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JEE Advanced 2023 Paper 2 · Chemistry · Coordination Compounds · hard

Let x be the total number of stereoisomers of the octahedral complex [Co(gly)3] (where gly^-=NH2CH2COO^- binds through N and O as an unsymmetrical…

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Let xx be the total number of stereoisomers of the octahedral complex [Co(gly)3]\mathrm{[Co(gly)_3]} (where gly−=NH2CH2COO−\mathrm{gly^-}=\mathrm{NH_2CH_2COO^-} binds through N and O as an unsymmetrical bidentate ligand) and yy the number of geometrical isomers of the square planar complex [Pt(NH3)(py)ClBr]\mathrm{[Pt(NH_3)(py)ClBr]} (py = pyridine). Find x+yx+y.
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Answer: 7

For [Co(gly)3]\mathrm{[Co(gly)_3]}, a chelate M(AB)3\mathrm{M(AB)_3}, the three N atoms may be arranged facially (fac, all three N mutually cis) or meridionally (mer). Each of fac and mer lacks a mirror plane and is chiral (a propeller-like Δ/Λ\Delta/\Lambda pair), giving 2×2=42\times2=4 stereoisomers, so x=4x=4. For the square planar complex of type Mabcd\mathrm{Mabcd}, fix one ligand, say NH3\mathrm{NH_3}, and place the three others opposite it: the trans partner of NH3\mathrm{NH_3} may be py, Cl or Br, giving y=3y=3 geometrical isomers (square planar complexes of this type are not chiral because the molecular plane is a mirror plane). Both counts were confirmed by enumerating all labelled arrangements modulo the rotation group of the octahedron (24 rotations, with chelate pairs required to be cis), which gave 4, and modulo the symmetry operations of the square plane, which gave 3. Hence x+y=4+3=7x+y=4+3=7.
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