An element X shows +3, oxidation state in its compounds. Out of the four compounds given below, choose the incorrect formula for the element X.

First of all, we are told that the unknown element $$X$$ always exhibits an oxidation state of $$+3$$ in all its compounds.

Whenever we write a stable chemical formula, the algebraic sum of all the charges present in the whole formula must be zero, because a compound as a whole is electrically neutral. That is,

$$\text{(Total positive charge)} + \text{(Total negative charge)} = 0.$$

We shall now test each of the four given formulae one by one, using the above neutrality requirement and the fact that the oxidation state of $$X$$ is $$+3$$.

Option A: $$X_2O_3$$

• Each oxygen atom almost always has the oxidation state $$-2.$$
• There are $$3$$ oxygen atoms, so the total negative charge contributed by oxygen is

$$3 \times (-2) = -6.$$

• Let the oxidation state of each $$X$$ be $$+3$$ (as given). There are $$2$$ atoms of $$X,$$ so their total positive charge is

$$2 \times (+3) = +6.$$

• Adding the two totals gives

$$+6 + (-6) = 0.$$

Since the overall charge is zero, the formula $$X_2O_3$$ is perfectly acceptable for an element having a $$+3$$ state.

Option B: $$X_2(SO_4)_3$$

• The sulphate ion $$SO_4^{2-}$$ possesses a charge of $$-2.$$
• There are $$3$$ sulphate ions, hence the total negative charge from all the sulphate ions equals

$$3 \times (-2) = -6.$$

• Again, each $$X$$ is in the $$+3$$ state, and there are $$2$$ such atoms, so the total positive charge is

$$2 \times (+3) = +6.$$

• Adding the two totals gives

$$+6 + (-6) = 0.$$

The neutrality condition is satisfied, therefore $$X_2(SO_4)_3$$ is also a correct formula for an element with oxidation state $$+3.$$

Option C: $$XPO_4$$

• The phosphate ion $$PO_4^{3-}$$ carries a charge of $$-3.$$
• There is only one phosphate ion present, so the total negative charge is simply $$-3.$$
• The compound contains one atom of $$X,$$ each of which is $$+3,$$ so the total positive charge is $$+3.$$

The sum of the charges is

$$+3 + (-3) = 0,$$

hence the formula $$XPO_4$$ is perfectly compatible with $$X^{3+}.$$

Option D: $$X_2Cl_3$$

• Chlorine (in chloride) has the oxidation state $$-1.$$
• There are $$3$$ chloride ions, so their total negative charge is

$$3 \times (-1) = -3.$$

• Each $$X$$ is still $$+3,$$ and there are $$2$$ such atoms, giving a total positive charge of

$$2 \times (+3) = +6.$$

• Adding the two totals gives

$$+6 + (-3) = +3.$$

This sum is not zero; it equals $$+3,$$ which means the formula $$X_2Cl_3$$ is not electrically neutral. Hence this compound cannot exist if $$X$$ is strictly in the $$+3$$ oxidation state.

All the other three options satisfy charge neutrality, but Option D does not. Hence, the correct answer is Option D.