The formula of calcium sulphate hemihydrate is

Options

A. `CaSO_4 . 2H_2O `
B. `CaSO_4 . 3/2 H_2O`
C. `CaSO_4 . H_2O`
D. `2CaSO_4 . H_2O`

Explanation

To determine the formula of calcium sulfate hemihydrate, we can follow these steps:

### Step 1: Understand the Components
Calcium sulfate is a chemical compound composed of calcium (Ca), sulfur (S), and oxygen (O). The hemihydrate form indicates that there is one half of a water molecule associated with each formula unit of calcium sulfate.

### Step 2: Write the Basic Formula
The basic formula for calcium sulfate is \( \text{CaSO}_4 \).

### Step 3: Add the Water Component
Since it is a hemihydrate, we need to add the water component. The term "hemihydrate" implies that for every one formula unit of calcium sulfate, there is half a water molecule. This can be represented as \( \frac{1}{2} \text{H}_2\text{O} \).

### Step 4: Combine the Components
Thus, the complete formula for calcium sulfate hemihydrate can be written as:
\[ \text{CaSO}_4 \cdot \frac{1}{2} \text{H}_2\text{O} \]
However, it is more commonly expressed in a different form, which is:
\[ \text{CaSO}_4 \cdot 0.5 \text{H}_2\text{O} \]
or equivalently:
\[ \text{CaSO}_4 \cdot 5 \text{H}_2\text{O} \]

### Step 5: Finalize the Formula
The final formula for calcium sulfate hemihydrate is:
\[ \text{CaSO}_4 \cdot 0.5 \text{H}_2\text{O} \]
This is often referred to as Plaster of Paris (POP).

### Conclusion
The correct answer is:
\[ \text{CaSO}_4 \cdot 0.5 \text{H}_2\text{O} \]

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