8.5 Acid-Base Titrations

A titration is a controlled acid–base reaction used to find the concentration (analyte) by slowly adding a solution of known concentration (titrant) until stoichiometric neutralization. You monitor pH (with a pH meter or indicator) and plot a titration curve (pH vs. volume of titrant). At the equivalence point the moles titrant added = moles analyte (use that to calculate concentration)—this holds for strong/weak and monoprotic/polyprotic titrations (CED 8.5.A.2). For weak acid titrations the half-equivalence point is key: [HA] = [A–], so pH = pKa and you can read pKa from the curve (CED 8.5.A.3). The pH at equivalence depends on the major species: strong acid + strong base → pH ≈ 7; weak acid titrated with strong base → basic equivalence pH due to conjugate-base hydrolysis (CED 8.5.A.4). Polyprotic acids show multiple equivalence points equal to the number of acidic protons (CED 8.5.A.5). For more examples and AP-style practice, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and Unit 8 overview (https://library.fiveable.me/ap-chemistry/unit-8). Need practice problems? Try Fiveable’s practice set (https://library.fiveable.me/practice/ap-chemistry).

pH changes during a titration because you’re changing the chemical makeup (and therefore the dominant acid/base species) of the solution as you add titrant, so the H+ (or OH−) concentration shifts. At first, if you titrate a weak acid with a strong base you form its conjugate base and create a buffer region where pH changes slowly. Around the half-equivalence point [HA] = [A−] and pH = pKa (useful for finding pKa; CED 8.5.A.3). Near the equivalence point the stoichiometry is such that moles titrant = moles analyte (CED 8.5.A.2), so the solution composition changes rapidly and pH often jumps—how big the jump depends on whether species are strong or weak (CED 8.5.A.4). After equivalence, excess titrant controls pH. A titration curve (pH vs. volume) summarizes all this and helps you identify buffer region, half-equivalence, and equivalence points (CED 8.5.A.1). For review and practice, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and Unit 8 resources (https://library.fiveable.me/ap-chemistry/unit-8); practice questions are at (https://library.fiveable.me/practice/ap-chemistry).

The equivalence point is where moles of titrant added = moles of analyte (so for a monoprotic acid, n_HA = n_OH–)—you use this to calculate the analyte’s concentration (CED 8.5.A.2). The half-equivalence point is halfway (volume) to that equivalence point in a weak acid/base titration. At the half-equivalence point [HA] = [A–], so pH = pKa (CED 8.5.A.3). Practically: the equivalence point tells you stoichiometry (and, for weak acid/strong base titrations, gives a basic pH because the conjugate base hydrolyzes—CED 8.5.A.4), while the half-equivalence point gives you the acid’s pKa directly from the measured pH (useful for buffer region reasoning). For quick review, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and more practice problems at (https://library.fiveable.me/practice/ap-chemistry).

A titration curve plots pH (y-axis) vs volume of titrant added (x-axis). Read it like this: - Start: identify whether analyte is acidic or basic by initial pH. - Buffer region: a relatively flat region before the big jump—here a weak acid + its conjugate base (or vice versa) resists pH change. - Half-equivalence point: the midpoint of the buffer region where [HA] = [A-], so pH = pKa (useful to find pKa for weak acids; CED 8.5.A.3). - Equivalence point: the steepest part of the curve where moles titrant = moles analyte (CED 8.5.A.2). Use the volume at equivalence to calculate analyte concentration. Note pH at equivalence depends on species present: ~7 for strong acid/strong base, basic if conjugate base present (weak acid titration), acidic if conjugate acid present (weak base titration) (CED 8.5.A.4). - Polyprotic acids: look for multiple jumps = multiple equivalence points; halfway to each gives the corresponding pKa (CED 8.5.A.5). For practice interpreting real curves and AP-style problems, check the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and more practice questions (https://library.fiveable.me/practice/ap-chemistry).

Think about what’s left in the flask at the equivalence point. - Strong acid + strong base: at equivalence you've converted H+ and OH− into H2O and only spectator ions (like Na+, Cl−) remain. Spectator ions don’t react with water, so [H+] and [OH−] are just from water autoionization → pH ≈ 7. This matches the CED point that “strong acid and strong base titrations result in neutral pH at the equivalence point” (8.5.A.4). - Weak acid + strong base: at equivalence the weak acid has been converted to its conjugate base (A−). A− is not a spectator—it hydrolyzes: A− + H2O ⇌ HA + OH−. That produces extra OH−, so pH > 7. That’s why the equivalence point is basic for weak-acid/strong-base titrations (also in 8.5.A.4). Use the half-equivalence point (8.5.A.3) to find pKa: at half-equivalence pH = pKa, which helps predict how basic the equivalence pH will be. For more guided examples and AP-style practice, check the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and the practice problems (https://library.fiveable.me/practice/ap-chemistry).

