Which of the following will show optical activity?

Options

A. `Cis-[Co(NH_(3))_(2)(en)_(2)]^(3+)`
B. `Trans-[Co(NH_(3))_(2)(en)_(2)]^(3+)`
C. `[Co(NH_(3))_(6)]^(3+)`
D. `Trans-[Co(H_(2)O)_(4)CI_(2)]^(+)`

Answer

To determine which of the given compounds shows optical activity, we need to analyze each compound based on its symmetry. Optical activity is exhibited by compounds that lack a plane of symmetry. Here’s a step-by-step solution:

### Step 1: Identify the Coordination Numbers
- **Cobalt Complexes**: All the given complexes are octahedral, which means they have a coordination number of 6. This is confirmed as follows:
- Monodentate ligands (like NH3) contribute 1 bond each.
- Bidentate ligands (like ethylenediamine, EN) contribute 2 bonds each.

### Step 2: Draw the Structures
- **First Compound**: Cobalt with 2 ethylenediamine (EN) and 4 NH3 ligands.
- **Cis Configuration**: The two EN ligands are on the same side.
- **Symmetry Check**: There is no plane of symmetry in this arrangement, indicating that it is optically active.

- **Second Compound**: Cobalt with 2 EN and 4 NH3 ligands in a **Trans Configuration**.
- **Trans Configuration**: The two EN ligands are on opposite sides.
- **Symmetry Check**: This arrangement has a plane of symmetry (NH3 ligands are symmetrical about the central plane), making it optically inactive.

- **Third Compound**: Cobalt with 6 NH3 ligands.
- **Symmetry Check**: All ligands are identical, leading to multiple planes of symmetry. Thus, it is optically inactive.

- **Fourth Compound**: Cobalt with 2 Cl and 4 H2O ligands in a **Trans Configuration**.
- **Symmetry Check**: Similar to the second compound, this arrangement has a plane of symmetry due to the arrangement of Cl and H2O ligands, making it optically inactive.

### Step 3: Conclusion
Only the first compound, with the cis configuration of ethylenediamine and NH3, lacks symmetry and is therefore optically active.

### Final Answer
**The first compound is the only one that shows optical activity.**

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