Chemistry: Atoms First 2e · Acid-Base Equilibria
Acid-Base Titrations
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A titration Gradual addition of a known-concentration solution to an unknown one until reaction is complete Full entry → adds a solution of known concentration (the titrant The solution of known concentration delivered from the buret Full entry →) gradually to a measured amount of a solution of unknown concentration (the analyte The substance being analyzed (unknown concentration) Full entry →) until the reaction between them is just complete. For acid–base titrations the reaction is a neutralization, and the point where added moles of titrant exactly match moles of analyte is the equivalence point The point where added moles of titrant exactly match analyte moles by stoichiometry Full entry →. The titrant volume, combined with the reaction stoichiometry, gives the unknown concentration. As titrant is added, pH is monitored to produce a titration curve (pH versus titrant volume), and an indicator A dye that changes color over a narrow pH range Full entry → — a dye whose color changes over a narrow pH window — signals when to stop. The curve's shape reveals the strengths of the acid and base: the pH at the equivalence point and the steep "jump" around it dictate which indicator will work, and polyprotic acids show multiple equivalence points.
Why this matters
Titration is one of the most common quantitative techniques in chemistry. Food chemists measure the acidity of vinegar, wine, and fruit juice; pharmaceutical labs assay active ingredients; water-treatment facilities measure alkalinity; clinical labs quantify analytes such as calcium or chloride in serum. The same logic — deliver a known reagent until reaction is complete, then compute from stoichiometry — underlies countless assays. Choosing the wrong indicator makes the endpoint The point where the indicator visibly changes color Full entry → miss the equivalence point, biasing every result.
The college version
Core Concepts
The setup and the vocabulary
A buret delivers the titrant in measured increments into the analyte solution, monitored by a pH meter or indicator. Three points must be distinguished:
- Equivalence point: the theoretical point where moles of titrant equal moles of analyte by stoichiometry. Calculated, not observed.
- Endpoint: the point where the indicator actually changes color. A good indicator puts the endpoint within a drop or two of the equivalence point.
- Indicator: a weak acid or base whose conjugate forms differ in color; it changes color over a characteristic transition range of about 1–2 pH units.
The convenient arithmetic unit is the millimole, since M × mL = mmol.
Strong acid – strong base curves
The pH starts low, rises slowly, then jumps dramatically — often from about pH 3 to pH 11 within a fraction of a milliliter — around the equivalence point, where pH = 7 because the salt (e.g., NaCl) does not hydrolyze. Any indicator whose transition range lies inside the jump works.
Weak acid – strong base curves
Before equivalence, the partially neutralized weak acid and its conjugate base form a buffer, so the curve is flat — the buffer region from the previous topic. At the half-equivalence point The point where half the titrant needed for equivalence has been added Full entry →, [HA] = [A-] and, from the Henderson–Hasselbalch equation, pH = pKa — a quick way to measure an unknown acid's pKa. At equivalence the solution is the conjugate base, which hydrolyzes, so pH > 7 (typically 8–10). The indicator must change color on the alkaline side — phenolphthalein (about 8.2–10.0) is the classic choice.
Weak base – strong acid curves
The mirror image: the curve starts alkaline, is buffered through the conjugate-acid region, and at equivalence contains the conjugate acid of the weak base, which hydrolyzes to give pH < 7 (typically 3–6). For example, titrating 0.100 M ammonia with 0.100 M HCl gives a 0.0500 M NH4+ solution at equivalence with pH ≈ 5.3, so an acidic-side indicator such as methyl orange (about 3.1–4.4) or methyl red (about 4.4–6.2) is appropriate.
Polyprotic acids
An acid like H3PO4 has one equivalence point per ionizable proton — three in all — with multiple buffer regions and jumps of decreasing size.
How It Works / Step-by-Step Process
Calculating pH along a titration curve
- Identify the neutralization stoichiometry; compute millimoles of analyte present.
- For each titrant volume, compute millimoles of H⁺ (or OH⁻) delivered and the amount remaining or in excess.
