What is the formula of the complex tris(ethylene diamine) chromium (III) sulphate?

[Cr(en)₃]₂(SO₄)₃

The correct answer is option 4. \([Cr(en)_3]_2(SO_4)_3\).

Let us break it down step by step:

Chromium (III) ion \((Cr^{3+})\): This part indicates that the central metal ion in the complex is chromium in the +3 oxidation state, meaning it has lost three electrons to achieve a stable configuration.

Tris(ethylene diamine): The term "tris" indicates that there are three ethylene diamine ligands, denoted as (en), coordinated to the chromium ion. Ethylene diamine (en) is a bidentate ligand, meaning it can donate two lone pairs of electrons to the metal ion.

Sulphate ion \((SO_4^{2-})\): This indicates the presence of sulfate ions in the compound. Each sulfate ion has a charge of -2.

The coordination complex formed between chromium (III) and ethylene diamine ligands carries a net positive charge due to the positive charge of the chromium ion and the neutral nature of the ethylene diamine ligands. To balance this positive charge, sulfate ions are required, as they carry a negative charge.

Since each sulfate ion has a charge of -2 and we need to balance the overall charge of the complex, which is +3, we need three sulfate ions to balance it out. This ensures that the overall charge of the compound remains neutral.

Therefore, the correct formula for the compound is \([Cr(en)_3]_2(SO_4)_3\), indicating that there are two tris(ethylene diamine) chromium (III) complex ions for every three sulfate ions.