Sulphate of a divalent metal M exists in hydrated form. If `0.10` mol of metal sulphate combines with `9.0` g of water to form the hydrated salt then, the formula of metal sulphate will be

Options

A. `MSO_4. H_2O`
B. `M_2SO_4 . 2H_2O`
C. `M_2SO_4 . 3H_2O`
D. `MSO_4 . 5H_2O`

Explanation

To determine the formula of the metal sulfate in its hydrated form, we can follow these steps:

### Step 1: Identify the formula of the metal sulfate
Since the metal (M) is divalent, it has a charge of +2. The sulfate ion (SO₄) has a charge of -2. Therefore, the formula for the metal sulfate will be:
\[ \text{M}SO_4 \]

### Step 2: Determine the amount of water in moles
We are given that 9.0 g of water combines with 0.10 mol of metal sulfate. To find the number of moles of water, we use the molar mass of water (H₂O), which is approximately 18 g/mol:
\[ \text{Moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}} = \frac{9.0 \, \text{g}}{18 \, \text{g/mol}} = 0.5 \, \text{mol} \]

### Step 3: Relate the moles of metal sulfate to moles of water
We have 0.10 mol of metal sulfate (M SO₄) combining with 0.5 mol of water. To find out how many moles of water combine with 1 mole of metal sulfate, we set up a ratio:
\[ \text{If } 0.10 \, \text{mol of M SO}_4 \text{ combines with } 0.5 \, \text{mol of H}_2O, \]
then for 1 mole of M SO₄:
\[ \text{Moles of water} = \frac{0.5 \, \text{mol}}{0.10 \, \text{mol}} = 5 \, \text{mol} \]

### Step 4: Write the formula of the hydrated salt
Since 1 mole of metal sulfate combines with 5 moles of water, the formula for the hydrated metal sulfate can be written as:
\[ \text{M}SO_4 \cdot 5 \text{H}_2O \]

### Conclusion
Thus, the formula of the metal sulfate in its hydrated form is:
\[ \text{M}SO_4 \cdot 5 \text{H}_2O \]