At the half-equivalence point (halfway to the volume of titrant needed for equivalence) exactly half the original weak acid has been converted to its conjugate base, so [HA] = [A–]. That means the solution is a buffer made of a conjugate acid–base pair. Plugging [HA] and [A–] into the Henderson–Hasselbalch equation: pH = pKa + log([A–]/[HA]) gives pH = pKa + log(1) = pKa. So the measured pH at the half-equivalence point equals the acid’s pKa. Practically, for a monoprotic weak acid titrated with strong base, the half-equivalence volume is Veq/2; reading pH there gives pKa (useful on the AP exam; see CED 8.5.A.3). For more examples and a quick review of titration curves and buffer regions, check the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and practice problems (https://library.fiveable.me/practice/ap-chemistry).

Use the equivalence-point mole relationship from the CED: at equivalence, moles titrant added = moles analyte (adjust for how many H+ or OH− each supplies). Steps: 1. Convert volumes to liters. 2. Calculate moles titrant = M_titrant × V_titrant. 3. Use stoichiometry: moles analyte = moles titrant × (stoich. factor from balanced reaction). For a monoprotic acid titrated by a strong base, factor = 1, so moles HA = moles OH−. For diprotic, factor = 1/2 if one mole base neutralizes two protons, etc. 4. Concentration analyte = moles analyte / V_analyte (L). Example (monoprotic): 0.100 M NaOH, 0.02500 L used to titrate 0.01000 L acid → moles OH− = 0.100×0.02500 = 2.50×10−3 mol. So [HA] = 2.50×10−3 / 0.01000 = 0.250 M. Remember: for weak acid titrations you can also use the half-equivalence pH = pKa to find Ka (CED 8.5.A.2–3). For more review and practice problems, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and tons of practice on Fiveable (https://library.fiveable.me/practice/ap-chemistry).

If you titrate the same strong base into a strong acid vs a weak acid, the titration curves and key points look different because of the acids’ strengths. - Starting pH: strong acid starts very low (near 1–2 for 0.1–0.01 M), weak acid starts higher (depends on Ka). - Buffer region: only the weak-acid titration shows a clear buffer region before equivalence where HA and A– coexist; the curve there is fairly flat. Use the half-equivalence point (half the volume to equivalence) to get pH = pKa (CED 8.5.A.3). - Equivalence point pH: strong acid + strong base → pH ≈ 7 at equivalence; weak acid + strong base → pH > 7 because the conjugate base hydrolyzes (CED 8.5.A.4). - Curve shape/steepness: strong/strong has a steeper vertical jump at equivalence (easier endpoint detection); weak-acid titration has a more gradual rise and smaller pH jump. That changes which indicator works best (phenolphthalein is commonly good for weak-acid → strong-base). - Stoichiometry rule still holds: moles titrant = moles analyte at equivalence (CED 8.5.A.2). For more review and practice on titration curves, half-equivalence points, and indicator choice, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and the Unit 8 overview (https://library.fiveable.me/ap-chemistry/unit-8). For extra practice problems, try Fiveable’s AP Chem practice set (https://library.fiveable.me/practice/ap-chemistry).

Each acidic proton in a polyprotic acid behaves like its own acid: you must add one mole of titrant per mole of acidic H removed. So a diprotic acid gives two equivalence points, a triprotic three, etc. On the titration curve each equivalence point shows where one proton has been fully neutralized (moles titrant = moles H+ removed), and between equivalence points you often see buffer regions where a conjugate acid/base pair dominates. For weak polyprotic acids those buffer regions hit half-equivalence points where pH ≈ pKa for that proton (useful for finding each pKa). Also note the pH at each equivalence depends on the species present (conjugate base hydrolysis for weak acids), not always pH 7. This is exactly what the CED expects you to explain (see 8.5.A.1–8.5.A.5). For a quick refresher, check the Topic 8.5 study guide on Fiveable (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and more practice problems (https://library.fiveable.me/practice/ap-chemistry).

“Major species” just means the chemical forms present in the largest amounts at a particular point in the titration—those species that control the solution’s pH and chemistry. In practice you look at what’s been added and what’s reacted: - Before any titrant: the analyte (e.g., HA for a weak acid) is the major species. - Buffer region: both HA and A– are abundant (major species); at the half-equivalence point [HA] = [A–], so pH = pKa (CED 8.5.A.3). - At equivalence: moles titrant = moles analyte (CED 8.5.A.2), so the original acid/base is gone and the conjugate or water is the major species. For strong acid + strong base the major species is water (pH ≈ 7); for weak acid titrated with strong base the conjugate base A– is major and hydrolyzes to give a basic pH (CED 8.5.A.4). - After equivalence: excess titrant (strong acid or base) is the major species. Identifying the major species lets you predict pH qualitatively (and do quantitative monoprotic calculations on the exam). For more examples and practice, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and practice problems (https://library.fiveable.me/practice/ap-chemistry).

