Which one of the following is the number of water molecules that share with two formula unit CaSO₄ in plaster of Paris ?
- (a)One
- (b)Two
- (c)Five
- (d)Ten
Correct — A, One. Plaster of Paris is calcium sulphate hemihydrate, written CaSO₄·½H₂O. A formula cannot really contain half a molecule of water, so the half is a bookkeeping device: it means that for every two formula units of calcium sulphate there is one molecule of water of crystallisation, shared between them. Doubling the formula makes this explicit — 2CaSO₄·H₂O. So the number of water molecules shared by two formula units of CaSO₄ is one, which is what the key marks.
- (b)Two — Two is the water count for gypsum, CaSO₄·2H₂O — the mineral plaster of Paris is made FROM, not the plaster itself. Gypsum carries two molecules of water per single formula unit; heating drives off three-quarters of that water and leaves the hemihydrate.
- (c)Five — Five is the water of crystallisation in blue vitriol, copper sulphate pentahydrate, CuSO₄·5H₂O. It belongs to a different salt from the same list that school chemistry asks about.
- (d)Ten — Ten is the water of crystallisation in washing soda, sodium carbonate decahydrate, Na₂CO₃·10H₂O — again a neighbour on the same list, planted to catch a candidate who remembers the numbers but not which salt each belongs to.
Water of crystallisation is water chemically bound into the crystal structure of a salt in a fixed proportion, and it is written after a dot in the formula. Heating gypsum, CaSO₄·2H₂O, to around 100 °C — the figure Indian school textbooks use — drives off most of that water and leaves calcium sulphate hemihydrate, CaSO₄·½H₂O, the white powder sold as plaster of Paris. Add water back and the reaction reverses: the hemihydrate takes up water, sets into a hard interlocking mass of gypsum crystals and expands very slightly as it does so. That slight expansion is why the set plaster fills a mould faithfully, and why it works for casts on broken limbs, for ceiling designs and for taking impressions.
The stem as printed is ungrammatical — 'the number of water molecules that share with two formula unit CaSO₄' — and it is reproduced here exactly as the booklet had it. The sense is nonetheless unambiguous, and it is the standard school-chemistry gloss on the half in CaSO₄·½H₂O: the half means two formula units of the salt share a single water molecule between them. Read that way the item is answerable exactly as it stands. The reliable way to prepare for this family of questions is to hold the hydrate numbers together as one short list — plaster of Paris a half, gypsum two, copper sulphate five, washing soda ten — because the three wrong options here are simply the other members of that list. Note the neat symmetry between plaster of Paris and gypsum: the same salt, differing only in how much water the crystal is carrying, and convertible each way by heating or by adding water.
- Plaster of Paris is calcium sulphate hemihydrate, CaSO₄·½H₂O, equivalently written 2CaSO₄·H₂O.
- The half water molecule means two formula units of CaSO₄ share one molecule of water.
- It is made by heating gypsum, CaSO₄·2H₂O, at about 100 °C.
- Adding water converts plaster of Paris back to gypsum and makes it set hard.
- Other common hydrates — copper sulphate has five water molecules, washing soda has ten.
- Answering with the water count of gypsum instead of that of plaster of Paris.
- Treating the half in the formula as an error rather than as a shared molecule between two formula units.
- Mixing up the pentahydrate and decahydrate numbers, which belong to copper sulphate and washing soda.
NDA asks for the formula of plaster of Paris or gypsum outright, or as here for the number of water molecules, and has also asked candidates to rank several hydrates by their water content.
Consider the following statements: 1. Banking soda is used in fire extinguishers. 2. Quicklime is used in the manufacture of glass. 3. Gypsum is used in the manufacture of Plaster of Paris. Which of the statements given above is/are correct?
- (a) 1 and 2
- (b) 2 and 3
- (c) 1 only
- (d) 1, 2 and 3
Answer(d) 1, 2 and 3
UPSC keys the gypsum-to-plaster-of-Paris link as correct, which is the relationship that fixes the water counts in this NDA item at two and a half respectively.
Which one of the following is the chemical formula of Plaster of Paris?
- (a) CaSO₄·½ H₂O
- (b) CaSO₄·2 H₂O
- (c) CaSO₄·5 H₂O
- (d) CaSO₄·4 H₂O
Answer(a) CaSO₄·½ H₂O
The same fact set as a formula question three years later. Reading the half in that keyed formula is exactly what this 2018 item asks a candidate to do in words.
Number of molecules of water of crystallization in copper sulphate, sodium carbonate and Gypsum are
- (a) 5, 10 and 2 respectively
- (b) 10, 2 and 5 respectively
- (c) 5, 2 and 10 respectively
- (d) 2, 5 and 10 respectively
Answer(a) 5, 10 and 2 respectively
The list of hydrate numbers from which all three wrong options of this item were drawn, keyed by NDA itself two years later.
- practice — not a real PYQ
Plaster of Paris is obtained by heating which one of the following?
- (a)Limestone
- (b)Gypsum
- (c)Bleaching powder
- (d)Washing soda
Answer(b) Gypsum — heating CaSO₄·2H₂O at about 100 °C drives off water and leaves CaSO₄·½H₂O.
- practice — not a real PYQ
The number of water molecules of crystallisation in washing soda is
- (a)two
- (b)five
- (c)seven
- (d)ten
Answer(d) ten — washing soda is sodium carbonate decahydrate, Na₂CO₃·10H₂O.