- Decide what controls pH: before equivalence, the buffer for weak acids or the excess for strong ones; at equivalence, salt hydrolysis (pH 7 for strong–strong); after equivalence, the excess titrant.
- Divide millimoles by the total volume in mL for molarity, then convert to pH.
Choosing an indicator
- Determine the equivalence-point pH from the curve or calculation.
- Pick an indicator whose transition range lies inside the steep jump around that pH.
Common Confusions
| Do Not Confuse | With | The Difference |
|---|---|---|
| Equivalence point | Endpoint | Equivalence is theoretical (stoichiometric); endpoint is what the indicator shows. A poor indicator choice separates them |
| pH = 7 at equivalence | Always true | True only for strong acid–strong base; weak acid–strong base gives pH > 7, weak base–strong acid gives pH < 7 |
| Half-equivalence point | Equivalence point | Half-equivalence is mid-buffer where pH = pKa; equivalence is complete neutralization |
| A strong acid's pH | A weak acid's pH at the same molarity | 0.100 M HCl has pH 1.00; 0.100 M acetic acid has pH 2.87 because it barely dissociates |
| Indicator "changes at pH 7" | Indicator behavior | Each indicator has its own transition range; many change well away from 7 |
| Millimoles | Milligrams | mmol = M × mL (amount); mg = mass. Confusing them wrecks the calculation |
Eli explains
The same idea, in plain words
Explain it like I’m 10
A titration is like filling a measuring cup to exactly the line: you pour a liquid of known strength drop by drop into a mystery liquid until the reaction is just finished, and the amount you poured tells you how strong the mystery liquid was. The indicator is like the cup's color-change line — it changes color at just the right moment so you know when to stop pouring.
Worked example
Example 1: Strong acid–strong base titration of HCl with NaOH
A 25.00 mL sample of 0.100 M HCl is titrated with 0.100 M NaOH. Find the pH (a) initially, (b) after 10.00 mL of NaOH, (c) at equivalence, and (d) after 35.00 mL of NaOH.
(a) Initial pH. HCl is a strong acid, so [H+] = 0.100 M:
pH = -log(0.100) = 1.00
(b) After 10.00 mL NaOH. Compute millimoles:
mmol H+ = 25.00 mL × 0.100 mmolmL = 2.500 mmol
mmol OH- added = 10.00 mL × 0.100 mmolmL = 1.000 mmol
The OH⁻ neutralizes an equal number of millimoles of H⁺, leaving 1.500 mmol of H⁺ in 25.00 + 10.00 = 35.00 mL:
[H+] = 1.500 mmol35.00 mL = 0.0429 M pH = -log(0.0429) = 1.37
(c) At equivalence. The 1:1 stoichiometry requires 2.500 mmol of NaOH — 2.500/0.100 = 25.00 mL. The salt NaCl does not hydrolyze, so:
pH = 7.00
(d) After 35.00 mL NaOH. Excess NaOH is 35.00 - 25.00 = 10.00 mL, giving 1.000 mmol OH⁻ in 25.00 + 35.00 = 60.00 mL:
[OH-] = 1.000 mmol60.00 mL = 0.0167 M
pOH = -log(0.0167) = 1.78 pH = 14.00 - 1.78 = 12.22
The pH swings from 7.00 to 12.22 only 10 mL past equivalence — the steep jump indicators exploit.
Example 2: Weak acid–strong base titration of acetic acid with NaOH
A 25.00 mL sample of 0.100 M acetic acid (Ka = 1.8 × 10-5) is titrated with 0.100 M NaOH. Find the pH (a) initially, (b) at the half-equivalence point, and (c) at equivalence.
