Step 1: Understanding the Question:
The question asks for the specific temperature (in Kelvin) required to heat gypsum to convert it into Plaster of Paris (POP).
Step 2: Key Formula or Approach:
The chemical formula of Gypsum is \(CaSO_4 \cdot 2H_2O\). Upon controlled heating, it loses a portion of its water of crystallization to form Plaster of Paris (\(CaSO_4 \cdot \frac{1}{2}H_2O\)).
The chemical equation is:
\[ CaSO_4 \cdot 2H_2O\text{(s)} \xrightarrow{\Delta} CaSO_4 \cdot \frac{1}{2}H_2O\text{(s)} + 1.5H_2O\text{(g)} \]
Step 3: Detailed Explanation:
• Gypsum is calcium sulphate dihydrate.
• When gypsum is carefully heated to a temperature of \(100^\circ\text{C}\), it loses three-fourths of its water of crystallization to form calcium sulphate hemihydrate, which is Plaster of Paris.
• To convert the temperature from Celsius to Kelvin:
\[ T\text{(K)} = T(^\circ\text{C}) + 273.15 = 100 + 273 = 373\text{ K} \]
• This temperature must be controlled precisely. If gypsum is heated above \(373\text{ K}\) (or \(100^\circ\text{C}\)), it loses all of its water of crystallization to form anhydrous calcium sulphate (\(CaSO_4\)):
\[ CaSO_4 \cdot 2H_2O \xrightarrow{\gt 373\text{ K}} CaSO_4 + 2H_2O \]
- This anhydrous form is called "dead burnt plaster," which does not set or harden when mixed with water, unlike Plaster of Paris.
• Therefore, the optimal heating temperature is \(373\text{ K}\).
Step 4: Final Answer:
Gypsum is heated at 373 K to form Plaster of Paris.