Water of reaction needed to react completely with 100 g of calcium sulphate hemihydrates to convert it to calcium sulphate dihydrate
## Core Concept
The core concept here involves understanding the chemical reaction of calcium sulphate hemihydrates (CaSO4·1/2H2O) converting to calcium sulphate dihydrate (CaSO4·2H2O). This process requires the addition of water to the hemihydrate form.
## Why the Correct Answer is Right
The chemical formula for calcium sulphate hemihydrate is CaSO4·1/2H2O, and for calcium sulphate dihydrate, it is CaSO4·2H2O. The conversion can be represented by the equation:
[ text{CaSO}_4 cdot frac{1}{2} text{H}_2text{O} + frac{3}{2} text{H}_2text{O} rightarrow text{CaSO}_4 cdot 2text{H}_2text{O} ]
The molar mass of CaSO4·1/2H2O is approximately 145 g/mol (136 for CaSO4 and 9 for 1/2H2O), and that of H2O is 18 g/mol. For 100 g of CaSO4·1/2H2O:
[ text{Moles of CaSO}_4 cdot frac{1}{2} text{H}_2text{O} = frac{100}{145} approx 0.6897 , text{mol} ]
Given that 1 mole of CaSO4·1/2H2O requires 1.5 moles of H2O to convert to CaSO4·2H2O:
[ text{Moles of H}_2text{O needed} = 0.6897 times 1.5 = 1.0346 , text{mol} ]
[ text{Mass of H}_2text{O needed} = 1.0346 times 18 approx 18.62 , text{g} ]
## Why Each Wrong Option is Incorrect
- **Option A:** This option suggests 18 g of water, which is close but not the precise calculation based on the molar masses and the stoichiometry of the reaction.
- **Option B:** This option suggests 20 g of water, which overestimates the amount needed based on our calculations.
- **Option D:** This option suggests a different amount of water, which does not align with the stoichiometric calculations.
## Clinical Pearl / High-Yield Fact
In medical and dental applications, the setting of plaster of Paris (calcium sulphate hemihydrate) to form calcium sulphate dihydrate is crucial. The reaction is exothermic and requires a specific amount of water for complete setting. Too little water can leave the plaster porous, while too much water weakens the set plaster. Understanding the stoichiometry helps in achieving the right consistency for various applications.
## Correct Answer Line
**Correct Answer: C. 18.6 g.**