X' is a smallest optically active alkanol. On dehydration it can form Y number of alkenes (including stereoisomers). On reaction with Lucas reagent it forms Z number of alkyl halides (including stereoisomers). Report your answer as ZY.

Answer

To solve the question, we need to identify the smallest optically active alkanol, determine how many alkenes it can form upon dehydration, and how many alkyl halides it can form when reacted with Lucas reagent.

### Step-by-Step Solution:

1. **Identify the Smallest Optically Active Alkanol (X):**
- The smallest optically active alkanol is **butan-2-ol** (C4H10O).
- Its structure is:
\[ \text{CH}_3 - \text{CH(OH)} - \text{CH}_2 - \text{CH}_3 \]
- In this structure, the carbon atom with the hydroxyl group (OH) is attached to four different groups, making it chiral and thus optically active.

2. **Determine the Number of Alkenes Formed on Dehydration (Y):**
- When butan-2-ol undergoes dehydration (removal of water), it can form alkenes. The dehydration reaction typically involves heating with sulfuric acid (H2SO4).
- The possible alkenes formed are:
- **But-2-ene** (C4H8), which can exist as:
- **Cis-but-2-ene**
- **Trans-but-2-ene**
- **But-1-ene** (C4H8), which does not have stereoisomers.
- Therefore, the total number of alkenes (including stereoisomers) is:
- 2 (from but-2-ene) + 1 (from but-1-ene) = **3 alkenes**.

3. **Determine the Number of Alkyl Halides Formed with Lucas Reagent (Z):**
- When butan-2-ol reacts with Lucas reagent (ZnCl2 and HCl), it undergoes a substitution reaction where the hydroxyl group (OH) is replaced by a chlorine atom (Cl).
- The product formed is:
- **2-chlorobutane** (C4H9Cl).
- The carbon with the chlorine atom is also chiral, leading to two enantiomers:
- **(R)-2-chlorobutane**
- **(S)-2-chlorobutane**
- Therefore, the total number of alkyl halides formed is **2**.

4. **Combine the Results to Report ZY:**
- From the above calculations, we have:
- Y (number of alkenes) = 3
- Z (number of alkyl halides) = 2
- The final answer is reported as ZY = **2** (Z) **3** (Y) = **23**.

### Final Answer:
**23**