Unit 4 Chemical Reactions

AP Chemistry Titration

How a titration finds an unknown concentration, how to read a buret and choose an indicator, and how lab errors change the result, in four worked examples.

A titration is stoichiometry done in the lab: you measure exactly how much of a solution of known concentration reacts with an unknown, then use the balanced equation to work back to the unknown. This page covers the Unit 4 calculation and lab skills. How pH changes along the way, including the pH at the equivalence point, is covered in AP Chemistry titration curve pH calculations.

What a Titration Measures

Titrant: the solution of known concentration in the buret.
Analyte: the substance of unknown amount or concentration in the flask.
Equivalence point: the moment the titrant has reacted exactly with all of the analyte, in the mole ratio of the balanced equation.
Endpoint: what you actually see, usually an indicator’s color change. A well-chosen indicator makes the endpoint land very close to the equivalence point.

The reaction has to be fast, go to completion, and have a known balanced equation. That is why titrations use acid-base reactions and some redox reactions, both covered in AP Chemistry types of chemical reactions.

How to Calculate an Unknown Concentration From Titration Data

Moles of titrant = molarity × volume in liters.
Moles of analyte = moles of titrant × the mole ratio from the balanced equation.
Concentration of analyte = moles of analyte ÷ volume of analyte in liters. Or, if the analyte was a weighed solid, find its molar mass or percent purity from the moles.

The shortcut M₁V₁ = M₂V₂ only works when the titrant and analyte react 1:1. It is really the dilution equation, explained in AP Chemistry dilution calculations; for any other ratio it gives a wrong answer, as Worked Example 2 shows. The molarity conversions behind every step are in AP Chemistry molarity.

How to Read a Buret and Record Titration Data

Fig. 1 · Titration setup and a buret reading

Read the bottom of the meniscus at eye level.
Record to the hundredths place (24.53 mL): the tenths come from the marks and the last digit is estimated.
Buret numbers increase downward, so the volume delivered is final reading − initial reading.

Because every reading has two decimal places, volumes from a buret usually carry four significant figures, which sets the precision of the answer. The counting rules are in AP Chemistry significant figures.

How to Choose an Indicator for an Acid-Base Titration

Titration	pH at equivalence	Suitable indicator
Strong acid with strong base	7	Phenolphthalein or bromothymol blue
Weak acid with strong base	Above 7	Phenolphthalein (changes around pH 8–10)
Weak base with strong acid	Below 7	Methyl orange (changes around pH 3–4)

Pick an indicator whose color change falls near the pH at the equivalence point. Why that pH is above or below 7 comes from the salt that forms, explained in AP Chemistry salt hydrolysis.

How Common Lab Errors Change a Titration Result

Error-analysis questions ask which way a mistake moves the calculated concentration of the analyte. Trace it through the volume of titrant recorded:

Error	Effect on titrant volume	Calculated analyte concentration
Buret rinsed with water, not titrant	Titrant diluted, so more is needed	Too high
Air bubble in the buret tip disappears	Recorded volume larger than delivered	Too high
Overshooting the endpoint	Too much titrant added	Too high
Some analyte spilled before titrating	Less titrant needed	Too low
Extra distilled water added to the flask	No change; the moles of analyte are the same	No change

Worked Example 1: Finding the Concentration of Hydrochloric Acid

A 25.00 mL sample of HCl is titrated with 0.1000 M NaOH. The equivalence point is reached after 31.45 mL. HCl + NaOH → NaCl + H₂O. Find [HCl].

Moles of NaOH: 0.1000 M × 0.03145 L = 0.003145 mol.
Moles of HCl: 1:1 ratio, so 0.003145 mol.
Concentration: 0.003145 mol ÷ 0.02500 L = 0.1258 M.

Convert both volumes to liters first. With a 1:1 ratio, M₁V₁ = M₂V₂ gives the same answer, but the mole route works every time.

Worked Example 2: Titrating Sulfuric Acid With a 1:2 Mole Ratio

A 20.00 mL sample of H₂SO₄ needs 28.64 mL of 0.1500 M NaOH. H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. Find [H₂SO₄].

Moles of NaOH: 0.1500 M × 0.02864 L = 0.004296 mol.
Moles of H₂SO₄: 0.004296 × (1 mol H₂SO₄ / 2 mol NaOH) = 0.002148 mol.
Concentration: 0.002148 mol ÷ 0.02000 L = 0.1074 M.

Using M₁V₁ = M₂V₂ here gives 0.2148 M, exactly twice the right answer, because each H₂SO₄ gives two H⁺.

Worked Example 3: Finding the Molar Mass of an Unknown Acid

A 0.5000 g sample of an unknown monoprotic acid is dissolved in water and titrated with 0.1000 M NaOH. The equivalence point is reached at 24.50 mL. Find the molar mass of the acid.

