Titration Analysis: How to Find an Unknown Concentration

What a titration does

A titration is one of the most precise tools in analytical chemistry. Instead of guessing a concentration from a quick test, you let chemistry measure itself: a solution of known concentration is added, drop by drop, to a measured volume of the unknown solution until the reaction between them is exactly complete. Because you know precisely how much reactant you added, stoichiometry tells you exactly how much was in the unknown.

The unknown solution is called the analyte, and the known solution added from the burette is the titrant. The entire technique rests on one idea — if the balanced equation tells you the mole ratio, the volumes tell you the concentration ratio.

The equipment and setup

A standard acid-base titration uses a few key pieces of glassware:

• Burette: a long graduated tube with a stopcock that delivers titrant in precisely measured volumes, readable to 0.01 mL.
• Erlenmeyer flask: holds the measured analyte; its narrow neck reduces splashing during swirling.
• Pipette: delivers an exact, known volume of the analyte into the flask.
• Indicator: a few drops of a dye that changes color at the right moment.

The procedure runs like this: pipette a known volume of analyte into the flask, add a few drops of indicator, fill the burette with titrant and record the starting level, then add titrant slowly while swirling — fast at first, then drop by drop as the color change approaches. Record the final burette reading; the difference is the titrant volume used.

Equivalence point vs endpoint

Two terms sound alike but mean different things, and the distinction is the heart of titration theory.

The equivalence point is the theoretical moment when exactly enough titrant has been added to react completely with the analyte — the stoichiometric point dictated by the balanced equation. You cannot see it directly.

The endpoint is the practical moment you actually observe: the permanent color change of the indicator. A good titration chooses an indicator whose color change happens as close as possible to the equivalence point, so the observed endpoint is an excellent stand-in for the true equivalence point.

For a strong acid titrated with a strong base, the equivalence point sits at pH 7. For a weak acid titrated with a strong base, the equivalence point is basic (pH > 7), because the conjugate base of the weak acid makes the solution slightly alkaline — so the indicator must be chosen accordingly.

Indicators: the color-change signal

An indicator is a weak acid or base whose two forms have different colors, and which switches form over a narrow pH range. Common choices include:

• Phenolphthalein: colorless to pink, pH 8.2–10. The classic choice for strong acid–strong base and weak acid–strong base titrations.
• Bromothymol blue: yellow to blue, pH 6.0–7.6. Useful near neutral equivalence points.
• Methyl orange: red to yellow, pH 3.1–4.4. Suited to titrations with acidic equivalence points, such as strong acid–weak base.

Only two or three drops go into the flask. The indicator is itself a chemical participant, so adding too much would consume a measurable amount of titrant and move the endpoint. The color change should be permanent — if the color fades after swirling, you have not quite reached the endpoint yet.

Doing the math: the titration calculation

Here is where the precision pays off. At the equivalence point, moles of titrant added equal moles of analyte neutralized (adjusted for the mole ratio). For the common 1:1 case, such as HCl with NaOH:

$$M_A V_A = M_B V_B$$

where $M_A$ and $V_A$ are the molarity and volume of the acid, and $M_B$ and $V_B$ are the molarity and volume of the base. Volumes may be in milliliters as long as both use the same unit, since the units cancel.

Worked example: 25.00 mL of HCl of unknown concentration is titrated with 0.100 M NaOH, and the endpoint arrives after 20.00 mL of NaOH.

1. Write the relation: $M_{HCl} \times 25.00\ \text{mL} = 0.100\ \text{M} \times 20.00\ \text{mL}$
2. Solve: $M_{HCl} = (0.100 \times 20.00) / 25.00 = 0.0800\ \text{M}$

For reactions that are not 1:1, such as H2SO4 with NaOH (1:2), multiply each side by its stoichiometric coefficient: $M_A V_A \times a = M_B V_B \times b$, where $a$ and $b$ come from the balanced equation.

Titration curves

Plotting pH against the volume of titrant added produces a titration curve, a powerful visual summary of the reaction. A strong acid–strong base curve starts at low pH, rises very slowly, then shoots nearly vertically through the equivalence point at pH 7 before leveling off in the basic region.

That steep vertical jump is why titrations are so precise: near the equivalence point, a single drop of titrant swings the pH by several units, so the indicator's color change pinpoints the volume sharply. Weak acid–strong base curves show a gentler rise and an equivalence point above pH 7, plus a flattened buffer region where pH resists change — the same buffering behavior that keeps blood pH stable.

Beyond acid-base titrations

The drop-by-drop technique extends well beyond acids and bases:

• Redox titrations use oxidation-reduction reactions, often with indicators that change color when oxidized or reduced, to analyze substances like iron content or vitamin C.
• Complexometric titrations use chelating agents such as EDTA to measure metal ions — the standard method for determining water hardness from calcium and magnesium.
• Precipitation titrations track the formation of an insoluble solid, for example titrating chloride with silver nitrate.

Whatever the reaction type, the logic is identical: add a known solution until the chemistry is just complete, measure the volume, and let stoichiometry reveal the unknown.

Variables and units

Common mistakes

Real-world applications

• Water treatment plants test alkalinity and hardness by titration before adjusting chemistry

• Food producers measure the acidity of vinegar, dairy, and wine to verify label claims

• Pharmaceutical quality control confirms the strength of drug solutions batch by batch

• Environmental laboratories determine dissolved pollutants and acid rain impact in water samples

• Clinical and agricultural labs analyze soil and fertilizer nutrient content