Plaster of Paris is:

### Step-by-Step Solution **1. Definition and Composition:** Plaster of Paris (PoP) is a quick-setting gypsum plaster consisting of a fine white powder (calcium sulphate hemihydrate). Its chemical name is **Calcium Sulphate Hemihydrate**. **2. Chemical Formula:** The term 'hemihydrate' refers to the presence of half a molecule of water of crystallization for every molecule of calcium sulphate. Therefore, the formula is written as: $$CaSO_4 \cdot \frac{1}{2}H_2O$$ **3. Formation from Gypsum:** It is prepared by heating Gypsum ($CaSO_4 \cdot 2H_2O$) to $373\text{ K}$ ($100^\circ\text{C}$). At this temperature, gypsum loses water molecules to become Plaster of Paris: $$CaSO_4 \cdot 2H_2O \xrightarrow{373\text{ K}} CaSO_4 \cdot \frac{1}{2}H_2O + 1\frac{1}{2}H_2O$$ **4. Analysis of Options:** * $Ca(OH)_2$ is Calcium Hydroxide (Slaked Lime). * $CaSO_4 \cdot \frac{1}{2}H_2O$ is Calcium Sulphate Hemihydrate (Plaster of Paris). * $CaCO_3$ is Calcium Carbonate (Limestone). * $CaO$ is Calcium Oxide (Quicklime). **Conclusion:** The correct formula for Plaster of Paris is **$CaSO_4 \cdot \frac{1}{2}H_2O$**.