The `I_(1),I_(2),I_(3),I_(4)` values of an element "M" are 120 kJ/mole, `600 kJ//"mole", 1000 kJ//"mole"` and `8000 kJ//"mole"`. Then the formula of its sulphate is

Options

A. `MSO_(4)`
B. `M_(2)(SO_(4))_(3)`
C. `M_(2)SO_(4)`
D. `M_(3)(SO_(4))_(2)`

Answer

To determine the formula of the sulfate of element "M" based on the given ionization energies (I1, I2, I3, I4), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ionization Energies**:
- The ionization energies provided are:
- I1 = 120 kJ/mole
- I2 = 600 kJ/mole
- I3 = 1000 kJ/mole
- I4 = 8000 kJ/mole

2. **Analyze the Ionization Energies**:
- The significant increase in energy from I3 (1000 kJ/mole) to I4 (8000 kJ/mole) indicates that removing the fourth electron requires a much larger amount of energy compared to the first three electrons. This suggests that the first three electrons can be removed relatively easily.

3. **Determine the Charge of the Ion**:
- Since the first three ionization energies are relatively low compared to the fourth, we can conclude that the element "M" can lose 3 electrons to form a stable ion. Therefore, the charge of the ion formed by "M" will be +3 (M^3+).

4. **Identify the Charge of the Sulfate Ion**:
- The sulfate ion (SO4) has a charge of -2 (SO4^2-).

5. **Combine the Charges to Form the Compound**:
- To balance the charges in the compound formed between M^3+ and SO4^2-, we need to determine the ratio of M to SO4.
- The least common multiple of the charges (3 and 2) is 6. Therefore, we need:
- 2 sulfate ions (2 × -2 = -4)
- 3 M ions (3 × +3 = +9)
- This means we need 3 M^3+ ions to balance with 2 SO4^2- ions.

6. **Write the Formula**:
- The formula for the compound will be M2(SO4)3, indicating that for every 2 M ions, there are 3 sulfate ions.

### Final Answer:
The formula of the sulfate of element "M" is **M2(SO4)3**.