Moles of NaOH: 0.1000 M × 0.02450 L = 0.002450 mol.
Moles of acid: monoprotic, so 1:1, giving 0.002450 mol.
Molar mass: 0.5000 g ÷ 0.002450 mol = 204.1 g/mol.

That matches potassium hydrogen phthalate, KHC₈H₄O₄ (204.22 g/mol), a common standard for titrations. The same moles-from-mass logic is in AP Chemistry molar mass.

Worked Example 4: A Redox Titration With Permanganate

A 20.00 mL sample of an Fe²⁺ solution is titrated with 0.02000 M KMnO₄; the endpoint is reached at 18.40 mL. MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O. Find [Fe²⁺].

Moles of MnO₄⁻: 0.02000 M × 0.01840 L = 3.680 × 10⁻⁴ mol.
Moles of Fe²⁺: 3.680 × 10⁻⁴ × 5 = 1.840 × 10⁻³ mol.
Concentration: 1.840 × 10⁻³ mol ÷ 0.02000 L = 0.09200 M.

No separate indicator is needed: permanganate is deep purple and Mn²⁺ is nearly colorless, so the endpoint is the first lasting pale pink. Balancing the equation that sets the 1:5 ratio is covered in balancing redox equations with half-reactions.

Five Titration Practice Questions With Answers

A 20.00 mL sample of HNO₃ is neutralized by 15.00 mL of 0.2000 M NaOH. What is [HNO₃]?
Show answer
0.2000 × 0.01500 = 0.003000 mol NaOH = mol HNO₃; 0.003000 ÷ 0.02000 L = 0.1500 M.
What volume of 0.1250 M HCl neutralizes 25.00 mL of 0.0800 M Ba(OH)₂?
Show answer
Ba(OH)₂ gives 2 OH⁻: 0.0800 × 0.02500 × 2 = 0.004000 mol OH⁻. Volume of HCl = 0.004000 ÷ 0.1250 = 0.0320 L = 32.0 mL.
A 0.750 g sample of impure KHP (204.22 g/mol) needs 30.20 mL of 0.1000 M NaOH. What is the percent KHP in the sample?
Show answer
0.1000 × 0.03020 = 0.003020 mol KHP; 0.003020 × 204.22 = 0.6167 g; 0.6167 ÷ 0.750 × 100 = 82.2%.
A student rinses the buret with distilled water but not with the NaOH titrant. Is the calculated acid concentration too high, too low, or unchanged?
Show answer
Too high. The water dilutes the NaOH, so more volume is needed to reach the endpoint, and the recorded volume overstates the moles of NaOH used.
Why is phenolphthalein a better indicator than methyl orange for titrating acetic acid with NaOH?
Show answer
The equivalence point is above pH 7 because the acetate ion is a weak base. Phenolphthalein changes color around pH 8–10, close to that point; methyl orange changes around pH 3–4, far too early.

Common Titration Mistakes

Using M₁V₁ = M₂V₂ when the mole ratio is not 1:1.
Forgetting to convert mL to L before multiplying by molarity.
Treating the endpoint and the equivalence point as the same thing. One is observed; the other is the stoichiometric point.
Reading the top of the meniscus or recording only one decimal place.
Assuming extra water in the flask changes the answer. It does not change the moles of analyte.
Ignoring the second H⁺ or OH⁻ from H₂SO₄ or Ba(OH)₂.

Titration calculations and lab-error questions show up regularly on the free-response section. To see how stronger free-response answers could move your overall estimate, try the AP Chem Score Calculator.

Frequently Asked Questions

What is a titration?

A titration is a lab method for finding the amount or concentration of an unknown substance, the analyte. A solution of known concentration, the titrant, is added from a buret until it has reacted completely with the analyte, and the volume used gives the moles of titrant through stoichiometry.

What is the difference between the equivalence point and the endpoint?

The equivalence point is when the titrant has exactly reacted with all of the analyte according to the balanced equation. The endpoint is what you observe, usually an indicator changing color. A good indicator makes the endpoint fall very close to the equivalence point.

How do you calculate concentration from titration data?

Multiply the titrant's molarity by the volume used in liters to get moles of titrant, use the mole ratio from the balanced equation to get moles of analyte, then divide by the analyte's volume in liters. For example, 31.45 mL of 0.1000 M NaOH neutralizing 25.00 mL of HCl gives 0.1258 M HCl.

Does adding water to the flask change a titration result?

No. Adding distilled water to the flask dilutes the analyte but does not change the number of moles of analyte, so the volume of titrant needed to reach the equivalence point stays the same.

Which indicator should I use for a titration?

Choose an indicator that changes color close to the pH at the equivalence point. Phenolphthalein, which changes around pH 8 to 10, suits a weak acid titrated with a strong base; methyl orange, around pH 3 to 4, suits a weak base titrated with a strong acid. For a strong acid with a strong base, either can work because the pH changes so sharply.

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