Look at what species is left at the equivalence point—that tells you the pH. - Strong acid + strong base → salt of a strong acid and strong base; neither conjugate undergoes hydrolysis → equivalence ≈ neutral (pH ≈ 7). - Weak acid titrated with strong base → conjugate base (A−) is the major species and hydrolyzes: A− + H2O ⇌ HA + OH− → equivalence point is basic (pH > 7). - Weak base titrated with strong acid → conjugate acid (BH+) is the major species and hydrolyzes: BH+ + H2O ⇌ B + H3O+ → equivalence point is acidic (pH < 7). For polyprotic acids, each equivalence point’s pH is set by the predominant species at that point; use the half-equivalence point to find pKa (pH = pKa) for weak acids (CED 8.5.A.3–8.5.A.4). Small shifts from 7 can occur due to ionic strength or temperature, but the conjugate-hydrolysis rule is what AP expects. For practice and worked examples see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and Unit 8 resources (https://library.fiveable.me/ap-chemistry/unit-8). For more problem practice, try the AP Chemistry practice set (https://library.fiveable.me/practice/ap-chemistry).

When you add titrant drop by drop, you’re doing tiny, controlled stoichiometric steps: each drop reacts with analyte molecules (H+ with OH– or vice versa), changing which species dominate the solution and therefore the pH. Early in a weak-acid/strong-base titration you form the conjugate base and create a buffer region where pH changes slowly; at the half-equivalence point [HA] = [A–] and pH = pKa (useful for finding pKa). Near the equivalence point the moles of titrant added ≈ moles of analyte (CED 8.5.A.2), so small additions cause large pH jumps because the buffering capacity is gone—that steep region defines the endpoint you detect with an indicator or pH meter. After equivalence, excess titrant controls pH; for weak acid titrations the conjugate base hydrolyzes to give a basic equivalence pH (CED 8.5.A.4). Dropwise addition gives the fine resolution needed to locate half-equivalence and equivalence points on the titration curve (pH vs. volume). For more practice and stepwise examples, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and thousands of practice problems (https://library.fiveable.me/practice/ap-chemistry).

At the half-equivalence point you’ve neutralized exactly half of the original moles of the weak acid HA with base. Start with n0 moles HA; after adding half the volume to reach half-equivalence you’ve converted n0/2 moles HA → n0/2 moles A−, leaving n0/2 moles HA unreacted. So moles HA = moles A−. Since they share the same total solution volume, their concentrations are equal: [HA] = [A−]. That’s why the half-equivalence point is a buffer region where the Henderson–Hasselbalch equation simplifies to pH = pKa (because log([A−]/[HA]) = log(1) = 0). This is exactly what the CED highlights: use the half-equivalence point to find pKa from the measured pH (8.5.A.3). For a clear walkthrough, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan). For extra practice problems, try the AP practice bank (https://library.fiveable.me/practice/ap-chemistry).

Find the equivalence point first (the steepest vertical part of the pH vs. volume curve). For a monoprotic weak acid titrated with strong base, the half-equivalence point is at half the volume of titrant needed to reach equivalence. At that half-equivalence point [HA] = [A–], so pH = pKa (Henderson–Hasselbalch), meaning pKa equals the pH read from the curve at that volume (CED 8.5.A.3). For a weak polyprotic acid, do the same for each proton: there’s a buffer region and a half-equivalence point between successive equivalence points—pH at each midpoint equals the corresponding pKa (CED 8.5.A.5). If you have a strong acid/strong base titration, you won’t get a useful half-equivalence pKa because no buffer region forms. For more examples and practice problems that match AP wording, see the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and the Unit 8 overview (https://library.fiveable.me/ap-chemistry/unit-8).

Titrations matter because they let you measure how much acid or base is in a real sample precisely—not just in a lab problem. In practice they’re used for quality control (pharmaceuticals, food and beverages), environmental testing (water hardness, pollutant neutralization), and making sure medicines/antacids contain the right dose. AP-relevant reasons: at the equivalence point the moles titrant = moles analyte so you can calculate concentration (CED 8.5.A.2), the half-equivalence point gives pKa for weak acids (8.5.A.3), and titration curves tell you whether the equivalence pH is acidic, basic, or neutral based on conjugate species (8.5.A.4). Knowing how indicators or a pH meter detect the end point ties directly to AP tasks like explaining titration curves and using them to determine concentrations. For a focused review, check the Topic 8.5 study guide (https://library.fiveable.me/ap-chemistry/unit-8/acid-base-titrations/study-guide/5ugPp0ykDKthSY3MiYan) and practice problems (https://library.fiveable.me/practice/ap-chemistry).