What you'll be able to do: Analyse gravimetric and redox titration data, including percent composition and sources of experimental error.
Two classical techniques turn the ideas in this unit into numbers on a lab bench: weighing a precipitate, and titrating with permanganate. Both are only as good as the technique, so understanding how errors propagate matters as much as the arithmetic.
These are recommended, not required. You can start this lesson at any time.
If an ion can be precipitated completely as a compound of known formula, then weighing that dry solid measures how much of the ion was present. The method needs no calibration curve and no standard solution, only an accurate balance and patient technique.
Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s)
Add a slight excess of precipitating agent to drive the reaction to completion, digest the mixture so crystals grow larger and filter more cleanly, wash the solid to remove adsorbed spectator ions, then dry to constant mass. Drying, cooling and reweighing to constant mass supplies evidence of a stable dry product under the specified conditions; it does not by itself prove purity or absence of decomposition.
A good precipitate has known composition, low enough solubility and particles that can be collected without loss. Add reagent slowly with mixing, allow the stated digestion time, and use the specified wash liquid and temperature. Too little reagent leaves analyte in solution; excessive or inappropriate washing can dissolve product. Cool the dried container as instructed before weighing, and subtract the empty container or filter tare. A stable mass of impure or decomposed material is still the wrong analytical product.
Convert the precipitate mass to moles, use the formula to find moles of the ion of interest, convert that to a mass, then divide by the original sample mass. The gravimetric factor is simply this chain expressed as a single multiplier.
For sulfate collected as BaSO₄, m(SO₄²⁻) = m(BaSO₄) × 96.06/233.39. The factor 0.4116 converts grams of precipitate into grams of sulfate because one mole of solid contains one mole of sulfate. If the requested analyte were sulfur, use 32.06/233.39 instead. The original sample mass stays in the denominator: percent sulfate = 100 m(BaSO₄)(96.06/233.39)/m(sample). A different requested analyte changes the numerator conversion even though the same solid was weighed.
percent = (mass of analyte / mass of sample) × 100
In acidic solution, MnO₄⁻ is reduced to the almost colourless Mn²⁺ while the analyte is oxidised. Because the purple colour disappears as it reacts, the first drop of excess titrant leaves a faint persistent pink, so no separate indicator is required. Sulfuric acid is used to acidify, because hydrochloric acid would itself be oxidised.
Use the standardized permanganate concentration, not simply a value calculated from an old preparation label. In acid, each MnO₄⁻ accepts five electrons while Fe²⁺ supplies one, giving a 1:5 titrant:iron ratio. A 25.00 mL aliquot consuming 18.60 mL of 0.0200 M titrant therefore contains 5(0.0200)(0.01860) = 0.00186 mol Fe²⁺. Divide by 0.02500 L for the aliquot's concentration. A diluted sample needs its separate dilution factor.
The endpoint is the faint pink persisting for the protocol's stated time, not a deep purple solution. Insufficient acidity can change the manganese product and invalidate the assumed five-electron ratio. Conditions determine the balanced reaction before the calculation begins.
MnO₄⁻ + 8 H⁺ + 5 e⁻ → Mn²⁺ + 4 H₂O
For any mistake, ask whether the measured quantity ends up too high or too low, then follow it through the calculation. A precipitate that is not fully dried weighs too much, so the reported percentage is too high. A burette rinsed with water instead of titrant delivers dilute titrant, so more volume is needed and the calculated analyte appears too high.
| Specific fault, with other quantities unchanged | Direct effect | Reported analyte result |
|---|---|---|
| Wet or contaminated precipitate weighed | Solid mass too high | Too high |
| Product lost through filter or transfer | Recovered solid mass too low | Too low |
| Extra titrant added beyond endpoint | Recorded volume too high | Too high |
| Titrant diluted in burette but old concentration used | More volume needed than calculation assumes | Too high |
| Distilled water added to analyte flask | Analyte moles unchanged | Equivalence amount unchanged |
State which quantity is being reported. Losing analyte after the original sample was weighed lowers a mass percentage; losing material before both sample and precipitate masses are measured is a different scenario. Error direction follows the actual numerator and denominator.
In gravimetric analysis, the measured precipitate mass is converted back to analyte amount by a mole ratio. If some precipitate is lost during filtration or transfer, the recorded mass is too low even if the remaining solid is perfectly dry.
The calculated analyte amount and percent composition are then too low. Contrast this with undried precipitate, which can make the mass too high.
Quantitative analysis based on measuring the mass of a pure isolated product.
Repeated drying, cooling and weighing until successive masses agree within the procedure’s tolerance; evidence of a stable endpoint, not proof of purity.
A titrant whose own colour change marks the endpoint, as permanganate does.
A slight excess of the precipitating agent ensures the analyte is removed completely.
Trace each procedural fault to whether the measured value becomes too high or too low.
percent = (mass of analyte / mass of sample) × 100
A 1.000 g sample containing sulfate is dissolved and treated with excess BaCl₂, yielding 0.750 g of dry BaSO₄. What is the percent sulfate by mass?
Try it first: Decide what the weighed solid tells you about moles before converting anything.
0 of 4 steps revealed.
A 25.00 mL sample of Fe²⁺ solution requires 18.60 mL of 0.0200 M KMnO₄ in acid to reach the first persistent pink. What is the iron concentration?
Try it first: Recall how many electrons permanganate accepts, since that sets the ratio.
0 of 4 steps revealed.
In the gravimetric experiment above, the student removes the filter paper before the precipitate reaches constant mass. What effect does this have on the reported percent sulfate?
0 of 4 steps revealed.
A student spills some BaSO₄ while transferring a dried sulfate precipitate to a balance. How does that affect the reported sulfate percent?
Try it first: Only collected BaSO₄ appears in the calculation.
0 of 3 steps revealed.
| Mistake | Why it's wrong | Check instead |
|---|---|---|
| Using hydrochloric acid to acidify a permanganate titration. | Chloride is itself oxidised by permanganate, consuming extra titrant. | Acidify with sulfuric acid, which is not oxidised. |
| Treating the precipitate mass as the analyte mass. | The solid includes the counter-ion added during precipitation. | Convert to moles, apply the formula ratio, then convert back to the analyte mass. |
| Assuming a spilled sample always lowers the reported percentage. | The direction depends on which measurement was affected and where it appears in the calculation. | Trace the specific quantity through each step of the arithmetic. |
| Weighing the precipitate once and calling it dry. | Residual solvent adds mass that is indistinguishable from product. | Dry and reweigh until two successive masses agree. |
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After the lesson · Question bank
Work through new problems on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
14 topic questions across 3 difficulty levels.
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Gravimetric analysis determines an unknown amount by converting it quantitatively into a pure, dry, insoluble solid and weighing it. Redox titration determines it by measuring the volume of an oxidising agent consumed, with permanganate acting as its own indicator. In both, the calculation runs from the measured quantity through moles and the mole ratio to the analyte, and every procedural fault can be traced to whether it makes the measured quantity too high or too low.
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