adds titrant until an indicator or instrument signals the end point. The chemically important equivalence point is where the reaction's stoichiometric amounts match. The difference between these points is a potential source of titration error and explains why indicators must be selected rather than added arbitrarily.

Core explanation

Suppose a solution contains an unknown amount of acid and a standardised base is delivered from a burette. If their reaction is fast, complete and known, the moles of base at equivalence reveal the acid moles through the balanced equation. For HCl + NaOH → NaCl + H₂O, the ratio is one to one. For H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O when both acidic protons are neutralised, two moles of hydroxide correspond to one mole of acid. Never assume equal molarities merely because equivalent volumes happened to be used.

The equivalence point is a theoretical stoichiometric condition. The end point is the visible colour change or measured signal chosen to estimate it. A suitable indicator changes within the sharp part of the titration curve, close enough to equivalence for the required accuracy. A pH meter, conductivity measurement or potential measurement can supply an instrumental endpoint. The difference between endpoint volume and true equivalence volume is an indicator or endpoint error; it can be positive or negative.

The titrant concentration must be known, often by standardisation. The analyte aliquot volume or mass must also be known. At equivalence, if aA + bB → products with A analyte and B titrant, n(A)/a = n(B)/b. Since n(B) = C(B)V(B), one can calculate n(A), then divide by the original analyte volume or mass. Work in litres when using mol L⁻¹. For a titration involving redox, precipitation or complexation, the same stoichiometric logic applies, but the reaction must be selective and its endpoint detectable.

Practical technique matters. Rinse the burette with titrant, remove air from its tip, record initial and final readings, swirl the analyte and slow addition near the endpoint. A drop beyond the colour change can be a significant fraction of a small titre. Replicate concordant titrations improve precision, but identical overshoot or wrong standard concentration can bias them all.

The simple algebra depends on the reaction and sample preparation being valid, not on memorising a formula alone.

Step-by-step reasoning

1. Write and balance the reaction between analyte and titrant. 2. Record titrant concentration and delivered volume from burette reading difference. 3. Calculate titrant moles using n = CV with volume in litres. 4. Apply the equation's coefficient ratio to find analyte moles. 5. Divide by aliquot volume or original sample mass and include dilution factors.

Visual explanation

Draw a burette above a flask, labelling titrant in the burette and analyte in the flask. Beside the flask, sketch a curve with titrant volume on the horizontal axis and measured signal vertically. Mark an ideal stoichiometric equivalence volume and a nearby observed endpoint volume, separated by a small horizontal gap.

Real-world analogy

Counting analyte through titration resembles counting guests by handing each person a fixed number of tickets. If the rule is two tickets per guest, the number of tickets used reveals guest count only if the distribution is complete and no ticket is handed to the wrong recipient. The balanced reaction supplies the ticket ratio; a poorly chosen endpoint is like stopping before or after the last guest.

Real-world example

A food laboratory can titrate an acid-containing sample after a known dilution to estimate titratable acidity. The endpoint must match the specified procedure because mixtures of weak acids do not have one universal “acid concentration” independent of pH range. The result may be reported as an equivalent amount of a chosen reference acid rather than a direct count of every individual acid molecule.

Why?

Why is a sharp endpoint useful? When the signal changes rapidly over a small added volume near equivalence, a small uncertainty in observed colour or instrument reading corresponds to a small uncertainty in volume. A gradual change makes endpoint placement less certain and can produce substantial titration error.

Common misconception

“The indicator changes exactly at equivalence by definition” is false. Indicator chemistry has its own equilibrium and transition range. Another mistake is equating the number of analyte and titrant moles without checking the balanced coefficients. A titration with a two-to-one ratio requires explicit stoichiometry even if the volumes look similar.

Worked example

A 25.00 mL HCl aliquot requires 23.40 mL of 0.1000 mol L⁻¹ NaOH to reach a suitable endpoint close to equivalence. NaOH moles = 0.1000 × 0.02340 = 0.002340 mol. Since HCl and NaOH react one to one, the aliquot had 0.002340 mol HCl. Its concentration is 0.002340/0.02500 = 0.09360 mol L⁻¹. The result assumes standardised base and negligible endpoint error; those assumptions should be checked in a real report.

Quick check

1. Does an indicator end point always equal the chemical equivalence point? Answer: No. The endpoint is an observed signal and can occur slightly before or after stoichiometric equivalence. A suitable indicator minimises the difference for the titration curve.

Exam focus

Name analyte and titrant, write the balanced equation and distinguish equivalence from endpoint. Convert millilitres to litres before applying molarity. Show coefficient ratios and account for any earlier dilution or back-titration steps. State whether the observed endpoint is an approximation to stoichiometric equivalence.

Advanced insight

The appropriate equivalence model depends on chemical completeness. A reaction with a small equilibrium constant or a competing reaction may not consume analyte quantitatively by the presumed point. Complexometric titrations therefore use pH control and indicators that support sufficiently complete complex formation; precipitation titrations require careful attention to solubility and adsorption effects.

Summary

Titrimetry turns a measured amount of standardised titrant into analyte amount through a balanced reaction. Equivalence is the chemical stoichiometric point; endpoint is the observed signal used to locate it. Reliable calculation also requires correct volume delivery, selectivity, an appropriate indicator and attention to dilution.

Practice questions

1. What moles of H₂SO₄ correspond to 0.0100 mol NaOH when both protons are neutralised? Answer: The balanced reaction uses two NaOH per H₂SO₄, so n(H₂SO₄) = 0.0100/2 = 0.00500 mol.

2. A burette changes from 0.85 to 19.72 mL. What volume enters the mole calculation? Answer: Delivered volume is 19.72 − 0.85 = 18.87 mL, or 0.01887 L for a molarity calculation.

3. Why can concordant titres still be biased? Answer: All runs may use an incorrectly standardised titrant, a poorly chosen indicator or a consistent overshoot. Agreement among runs assesses repeatability, not necessarily trueness.