Question

The total number of geometrical and optical isomers possible with \([CoCl_2(en)_2]Cl\) are respectively

• A. \(0,\;2\)
• B. \(2,\;0\)
• C. \(2,\;2\)
• D. \(2,\;4\)

Hint:

For octahedral complexes of type \[ [M(en)_2X_2] \]

• cis form \(\rightarrow\) optically active

• trans form \(\rightarrow\) optically inactive
Therefore: \[ 2 \text{ geometrical isomers} \] and \[ 2 \text{ optical isomers} \]

Answer 1

The Correct Option is C

Step 1: Identify the complex.
The cation is $[CoCl_2(en)_2]^+$, an octahedral complex with two bidentate $en$ ligands and two chloride ligands.

Step 2: Count geometrical isomers.
For the $[M(en)_2X_2]$ type, the two chlorides can sit next to each other (cis) or opposite (trans). That gives $2$ geometrical isomers.

Step 3: Test the trans form for optical activity.
The trans isomer has a plane of symmetry, so it is superimposable on its mirror image and is optically inactive.

Step 4: Test the cis form.
The cis isomer has no plane of symmetry, so it is chiral and exists as a pair of mirror images (d and l).

Step 5: Count optical isomers.
Only the cis form is optically active, and it gives $2$ optical isomers.

Step 6: State the totals.
Geometrical isomers $= 2$ and optical isomers $= 2$.
\[ \boxed{2,\ 2} \]