Number of stereoisomers possible for the complexes, $$[CrCl_3(py)_3]$$ and $$[CrCl_2(ox)_2]^{3-}$$ are respectively (py = pyridine, ox = oxalate)

The coordination number of chromium in both complexes is $$6$$, so the expected shape is octahedral.

The complex contains three chloride ions and three pyridine molecules: the general type is $$[MA_3B_3]$$ where $$A = Cl^-$$ and $$B = py$$.

For an octahedral $$[MA_3B_3]$$ species two geometrical arrangements are possible:

1. fac-isomer  (all three identical ligands occupy one face of the octahedron).
2. mer-isomer  (the three identical ligands lie in one meridian plane).

Neither fac nor mer form is chiral because each possesses a mirror plane (fac) or an inversion centre (mer). Hence there is no optical isomerism.

Therefore the number of stereoisomers for $$[CrCl_3(py)_3]$$ is $$2$$.

The coordination sphere has two monodentate $$Cl^-$$ ligands and two identical bidentate $$ox^{2-}$$ ligands. The general formulation can be written as $$[M(LL)_2X_2]$$.

Step 1 - Geometrical isomerism:
  • cis-isomer - the two $$Cl^-$$ ligands are adjacent (angle $$90^\circ$$).
  • trans-isomer - the two $$Cl^-$$ ligands are opposite (angle $$180^\circ$$).

Step 2 - Optical activity:
  • trans-isomer possesses a centre of symmetry, so it is achiral (only one form).
  • cis-isomer has no symmetry element that relates left and right: the two bidentate chelate rings wind around the metal in a helical manner, giving two non-superimposable mirror images (d- and l-forms).

Hence:

trans → 1 stereoisomer
cis → 2 stereoisomers (enantiomeric pair)

Total stereoisomers for $$[CrCl_2(ox)_2]^{3-}$$  = $$1 + 2 = 3$$.

Therefore, the required numbers of stereoisomers are:

$$[CrCl_3(py)_3]$$ : $$2$$   and   $$[CrCl_2(ox)_2]^{3-}$$ : $$3$$.

The correct option is Option C (2 & 3).