Acid-Base Titrations
Later titration connection: identify species across the pH curve before choosing a chemical model.
Before this connection: Acids, bases, and pH: conjugate pairs and proton-transfer equilibria.
AP Chemistry Topic 8.5 · CED printed p. 152, 153 / PDF p. 159, 160. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Mixture stoichiometry
- Weak conjugate equilibria
- Graph interpretation
A titration curve plots measured pH against volume of titrant delivered. Read the horizontal axis in mL and the vertical axis as pH, not hydronium concentration. The equivalence point is defined by stoichiometry, not by a color: the titrant amount has exactly reacted with the relevant analyte amount. For a monoprotic acid titrated by hydroxide, nacid = nOH− at equivalence, so use Ctitrant × Vequivalence and divide by the original sample volume. The method works for strong or weak analytes because the reaction with a suitable strong titrant is essentially quantitative.
For a weak monoprotic acid, the curve starts with weak-acid equilibrium, passes through a HA/A− buffer region, reaches a conjugate-base solution at equivalence, and then becomes excess strong base. At half-equivalence, equal HA and A− amounts give pH ≈ pKa. At equivalence, A− produces hydroxide; for a weak base titrated by strong acid, HB+ produces hydronium. Strong acid/strong base equivalence is neutral, with pH 7 only at 25 °C. The steep region helps locate equivalence, while an indicator’s endpoint is an observed color change selected to fall within it. pH-meter calibration, titrant concentration, and actual delivery volume matter to the inference.
A polyprotic curve can show successive steps. Each additional equivalent of strong base removes another proton; identify the dominant forms as H2A, HA−, and A2− for a diprotic example. With sufficiently separated steps, each half-step estimates the relevant pKa. Some steps overlap, so a missing resolved jump is not absolute proof that a proton is absent. AP asks qualitative dominant-species and pKa reasoning for polyprotic curves, not the calculation of every species concentration. For monoprotic curves, the ordinary quantitative mixture calculations are in scope.
Let's work through it
- A 20.00 mL weak-base sample requires 30.00 mL 0.1000 M HCl to reach its single equivalence point.
- The base is monoprotic as a proton acceptor: nB = nHCl = 0.003000 mol, so original [B] = 0.1500 M.
- At 15.00 mL, B and HB+ amounts are equal. If the pH there is 9.20, pKa(HB+) ≈ 9.20; pKb(B) = 14.00 − 9.20 = 4.80 at 25 °C.
- At 30.00 mL, HB+ dominates and its acid equilibrium gives a pH below neutral. The equivalence volume comes from stoichiometry; the acidic pH comes from the remaining species.
Make the picture move
Interactive concept model
The species change across a titration curve.
Predict first. Visit 0, 12.5, 25.0, and 37.5 mL. Identify the species controlling pH at each point. Is equivalence necessarily pH 7?
HA + OH⁻ → A⁻ + H₂O; Kₐ = [H⁺][A⁻]/[HA]; K_w = [H⁺][OH⁻]
- Ideal weak-acid titration
- Labeled selected or reference state
On a small screen, scroll inside the graph or diagram to read its labels. The values and explanation also appear below.
At 12.5 mL, pH = 4.74. Half-equivalence: pH ≈ pKₐ. [HA] = 0.0333 M and [A⁻] = 0.0334 M.
Read the data and comparisons
| Added base (mL) | pH | [HA] (mol L⁻¹) | [A⁻] (mol L⁻¹) |
|---|---|---|---|
| 0.0 | 2.87 | 0.0987 | 0.00134 |
| 12.5 | 4.74 | 0.0333 | 0.0334 |
| 25.0 | 8.72 | 5.24 × 10^-6 | 0.05 |
| 37.5 | 12.30 | 1.10 × 10^-9 | 0.04 |
| 50.0 | 12.52 | 5.50 × 10^-10 | 0.0333 |
Macroscopic / data. The pH curve is a computed data representation, with a changing total liquid volume.
Particle view. HA, A⁻, H⁺, OH⁻, and spectator Na⁺ satisfy matter and charge conservation. Equivalence does not remove the hydrolysis equilibrium.
Symbolic view. Total acid-species concentration = 0.0667 M; [H⁺] = 1.82 × 10^-5 M; [OH⁻] = 5.50 × 10^-10 M.
Why it works. The initial 25.0 mL of 0.100 M HA contains 0.00250 mol of acid. Equivalence takes 25.0 mL of 0.100 M base regardless of pKₐ. At half-equivalence, comparable HA and A⁻ give pH approximately pKₐ. Within the buffer region, pH = pKₐ + log₁₀([A⁻]/[HA]) follows by rearranging Kₐ; estimating this ratio from neutralization requires appreciable amounts of both species. At equivalence A⁻ reacts with water, so a weak-acid titration is basic. Beyond equivalence excess OH⁻ dominates.
Conditions and limits. Monoprotic hypothetical HA and a fully dissociated strong base with Na⁺ as spectator; 25 °C, K_w = 1.0 × 10⁻¹⁴, ideal dilute activities approximated by concentrations divided by a 1 mol L⁻¹ standard state, additive volumes, no other equilibria. The curve solves acid mass balance, charge balance, Kₐ, and K_w together at every volume; it does not misuse Henderson–Hasselbalch at endpoints. The numerical solver is an implementation detail, not required AP work. pH is displayed to two decimal places.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
Is equivalence the same as endpoint?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
Is equivalence the same as endpoint?
