When has a titration added exactly enough?
You will be able to: Locate equivalence using the reaction ratio and infer an unknown concentration.
When has a titration added exactly enough?
Adding known base drop by drop to an acid is a chemical measuring tool. The useful stopping amount is set by reacting moles, not by equal liquid volumes.
A useful starting point: How much gas does a reaction produce? →
Words and symbols before equations
- Analyte
- Sample whose amount or concentration is being determined.
- Titrant
- Solution of known concentration delivered to react with the analyte.
- Equivalence point
- Stoichiometric amount of titrant has reacted with the analyte.
- Endpoint
- Observed signal used to estimate equivalence, such as an indicator change.
What this picture assumes
25.0 mL of 0.100 M monoprotic strong acid; 0.100 M strong base; quantitative 1:1 reaction. Amount graph, not pH. Water autoionization and spectator-ion concentrations are omitted from these excess-amount curves.
Read the picture in three steps
- Read the species and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- Added 0 mmol OH⁻. Acid remaining 2.5 mmol; excess OH⁻ 0 mmol. Before equivalence: acid in excess.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
For H⁺ + OH⁻ → H₂O, equivalence occurs when initial acid moles equal added hydroxide moles. For another balanced equation, use its coefficient ratio.
The delivered titrant volume is final buret reading minus initial reading. Multiply that volume by known concentration to obtain added moles.
Use the reaction ratio to find analyte moles, then divide by the original analyte volume. The total mixed volume is not the original analyte sample volume.
The Explore graph plots remaining acid and excess base amounts against added base volume. Its intersection at zero identifies stoichiometric equivalence; it is not a pH curve or a requirement that all titrations have pH 7.
| Feature | Equivalence | Endpoint |
|---|---|---|
| Meaning | Stoichiometric reacting amounts | Observed signal |
| Basis | Balanced equation | Measurement or indicator |
| Possible difference | Chemical target | May slightly miss the target |
A worked example, step by step
A 25.0 mL HCl sample requires 20.0 mL of 0.100 mol/L NaOH at equivalence. Find HCl concentration.
- n(OH⁻) = 0.100 × 0.0200 = 0.00200 mol.
- H⁺ and OH⁻ react 1:1, so original acid amount = 0.00200 mol.
- Original acid volume is 0.0250 L: c = 0.00200/0.0250 = 0.0800 mol/L.
- Equal moles did not require equal volumes because the two concentrations differ.
Equivalence means the balanced mole ratio, not equal volumes, equal concentrations, or universally pH 7.
Do spectators such as Na⁺ and Cl⁻ vanish at equivalence?
Compare with an explanation
No. They remain in solution; equivalence concerns the reacting analyte and titrant amounts.
Predict. Change one thing. Explain.
For the fixed 25.0 mL, 0.100 M acid sample, increase 0.100 M base volume through 25.0 mL. Describe the species in excess before, at and after equivalence.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Added 0 mmol OH⁻. Acid remaining 2.5 mmol; excess OH⁻ 0 mmol. Before equivalence: acid in excess.
25.0 mL of 0.100 M monoprotic strong acid; 0.100 M strong base; quantitative 1:1 reaction. Amount graph, not pH. Water autoionization and spectator-ion concentrations are omitted from these excess-amount curves.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using conserved atoms/charge, reaction ratios, particle identity or electron/proton transfer. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionFor a supplied complete reaction H₂A + 2OH⁻ → A²⁻ + 2H₂O, 10.0 mL acid needs 16.0 mL of 0.100 M hydroxide. Find analyte concentration and explain the factor of two.
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Compare with the answer and four-point rubric
- 1 point: Added OH⁻ = 0.100 × 0.0160 = 0.00160 mol.
- 1 point: Each H₂A consumes two OH⁻, so H₂A = 0.000800 mol.
- 1 point: c(H₂A) = 0.000800/0.0100 = 0.0800 M.
- 1 point: The factor of two follows the balanced equation; assuming 1:1 would double the inferred concentration.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What defines equivalence?
Stoichiometrically matching reacting amounts.
RECALL 2What is an endpoint?
The observed signal used to estimate equivalence.
RECALL 3Which analyte volume gives original concentration?
The original sample volume, not the final mixed volume.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
When has a titration added exactly enough?
- For aA + bB → products: nA/a = nB/b at equivalence.
- Delivered buret volume = final reading − initial reading.
Remember: Equivalence means the balanced mole ratio, not equal volumes, equal concentrations, or universally pH 7.
Conditions: 25.0 mL of 0.100 M monoprotic strong acid; 0.100 M strong base; quantitative 1:1 reaction. Amount graph, not pH. Water autoionization and spectator-ion concentrations are omitted from these excess-amount curves.
Refresh Kid · AP Chemistry Unit 4 · Objectives 4.6.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 4.6, objective 4.6.A. CED effective Fall 2024 and June 2026 clarifications checked September 16, 2026. Unit 4: Chemical Reactions, Topics 4.1–4.9. Focused lesson names, examples, models and assessments are original Refresh Kid teaching materials, not additional official topics or official AP questions. Official corrections.
The model states its assumptions beside the diagram. Solubility facts for sodium, potassium, ammonium and nitrate salts are included; other precipitation cases give the needed information. Lewis acid-base theory and the labels oxidizing/reducing agent are not treated as required exam content. Quantitative pH, equilibrium and electrochemical potentials are developed in later units. Stoichiometric models state complete-reaction assumptions; they are not mechanisms or equilibrium simulations.
Teaching resources: The Organic Chemistry Tutor video titles/descriptions and topic coverage were checked for optional links; no claim is made to have watched every video. No creator scripts, examples, worksheets or artwork were copied. GitHub’s 3D website collection and its Three.js camera-control example informed the idea of controllable spatial inspection. Scientific diagrams, geometry and interactions here are original. The self-hosted Three.js runtime retains its MIT license. Camera rotation changes the view, not the chemistry.
Independent teacher review and observation of students remain pending. Implementation checks do not certify scientific accuracy, accessibility or learning effectiveness. This is a review edition.
Optional official resource: Released AP Chemistry questions and scoring guides. This archive contains questions across units; it is not an assignment of every question to this lesson.
The teaching sequence is informed by the IES learning guide; this exact implementation has not been evaluated with learners.
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