Question

Determine the values of X, Y and Z for the following complexes and calculate the sum X + Y + Z.
X = number of geometrical isomers of [Pt(NH$_3$)(Cl)(Br)(Py)]
Y = Number of optically inactive isomers of [Cr(en)$_2$Cl$_2$]$^{+1$}
Z = Number of stereoisomers of [Co(NH$_3$)$_3$(NO$_3$)$_3$]

Hint:

Standard count: M(AA)2b2 has 2 GI (cis/trans), 3 Stereoisomers (cis-d, cis-l, trans). Only Trans is inactive.

Answer 1

Correct Answer: 6

X: $[\text{Mabcd}]$ Square Planar. Isomers are 3. (Fix a, relative positions of b, c, d give 3 distinct arrangements).
Y: $[\text{Cr}(\text{en})_2\text{Cl}_2]^+$. Geometrical isomers are Cis and Trans.
Cis form is chiral (Optically Active).
Trans form has a plane of symmetry (Optically Inactive).
Number of optically inactive isomers = 1 (Trans).
Z: $[\text{Co}(\text{NH}_3)_3(\text{NO}_3)_3]$. Type $[\text{Ma}_3\text{b}_3]$.
Isomers are Facial (Fac) and Meridional (Mer). Both have planes of symmetry and are achiral.
Total stereoisomers = 2.
Sum $X + Y + Z = 3 + 1 + 2 = 6$.