In which of the following cases is the value of x maximum.

Options

A. `CaSO_(4)*xH_(2)O`
B. `BaSO_(4)*xH_(2)O`
C. `MgSO_(4)*xH_(2)O`
D. all have same value of x as all metal ions belong to same group.

Explanation

To determine which of the given hydrated salts has the maximum value of x in the formula \( \text{M}_x\text{H}_2\text{O} \), we will analyze each option step by step.

### Step 1: Identify the Hydrated Salts
We have the following options:
1. Calcium sulphate \( \text{CaSO}_4 \cdot x\text{H}_2\text{O} \)
2. Barium sulphate \( \text{BaSO}_4 \cdot x\text{H}_2\text{O} \)
3. Magnesium sulphate \( \text{MgSO}_4 \cdot x\text{H}_2\text{O} \)

### Step 2: Determine the Water of Crystallization for Each Salt
- **Calcium Sulphate**: The common hydrated form is gypsum, which is \( \text{CaSO}_4 \cdot 2\text{H}_2\text{O} \). Therefore, \( x = 2 \).

- **Barium Sulphate**: This salt is typically not hydrated in common forms, but if we consider \( \text{BaSO}_4 \cdot x\text{H}_2\text{O} \), it is usually taken as having no water of crystallization, so \( x = 0 \).

- **Magnesium Sulphate**: The well-known hydrated form is Epsom salt, which is \( \text{MgSO}_4 \cdot 7\text{H}_2\text{O} \). Thus, \( x = 7 \).

### Step 3: Compare the Values of x
Now we will compare the values of x for the three salts:
- Calcium Sulphate: \( x = 2 \)
- Barium Sulphate: \( x = 0 \)
- Magnesium Sulphate: \( x = 7 \)

### Step 4: Identify the Maximum Value of x
From the values calculated:
- The maximum value of x is from Magnesium Sulphate, which has \( x = 7 \).

### Conclusion
The hydrated salt with the maximum value of x is Magnesium Sulphate \( \text{MgSO}_4 \cdot 7\text{H}_2\text{O} \).

### Final Answer
The answer is **Magnesium Sulphate \( \text{MgSO}_4 \cdot 7\text{H}_2\text{O} \)**.

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