Count it, or weigh it.
Two flasks look identical; one holds twice the chloride. Measure the difference by the reagent it takes to react (titration), or by the mass of solid it becomes (gravimetry).
Every method asks the same four questions.
Analyte + reagent, in a fixed ratio.
It goes almost fully to products: the equilibrium constant, K, is very large.
A visible signal: a colour, a solid, or no more cloudiness.
Ratio × amount of reagent used, or mass of solid formed.
Equivalence vs end point.
Equivalence: reagent exactly matches analyte. End point: where we see it. The gap is titration error; a good indicator keeps it under one drop.
An acid hands H⁺ to a base. Count the base it takes.
H⁺ + OH⁻ → H₂O. A weak acid works too: HA + OH⁻ → A⁻ + H₂O.
Water barely splits back (K ≈ 10¹⁴ for H⁺ + OH⁻).
The indicator is a weak acid. HIn and In⁻ differ in colour; it flips over ~2 pH units.
Mole ratio from the equation × C × V of titrant.
Pharmacy: non-aqueous perchloric acid titration is the standard pharmacopoeial assay for many weak-base drugs.
Pick the indicator for the equivalence pH.
Silver grabs chloride and drops out as a solid. Count the silver.
Ag⁺ + Cl⁻ → AgCl(s), 1 : 1.
AgCl barely dissolves (Ksp ≈ 1.8 × 10⁻¹⁰): almost no Cl⁻ is left.
Three ways: Mohr, Volhard, Fajans.
mol Cl⁻ = mol Ag⁺ used.
Pharmacy: chloride content of sodium chloride and potassium chloride preparations.
Three ways to see the end.
Mohr
Ag⁺ direct. Chromate turns red-brown (Ag₂CrO₄). Needs pH ≈ 6.5–10.
- titrant
- Ag⁺, direct
- indicator
- Chromate, CrO₄²⁻
- you see
- Red-brown Ag₂CrO₄
- needs
- pH ≈ 6.5–10
Volhard
Excess Ag⁺, back-titrated with SCN⁻. Fe³⁺ turns red. Needs acid (HNO₃).
- titrant
- Excess Ag⁺, back with SCN⁻
- indicator
- Fe³⁺
- you see
- Red Fe(SCN)²⁺
- needs
- Acid (HNO₃)
Fajans
Ag⁺ direct. A dye turns the solid's surface pink. Needs colloidal AgCl.
- titrant
- Ag⁺, direct
- indicator
- Adsorption dye
- you see
- Pink solid surface
- needs
- Colloidal AgCl
Mohr: who precipitates first.
AgCl needs far less Ag⁺ to form than Ag₂CrO₄ does, so chromate waits until the chloride is gone.
Fajans: the surface flips.
The dye never reacts. It sticks to the solid once the surface turns positive.
One gives electrons, the other takes them. Count the electrons.
MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O
A big potential gap: MnO₄⁻/Mn²⁺ +1.51 V vs Fe³⁺/Fe²⁺ +0.77 V.
Permanganate is its own indicator: purple persists once the analyte runs out. Iodine: starch turns blue-black.
Balance electrons first: MnO₄⁻ takes 5, Fe²⁺ gives 1, so 1 : 5.
The titrant is the indicator.
Iodine, two ways.
Iodimetry · direct
Standard I₂ oxidises the analyte. Example: ascorbic acid.
- happens
- I₂ oxidises the analyte
- titrant
- Standard I₂
- example
- Ascorbic acid
Iodometry · indirect
The analyte frees I₂ from excess I⁻; titrate that I₂ with thiosulfate. Example: oxidants (Cu²⁺, peroxides).
- happens
- Analyte oxidises excess I⁻ to I₂; titrate the I₂ released
- titrant
- Thiosulfate, S₂O₃²⁻
- example
- Oxidants (Cu²⁺, peroxides)
Pharmacy: hydrogen peroxide solution by permanganate; ascorbic acid by iodine; ferrous salts by cerium(IV).
EDTA wraps a metal ion like a claw. Count the claws.
M²⁺ + EDTA⁴⁻ → [M–EDTA]²⁻. Always 1 : 1.
Six arms grip at once: very stable (log Kf ≈ 10.7 for Ca²⁺).
Eriochrome Black T is wine-red holding the metal, blue when free.
mol metal = mol EDTA. The simplest ratio here.
Pharmacy: calcium salts (e.g. calcium gluconate), zinc salts, and Al/Mg in antacids.
The end point is a steal.
The indicator must hold the metal more weakly than EDTA does, or it never lets go.
Make a pure solid of known formula. Weigh it.
Ba²⁺ + SO₄²⁻ → BaSO₄(s)
BaSO₄ barely dissolves (Ksp ≈ 1.1 × 10⁻¹⁰); excess Ba²⁺ pushes it further.
Add a drop more reagent to the clear liquid. No new cloudiness: complete.
Mass of solid × gravimetric factor = mass of analyte.
From cloud to crucible.
A good precipitate is very insoluble, pure, of known formula, with crystals big enough to filter.
Pharmacy: loss on drying, sulfated ash and residue on ignition are gravimetric tests.
What goes wrong: occlusion.
A crystal that grows too fast traps stray ions. Washing can't reach them, so the mass reads high. Slow, hot, dilute precipitation and digestion prevent it.
Which method would you use?
Pick a method, then how you'd see the end. Wrong picks tell you why. Nothing is saved.