Titrations

Why it matters

Titration is one of the oldest quantitative methods, and it is still everywhere: acid content of foods and wines, water hardness, the assay of a drug substance in a pharmacopoeia, the moisture in a solvent by Karl Fischer titration. It is cheap, accurate to a few parts per thousand in good hands, and traceable to a weighed primary standard. Every analytical chemist is expected to calculate a titration result correctly and to know where its errors come from.

Safety and scope. Acids, bases, silver salts and other reagents in this lesson are hazardous. Bench work happens only in a teaching or employer lab, with your instructor or supervisor, after the lab's chemical-hygiene training (OSHA laboratories, checked on 2026-10-23). The activity is a data exercise: never attempt these procedures at home.

The core idea

A titrant of known concentration is added from a burette to a measured volume (or mass) of analyte until the reaction between them is complete.

• The equivalence point is where the moles of titrant exactly match the moles of analyte, according to the balanced equation.
• The endpoint is what you actually observe: an indicator color change, or a jump in a pH or potential curve. A good method makes the endpoint fall as close to the equivalence point as possible.

The calculation is stoichiometry:

moles titrant = M_titrant x V_titrant (L)
moles analyte = moles titrant x (mol analyte / mol titrant)
C_analyte     = moles analyte / V_analyte (L)

Because both volumes are in the same unit, you can work in mL directly: C = M x V_titrant x ratio / V_analyte.

Worked example 1: a monoprotic acid

25.00 mL of hydrochloric acid is titrated with 0.1000 M NaOH; the endpoint is at 21.40 mL. HCl + NaOH -> NaCl + H2O, so the ratio is 1.

C(HCl) = 0.1000 x 21.40 x 1 / 25.00 = 0.08560 M

Worked example 2: a diprotic acid

25.00 mL of sulfuric acid needs 18.72 mL of the same NaOH. H2SO4 + 2 NaOH -> Na2SO4 + 2 H2O, so there is 1 mol of acid per 2 mol of titrant: ratio = 0.5.

C(H2SO4) = 0.1000 x 18.72 x 0.5 / 25.00 = 0.03744 M

Getting this ratio upside down (using 2 instead of 0.5) is the most common titration error on exams and in notebooks.

Standardization and blanks

NaOH solutions absorb carbon dioxide and change concentration, so they are standardized against a primary standard such as potassium hydrogen phthalate (KHP, 204.22 g/mol, monoprotic). If 0.5105 g of KHP needs 24.85 mL of NaOH:

M(NaOH) = (0.5105 / 204.22) / (24.85 / 1000) = 0.1006 M

A blank titration (the same procedure with no analyte) measures how much titrant the solvent and indicator consume. Subtract the blank volume from each sample volume before calculating.

Endpoint detection and titration types

• Acid-base: indicators such as phenolphthalein, or a pH electrode (potentiometric titration), where the endpoint is the steepest point of the curve (the maximum of the first derivative).
• Redox: for example permanganate or iodine-thiosulfate titrations.
• Complexometric: EDTA titrations for calcium and magnesium (water hardness).
• Precipitation: silver nitrate for chloride.
• Back titration: add a known excess of reagent, then titrate what is left. Useful when the analyte reacts slowly or is insoluble.

Modern labs use autotitrators that dose titrant in small steps, record the curve and pick the endpoint mathematically, but the chemistry and the calculation are the same.

Replicates and reporting

Titrate at least three replicates. Report the mean with an appropriate number of significant figures and the relative standard deviation (RSD). Replicates that agree within a few tenths of a percent are typical for a well-run manual titration.

Common mistakes

• Using the wrong mole ratio for polyprotic acids or redox reactions.
• Reading the burette at the top of the meniscus instead of the bottom, or with parallax.
• Forgetting the blank correction.
• Using an indicator whose color change does not match the pH at equivalence (for example methyl orange for a weak acid with a strong base).
• Mixing units: milliliters in one place and liters in another.

Quick recap

• C_analyte = M_titrant x V_titrant x (mol analyte / mol titrant) / V_analyte.
• Standardize titrants against a primary standard such as KHP; subtract blanks.
• The endpoint approximates the equivalence point; potentiometric detection uses the steepest part of the curve.
• Run replicates and report the mean and RSD.

Try it

Open the Do tab. A Python titration calculator is written except for the concentration formula.