If the phosphate of a metal has the formula `MPO_(4)` the formula of the metallic sulphate is _____________

Answer

To determine the formula of the metallic sulfate given that the phosphate of a metal has the formula \( MPO_4 \), we can follow these steps:

### Step 1: Identify the charge of the metal
From the formula \( MPO_4 \), we know that the phosphate ion \( PO_4^{3-} \) has a charge of -3. Since the compound is neutral, the metal \( M \) must have a charge of +3 to balance the -3 charge of the phosphate ion. Therefore, we can conclude that:
- Charge of metal \( M = +3 \)

### Step 2: Determine the charge of the sulfate ion
The sulfate ion \( SO_4^{2-} \) has a charge of -2.

### Step 3: Use the charges to find the formula of the metallic sulfate
Now, we need to combine the metal \( M \) with the sulfate ion \( SO_4^{2-} \). We have:
- Charge of \( M = +3 \)
- Charge of \( SO_4 = -2 \)

To find the formula of the metallic sulfate, we can use the method of cross-multiplication:
- The number of sulfate ions needed to balance the +3 charge of the metal can be calculated as follows:
- The least common multiple (LCM) of the charges (3 and 2) is 6.
- Therefore, we need 2 sulfate ions (each with a charge of -2) to balance the +3 charge from the metal.

### Step 4: Write the formula
To balance the charges:
- We need 3 metal ions \( M^{3+} \) to balance 2 sulfate ions \( SO_4^{2-} \).
- Therefore, the formula for the metallic sulfate will be \( M_2(SO_4)_3 \).

### Final Answer:
The formula of the metallic sulfate is \( M_2(SO_4)_3 \).

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