AP Chemistry · Lesson 3

Titration and solution analysis

Know Know it

In a titration, a solution of known concentration (the titrant) is added from a buret to a measured sample until the reaction is just complete. At the equivalence point, the moles of titrant added match the moles the balanced equation needs. An indicator changes color at the end point, which is chosen to be very close to the equivalence point.

The calculation is solution stoichiometry: moles of titrant = molarity × volume in liters; use the mole ratio to get moles of the sample; divide by the sample volume for its molarity, or divide a mass by the moles for a molar mass.

The volume delivered is the final buret reading minus the initial reading. Repeat the titration and average the trials that agree closely.

Calculator On the exam

You may use a scientific or graphing calculator on both sections of the exam; a four-function calculator is allowed but not recommended. A reference booklet of equations and constants is provided. Keep every digit until the last step, then round to the significant figures of your measured data, and write the units with your answer.

Worked example Easy

A 25.00 mL sample of HCl is titrated with 0.1000 M NaOH. The end point is reached after 18.40 mL of NaOH is added. What is the concentration of the HCl? (HCl + NaOH → NaCl + H₂O)

  1. 0.03680 M
  2. 0.1359 M
  3. 0.07360 MAnswer
  4. 0.1472 M

How to solve it

  1. Moles of titrant: 0.1000 mol/L × 0.01840 L = 0.001840 mol NaOH.
  2. Ratio 1 : 1, so 0.001840 mol HCl in the flask.
  3. Concentration: 0.001840 mol ÷ 0.02500 L = 0.07360 M (4 significant figures, like the data).

Why each choice is right or wrong

  • A. Incorrect. 0.03680 M halves the moles of HCl, but HCl and NaOH react 1 : 1.
  • B. Incorrect. 0.1359 M swaps the two volumes (0.1000 × 25.00/18.40); the moles of NaOH come from the 18.40 mL that was added.
  • C. Correct. Moles NaOH = 0.1000 × 0.01840 = 0.001840 mol = moles HCl, and 0.001840 ÷ 0.02500 L = 0.07360 M.
  • D. Incorrect. 0.1472 M doubles the moles of HCl, as if each HCl needed two NaOH; the ratio is 1 : 1.

Trap M₁V₁ = M₂V₂ needs a 1 : 1 ratio

The shortcut M₁V₁ = M₂V₂ only works when the titrant and the sample react 1 : 1. For a 2 : 1 or 5 : 1 reaction, go through moles and use the mole ratio from the balanced equation.

Explain Explain it

Task verbs: calculate, predict

To predict how a lab error changes a titration result, follow it into the calculation. Ask: does the error change the volume of titrant read from the buret, or the amount of sample in the flask? A larger titrant volume makes the calculated moles of sample larger; a smaller one makes them smaller.

Adding distilled water to the flask does not change the moles of sample, so it does not change the volume needed to reach the equivalence point.

Worked example Medium

A 0.3150 g sample of a solid acid, H₂A, which has two acidic hydrogens, is dissolved in water. Titrating it until both hydrogens are neutralized takes 35.00 mL of 0.1000 M NaOH (H₂A + 2NaOH → Na₂A + 2H₂O). What is the molar mass of H₂A?

  1. 90.00 g/mol
  2. 45.00 g/mol
  3. 0.1800 g/mol
  4. 180.0 g/molAnswer

How to solve it

  1. Moles NaOH: 0.1000 × 0.03500 L = 0.003500 mol.
  2. Ratio 1 H₂A : 2 NaOH, so 0.001750 mol H₂A.
  3. Molar mass = 0.3150 g ÷ 0.001750 mol = 180.0 g/mol.

Why each choice is right or wrong

  • A. Incorrect. 90.00 g/mol treats the acid as if it reacted 1 : 1 with NaOH; each H₂A uses 2 NaOH, so there are half as many moles of acid.
  • B. Incorrect. 45.00 g/mol doubles the moles of acid instead of halving them, so it gets the ratio upside down.
  • C. Incorrect. 0.1800 g/mol leaves the volume in milliliters (0.1000 × 35.00); the volume must be 0.03500 L.
  • D. Correct. Moles NaOH = 0.1000 × 0.03500 = 0.003500 mol, so moles H₂A = 0.001750 mol, and 0.3150 g ÷ 0.001750 mol = 180.0 g/mol.

Predict Your turn

A student rinses a buret with distilled water and then fills it with 0.100 M NaOH without first rinsing it with the NaOH solution. She uses it to titrate a sample of HCl of unknown concentration and calculates the concentration with 0.100 M for the NaOH. Predict whether her calculated HCl concentration will be too high or too low, and explain why.

Write it, then compare. Nothing you type here is saved or graded.

Compare with a model answer

A full answer does this

  • Predicts that the calculated HCl concentration will be too high
  • Explains that water left in the buret dilutes the NaOH, so a larger volume is needed to reach the end point

Model answer

Her calculated HCl concentration will be too high. The water left in the buret dilutes the NaOH, so it is weaker than 0.100 M and she must add a larger volume to reach the end point. She multiplies that larger volume by 0.100 M, so she overestimates the moles of NaOH, and therefore the moles and concentration of HCl.

Apply Apply it

Practice these topics. AP Practice questions on exactly what this lesson covers, with an explanation for every answer.