Worked answer and reason
Equivalence is the stoichiometric condition; endpoint is the observed signal used to approximate it.
Indicator selection controls how closely the observed signal matches the chemical condition.
Retrieval 2
At weak-acid half-equivalence, what lets you read pKa?
Worked answer and reason
HA and A− have equal concentrations, so their ratio term is one.
The conjugate-pair equilibrium connects pH and pKa.
Catch the tempting mistake
- The initial weak-acid pH equals its pKa.
- That equality occurs when the two conjugate forms are equal, usually near half-equivalence, not in the initial acid-only solution.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 8 problem 8 · ap synthesis · data
- Unit 8 problem 9 · ap application · data
Scientific calculator workspace
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Scientific calculator
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For the teacher
- Require students to mark major species under each curve region before choosing formulas. In error tasks, trace the flawed measurement through n = CV.
- Use the titled original diprotic curve to connect two resolved proton-transfer stages, dominant forms, and approximate half-step pKa readings. Contrast its deliberately separated pKa values with an unresolved curve; do not assign numerical polyprotic species-concentration calculations.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 8.5.A
- Explain results from the titration of a mono- or polyprotic acid or base solution, in relation to the properties of the solution and its components.
- 8.5.A.1
- An acid-base reaction can be carried out under controlled conditions in a titration. A titration curve, plotting pH against the volume of titrant added, is useful for summarizing results from a titration.
- 8.5.A.2
- At the equivalence point for titrations of monoprotic acids or bases, the number of moles of titrant added is equal to the number of moles of analyte originally present. This relationship can be used to obtain the concentration of the analyte. This is the case for titrations of strong acids/bases and weak acids/bases.
- 8.5.A.3
- For titrations of weak acids/bases, it is useful to consider the point halfway to the equivalence point, that is, the half-equivalence point. At this point, there are equal concentrations of each species in the conjugate acid-base pair, for example, for a weak acid [HA] = [A−]. Because pH = pK_a when the conjugate acid and base have equal concentrations, the pK_a can be determined from the pH at the half-equivalence point in a titration.
- 8.5.A.4
- At the equivalence point, pH is determined by the major species in solution. Strong acid and strong base titrations result in neutral pH at the equivalence point. However, in titrations of weak acids (weak bases), the conjugate base of the weak acid (conjugate acid of the weak base) is present at the equivalence point and can undergo proton-transfer reactions with the surrounding water, producing basic (acidic) solutions.
- 8.5.A.5
- For polyprotic acids, titration curves can be used to determine the number of acidic protons. In doing so, the major species present at any point along the curve can be identified, along with the pK_a associated with each proton in a weak polyprotic acid.
- Computation of the concentration of each species present in the titration curve for polyprotic acids will not be assessed on the AP Exam. Such computations for titration of monoprotic acids are within the scope of the course (see 8.4.A.2 and 8.4.A.3), as is qualitative reasoning regarding what species are present in large versus small concentrations at any point in a titration of a polyprotic acid.
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 — Required topic-numbered learning objectives and essential knowledge, all continuations and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- OpenStax Chemistry 2e §14.7, Acid–Base Titrations — Titration regions, equivalence species, and indicator behavior.
Glossary and deeper reading · 9 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Mixture
A mixture contains two or more substances whose proportions can vary. Its components retain their chemical identities until a chemical reaction changes them. For example, water and ethanol can form mixtures with many different compositions.
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Stoichiometry
Stoichiometry uses a balanced chemical equation to relate amounts of reactants and products. Equation coefficients provide mole ratios rather than direct mass ratios. For example, forming water from hydrogen and oxygen consumes two moles of hydrogen molecules per mole of oxygen molecules.
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Mole
A mole is an amount of substance containing exactly 6.02214076 × 10²³ specified entities. The entities can be atoms, molecules, ions, or formula units, so the counted entity must be named. For example, one mole of oxygen molecules contains two moles of oxygen atoms.
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pH
pH is the negative base-ten logarithm of hydronium activity. In suitable dilute models, activity is approximated by molar concentration relative to the standard concentration. For example, lowering hydronium concentration by a factor of ten raises pH by one unit.
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Titrant
A titrant is the reagent added in measured amounts during a titration. Its concentration and reaction stoichiometry connect the delivered volume to the analyte amount. For example, a standardized base solution can be the titrant for an unknown acid.
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Chemical equilibrium
Chemical equilibrium is a dynamic state in which forward and reverse reaction rates are equal. Macroscopic composition remains constant in a closed system under fixed conditions, but reactant and product concentrations need not be equal. For example, a reversible reaction can reach equilibrium with much more reactant than product.
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Buffer
A buffer contains appreciable amounts of a weak acid and its conjugate base, or the corresponding weak-base pair. Those partners consume small added amounts of strong base or acid, limiting the pH change within the buffer's capacity. For example, an acetic acid–acetate mixture can resist modest additions of acid or base.
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Polyprotic acid
A polyprotic acid can donate more than one proton per molecule in successive steps. Each step has its own equilibrium constant, so the protons need not dissociate to the same extent. For example, phosphoric acid can lose three protons through separate equilibria.
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Strong acid or base
A strong acid transfers protons essentially completely to water in the applicable aqueous-solution model. A dissolved strong hydroxide base dissociates into its constituent ions and supplies hydroxide; it does not have to react with water to generate that hydroxide. Strength is distinct from concentration and, for a solid base, from how much can dissolve. For example, dissolved sodium hydroxide supplies sodium and hydroxide ions even when the prepared solution is dilute.