Titration Stoichiometry, Back-Titration and Accuracy vs Precision
Quantitative analysis problems all reduce to the same core move: convert a measured volume and concentration into moles, then track those moles through whatever stoichiometry the problem describes. Alongside that, knowing the difference between accuracy and precision lets you read a data set correctly.
EDTA Titration Stoichiometry for a Calcium Carbonate Tablet is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Working an EDTA titration back to the original tablet composition
EDTA forms a 1:1 complex with Ca²⁺, so a straightforward titration problem is pure mole-tracking: find the moles of CaCO₃ in the original sample from its mass and molar mass, convert to a molarity for the prepared solution, scale down to the moles present in the titrated aliquot, then divide by the EDTA concentration to get the burette volume needed.
A 10.0 mL aliquot then contains 0.0125 M x 0.010 L = 1.25 x 10⁻⁴ mol Ca²⁺, which needs 1.25 x 10⁻⁴ mol / 0.0198 M = 6.31 mL of EDTA (using the 1:1 stoichiometry). Work every step in moles, and only convert to volume or mass at the very last step you actually need it.
Back-titration: using excess reagent, then measuring what is left over
When a sample cannot be titrated directly (for example, because it also contains an inert or hard-to-react impurity), back-titration adds a known EXCESS of one reagent to react with the sample completely, then titrates whatever excess remains with a second reagent to find out how much was actually used up by the sample. For a sample of MCl₂ contaminated with M(OH)₂ dissolved in a known excess of HCl: total moles HCl added minus moles HCl neutralised by the second titrant (NaOH) gives the moles of HCl that reacted with the sample itself. Since MCl₂ does not react with HCl at all (it is already a neutral salt), only the M(OH)₂ impurity consumes HCl, in a 1:2 ratio (M(OH)₂ + 2HCl → MCl₂ + 2H₂O). Divide the HCl consumed by 2 to get moles of M(OH)₂, convert to mass using the given molar mass, and divide by the total sample mass to get the percentage impurity.
Accuracy is closeness to the true value; precision is closeness among repeated measurements
Accuracy describes how close a set of measurements sits to the TRUE (expected) value; precision describes how close the measurements sit to EACH OTHER, regardless of whether that cluster is anywhere near the true value. A data set can be accurate on average (its mean is close to the true value) while still being imprecise (the individual readings are scattered widely around that average) — this is exactly what good-accuracy-poor-precision looks like: readings that average out close to the expected value, but that individually vary more than a tightly clustered, well-controlled titration should. Do not confuse this with a tightly clustered set that is centred on the WRONG value (that is good precision, poor accuracy instead), or a set that is both scattered AND off-centre (poor accuracy and poor precision together).
OlympIQ exam lens
- ✓Work titration problems in moles throughout; convert to mass or volume only at the final step
- ✓EDTA complexes Ca²⁺ in a 1:1 ratio — moles EDTA used equals moles Ca²⁺ present in the titrated aliquot
- ✓Back-titration: (total moles of the excess reagent) minus (moles neutralised by the second titrant) equals moles that reacted with the sample itself
- ✓In a back-titration, only the reactive impurity consumes the excess reagent — an inert component (like MCl₂ with HCl) does not
- ✓Accuracy = closeness to the true value; precision = closeness among repeated measurements — a data set can have one without the other
Do not assume a tightly clustered set of titration readings is automatically the accurate one. Tight clustering only shows good PRECISION — check separately whether that cluster is actually centred near the true, expected value before calling it accurate too.
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