Complex X of composition Cr(H₂O)₆Clₙ has a spin only magnetic moment of 3.83 BM. It reacts with AgNO₃ and shows geometrical isomerism. The IUPAC nomenclature of X is :

Solution

Chemistry ma’am · 4 steps

Let the magnetic moment fix chromium's oxidation state, then let isomerism pick which hydrate isomer X is.

1. Unpaired electrons. Use μ = √n(n+2) BM. With n = 3, μ = √15 ≈ 3.87 BM, which matches 3.83 BM. So chromium has 3 unpaired electrons.
2. Oxidation state. Three unpaired electrons means d³, which is Cr³⁺. Water is neutral, so the formula needs three chlorides, n = 3, and the composition is CrCl₃.6H₂O.

   Possible formula of X	Reacts with AgNO₃?	Geometrical isomerism?
   [Cr(H₂O)₆]Cl₃	yes, 3 ionic Cl⁻	no, all six ligands are the same
   [Cr(H₂O)₅Cl]Cl₂.H₂O	yes, 2 ionic Cl⁻	no, an MA₅B complex has only one arrangement
   [Cr(H₂O)₄Cl₂]Cl.2H₂O	yes, 1 ionic Cl⁻	yes, MA₄B₂ has cis and trans forms

3. Naming it. List ligands in alphabetical order, so aqua comes before chlorido. Then give the metal with its oxidation state, the counter ion, and the water of crystallisation.
4. So. X is [Cr(H₂O)₄Cl₂]Cl.2H₂O, named tetraaquadichloridochromium(III) chloride dihydrate, which is option (c).

The idea to keep. In such questions, the magnetic moment gives the unpaired electrons and so the oxidation state. Then use isomerism or the AgNO₃ test to decide which ligands sit inside the bracket.

Answer from the NTA final answer key. Solution by PrepWiser.