Which of the following will show optical isomers?
(I) cis-`[Co(NH_(3))_(2)(en)_(2)]^(3+)`
(II) trans-`[IrCl_(2)(C_(2)O_(4))_(2)]^(3-)`
(III) `[Rh(en)_(3)]^(3+)`
(IV) cis-`[IR(H_(2)O)_(3)Cl_(3)]`

Options

A. I, III only correct
B. II, IV only correct
C. I, III, IV only correct
D. III only correct

Answer

To determine which of the given coordination compounds show optical isomers, we need to analyze each compound for the presence of chirality. A compound is chiral if it does not have a plane of symmetry and its mirror image is non-superimposable on itself.

### Step-by-step Solution:

1. **Analyzing Compound I: cis-`[Co(NH3)2(en)2]^(3+)`**
- The structure consists of a cobalt ion coordinated with two ammonia (NH3) ligands and two ethylenediamine (en) ligands.
- The cis configuration means that the two NH3 ligands are adjacent to each other, while the two bidentate en ligands occupy the remaining coordination sites.
- When we draw the mirror image of this compound, it will be non-superimposable due to the arrangement of the ligands.
- **Conclusion**: This compound shows optical isomerism.

2. **Analyzing Compound II: trans-`[IrCl2(C2O4)2]^(3-)`**
- In this case, the iridium ion is coordinated with two chloride (Cl) ligands and two oxalate (C2O4) ligands in a trans configuration.
- The trans arrangement means that the two Cl ligands are opposite each other, leading to a plane of symmetry.
- When we draw the mirror image, it will be superimposable on the original structure.
- **Conclusion**: This compound does not show optical isomerism.

3. **Analyzing Compound III: `[Rh(en)3]^(3+)`**
- Here, rhodium is coordinated with three ethylenediamine (en) ligands.
- The arrangement of three bidentate ligands creates a situation where there is no plane of symmetry.
- The mirror image of this compound will also be non-superimposable.
- **Conclusion**: This compound shows optical isomerism.

4. **Analyzing Compound IV: cis-`[Ir(H2O)3Cl3]`**
- This compound has iridium coordinated with three water (H2O) ligands and three chloride (Cl) ligands in a cis configuration.
- The arrangement leads to a structure that does not have a plane of symmetry.
- The mirror image will be non-superimposable.
- **Conclusion**: This compound shows optical isomerism.

### Final Answer:
The compounds that show optical isomers are:
- (I) cis-`[Co(NH3)2(en)2]^(3+)`
- (III) `[Rh(en)3]^(3+)`
- (IV) cis-`[Ir(H2O)3Cl3]`