The formula of a metal sulphate is `M_2(SO_4)_3` the formula of its phosphate will be

Options

A. `M_2(PO_4)_3`
B. `M_3(PO_4)_2`
C. `MPO_4`
D. `M_2PO_4`

Explanation

To determine the formula of the phosphate of a metal whose sulfate is given as \( M_2(SO_4)_3 \), we can follow these steps:

### Step 1: Analyze the given sulfate formula
The formula of the metal sulfate is \( M_2(SO_4)_3 \). This indicates that there are 2 metal ions (M) for every 3 sulfate ions (\( SO_4^{2-} \)).

### Step 2: Determine the valence of the metal
From the sulfate formula, we can deduce the valence of the metal (M). Since the sulfate ion has a charge of -2 and there are 3 sulfate ions, the total negative charge contributed by the sulfate ions is:
\[ 3 \times (-2) = -6 \]
To balance this, the total positive charge from the metal ions must be +6. Since there are 2 metal ions, the charge of each metal ion must be:
\[ \frac{+6}{2} = +3 \]
Thus, the valence of the metal (M) is +3.

### Step 3: Write the formula for the phosphate
The phosphate ion (\( PO_4^{3-} \)) has a charge of -3. To find the formula of the metal phosphate, we need to balance the charges between the metal and the phosphate.

### Step 4: Combine the metal and phosphate
Since the metal has a valence of +3 and the phosphate has a valence of -3, they can combine in a 1:1 ratio. Therefore, the formula for the metal phosphate will be:
\[ MPO_4 \]

### Final Answer
The formula of the phosphate of the metal is \( MPO_4 \).

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