(a) Initial pH. Let x = [H+] and use the weak-acid approximation:
Ka = x20.100 - x ≈ x20.100
x = Ka × 0.100 = 1.8 × 10-5 × 0.100 = 1.8 × 10-6 = 1.3 × 10-3 M
pH = -log(1.3 × 10-3) = 2.87
(b) Half-equivalence point (12.5 mL NaOH). Half the acid is converted to acetate, so [HA] = [A-] and the Henderson–Hasselbalch log term is zero:
pH = pKa = -log(1.8 × 10-5) = 4.74
(c) Equivalence point (25.0 mL NaOH). All acid has become acetate: 2.50 mmol in 25.00 + 25.00 = 50.00 mL:
[C2H3O2-] = 2.50 mmol50.00 mL = 0.0500 M
Acetate is a weak base with Kb = Kw/Ka = 1.0 × 10-14/1.8 × 10-5 = 5.6 × 10-10. Then:
[OH-] = Kb × 0.0500 = 5.6 × 10-10 × 0.0500 = 5.3 × 10-6 M
pOH = -log(5.3 × 10-6) = 5.28 pH = 14.00 - 5.28 = 8.72
The equivalence point is alkaline (8.72), so phenolphthalein — whose transition range (about 8.2–10.0) brackets 8.72 — is correct. Methyl orange would change color near pH 4, far too early.
Key takeaways
- Equivalence point: moles of titrant = moles of analyte; endpoint: where the indicator changes color.
- Strong acid–strong base: equivalence pH = 7; weak acid–strong base: pH > 7; weak base–strong acid: pH < 7.
- Half-equivalence point of a weak acid titration: [HA] = [A-], so pH = pKa.
- The indicator's transition range must fall on the steep part of the curve, near the equivalence-point pH.
- Use millimoles: M × mL = mmol; at equivalence, mmol acid = mmol base.
- Before equivalence in a weak acid titration, the solution is a buffer; after equivalence, excess strong titrant sets the pH.
- Phenolphthalein (8.2–10.0) suits weak acid–strong base; methyl orange (3.1–4.4) suits weak base–strong acid.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
Distinguish equivalence point, endpoint, and indicator transition range.
Show answer
Equivalence point: stoichiometrically exact match of titrant and analyte (calculated, not observed). Endpoint: where the indicator visibly changes. Transition range: the 1–2 unit pH window of the indicator's color change; it must lie on the steep part of the curve.
A 20.00 mL sample of HCl requires 32.50 mL of 0.100 M NaOH for equivalence. What is the HCl concentration?
Show answer
mmol NaOH = 32.50 × 0.100 = 3.25 mmol. Stoichiometry is 1:1, so the sample held 3.25 mmol HCl in 20.00 mL: [HCl] = 3.25/20.00 = 0.1625 M.
Why is the equivalence-point pH of a weak acid–strong base titration greater than 7?
Show answer
At equivalence the solution is the conjugate base of the weak acid (e.g., acetate), which hydrolyzes to produce OH⁻, raising pH above 7.
Where on a weak acid–strong base curve is pH exactly equal to pKa, and what is the buffer doing there?
Show answer
At the half-equivalence point, where [HA] = [A-] and the solution is a buffer at maximum capacity; the log term is zero, so pH = pKa.
Which indicator — phenolphthalein or methyl orange — for titrating acetic acid with NaOH, and why?
Show answer
Phenolphthalein: the equivalence pH is about 8.7, and its transition range (about 8.2–10.0) brackets that value.
Why is the pH jump around the equivalence point of a strong acid–strong base titration so steep?
Show answer
Once the acid is exhausted, a tiny excess of OH⁻ (or H⁺) dominates the pH because a 1:1 strong-strong reaction leaves no buffering — the curve jumps from about pH 3 to 11 within a fraction of a milliliter.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- titration
- Gradual addition of a known-concentration solution to an unknown one until reaction is complete
- titrant
- The solution of known concentration delivered from the buret
- analyte
- The substance being analyzed (unknown concentration)
- equivalence point
- The point where added moles of titrant exactly match analyte moles by stoichiometry
- endpoint
- The point where the indicator visibly changes color
- indicator
- A dye that changes color over a narrow pH range
- half-equivalence point
- The point where half the titrant needed for equivalence has been added
Sources & references
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