Choose the incorrect formula out of the four compounds for an element X below :

Options

A. `X_(2)Cl_(3)`
B. `X_(2)O_(3)`
C. `X_(2)(SO_(4))_(3)`
D. `XPO_(4)`

Explanation

To solve the question of identifying the incorrect formula for the element X among the provided options, we will analyze each option based on the oxidation states of the elements involved.

### Step-by-Step Solution:

1. **Understand the Concept of Oxidation States**:
- The oxidation state of an element indicates the degree of oxidation (loss of electrons) of that element in a compound. For compounds, the sum of the oxidation states must equal the overall charge of the compound.

2. **Analyze Option 1: X2Cl3**:
- Chlorine (Cl) typically has an oxidation state of -1.
- In X2Cl3, there are 3 chlorine atoms contributing a total oxidation state of \(3 \times (-1) = -3\).
- To balance this, element X must have a total oxidation state of +3.
- Therefore, the oxidation state of X in X2Cl3 is \(+\frac{3}{2} = +1.5\), which is not a common oxidation state for most elements.
- Thus, this formula is incorrect.

3. **Analyze Option 2: X2O3**:
- Oxygen (O) typically has an oxidation state of -2.
- In X2O3, there are 3 oxygen atoms contributing a total oxidation state of \(3 \times (-2) = -6\).
- To balance this, element X must have a total oxidation state of +6, which means each X has an oxidation state of \(+\frac{6}{2} = +3\).
- Therefore, this formula is correct.

4. **Analyze Option 3: X2(SO4)3**:
- The sulfate ion (SO4) has an oxidation state of -2.
- In X2(SO4)3, there are 3 sulfate ions contributing a total oxidation state of \(3 \times (-2) = -6\).
- To balance this, element X must have a total oxidation state of +6, which means each X has an oxidation state of \(+\frac{6}{2} = +3\).
- Therefore, this formula is also correct.

5. **Analyze Option 4: XPO4**:
- The phosphate ion (PO4) has an oxidation state of -3.
- In XPO4, the phosphate contributes -3, so to balance this, element X must have an oxidation state of +3.
- Therefore, this formula is also correct.

### Conclusion:
After analyzing all options, we conclude that the incorrect formula for the element X is **X2Cl3**.