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JEE Main 2022 · Chemistry · Coordination Compounds · medium

When 0.01 mol of a hydrated chromium(III) chloride of overall composition CrCl3·6H2O is dissolved in water and treated with excess AgNO3, 2.87 g of…

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When 0.010.01 mol of a hydrated chromium(III) chloride of overall composition CrCl3⋅6H2O\mathrm{CrCl_3\cdot6H_2O} is dissolved in water and treated with excess AgNO3\mathrm{AgNO_3}, 2.87 g2.87\ \mathrm g of AgCl (M=143.5M=143.5) precipitates immediately. The formulation of the compound and its spin-only magnetic moment are
  1. A. [CrCl(H2O)5]Cl2⋅H2O\mathrm{[CrCl(H_2O)_5]Cl_2\cdot H_2O}; 3.873.87 BM
  2. B. [CrCl2(H2O)4]Cl⋅2H2O\mathrm{[CrCl_2(H_2O)_4]Cl\cdot2H_2O}; 3.873.87 BM
  3. C. [Cr(H2O)6]Cl3\mathrm{[Cr(H_2O)_6]Cl_3}; 3.873.87 BM
  4. D. [CrCl(H2O)5]Cl2⋅H2O\mathrm{[CrCl(H_2O)_5]Cl_2\cdot H_2O}; 2.832.83 BM
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Answer: (A) [CrCl(H2O)5]Cl2⋅H2O\mathrm{[CrCl(H_2O)_5]Cl_2\cdot H_2O}; 3.873.87 BM

AgCl formed =2.87/143.5=0.020=2.87/143.5=0.020 mol from 0.0100.010 mol of salt, so two chlorides per formula unit are ionisable (outside the coordination sphere) and one is bound to Cr. Thus the complex ion is [CrCl(H2O)5]2+\mathrm{[CrCl(H_2O)_5]^{2+}} with one water of crystallisation: [CrCl(H2O)5]Cl2⋅H2O\mathrm{[CrCl(H_2O)_5]Cl_2\cdot H_2O}. The hexaaqua isomer would give 0.030.03 mol AgCl and the dichloro isomer only 0.010.01 mol. Chromium is +3+3, d3d^3, with three unpaired electrons regardless of ligand field, so μ=3⋅5=3.87\mu=\sqrt{3\cdot5}=3.87 BM.
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