How many stereoisomers of the following molecule are possible? `HOOC-CH= C= CH-COOH`

Options

A. Two optical isomers
B. Two geometrical isomers
C. Two optical & two geometrical isomers
D. None

Answer

To determine the number of stereoisomers for the molecule `HOOC-CH= C= CH-COOH`, we need to analyze its structure and identify the presence of stereocenters and the possibility of geometrical isomerism.

### Step 1: Identify the Structure
The molecule can be represented as follows:
- It has two carboxylic acid groups (-COOH) at both ends.
- It contains a chain of carbon atoms with double bonds (C=C).

### Step 2: Identify Stereocenters
A stereocenter is a carbon atom that is bonded to four different groups. In this molecule:
- The carbon atoms involved in the double bonds (C=C) do not qualify as stereocenters because they do not have four different substituents.
- However, the carbon atoms adjacent to the double bonds can have different groups attached to them, leading to the possibility of stereoisomerism.

### Step 3: Consider Geometrical Isomerism
Geometrical isomers occur due to restricted rotation around double bonds. In this molecule:
- The presence of the double bonds means we can have cis/trans (E/Z) isomerism.
- The two double bonds in the molecule allow for the formation of geometrical isomers.

### Step 4: Determine Optical Isomers
Optical isomers arise when there is no plane of symmetry in the molecule.
- The presence of the two carboxylic acid groups at the ends and the arrangement of the substituents around the double bonds means that the molecule can exist in two non-superimposable mirror images (enantiomers).

### Step 5: Count the Stereoisomers
1. **Geometrical Isomers**: The two double bonds can lead to different configurations (cis/trans).
2. **Optical Isomers**: Each configuration can have two enantiomers due to the lack of a plane of symmetry.

Thus, for the two double bonds, we can have:
- **2 geometrical isomers** (E/Z configurations).
- Each geometrical isomer can have **2 optical isomers**.

### Final Calculation:
Total stereoisomers = Number of geometrical isomers × Number of optical isomers per geometrical isomer
= 2 (geometrical) × 2 (optical) = 4 stereoisomers.

### Conclusion:
The total number of stereoisomers for the molecule `HOOC-CH= C= CH-COOH` is **4**.

---