How many alcohols from the following set will yield geometric isomers on dehydration?
Propan -2- ol, 2 - methylpropan -1-ol, pentan -2- ol, ethanol, propan -1- ol, 2- methylpropan -2- ol, butan -1- ol, butan -2- ol, hexan -3- ol

Answer

To determine how many alcohols from the given set yield geometric isomers upon dehydration, we need to analyze each alcohol and see if the dehydration reaction can produce alkenes with different substituents on either side of the double bond. Geometric isomers (cis/trans or E/Z isomers) occur when there are different groups attached to the carbon atoms involved in the double bond.

### Step-by-Step Solution:

1. **Identify the Alcohols**: The alcohols given are:
- Propan-2-ol
- 2-methylpropan-1-ol
- Pentan-2-ol
- Ethanol
- Propan-1-ol
- 2-methylpropan-2-ol
- Butan-1-ol
- Butan-2-ol
- Hexan-3-ol

2. **Analyze Each Alcohol for Dehydration**:
- **Propan-2-ol**:
- Structure: CH3-CHOH-CH3
- Upon dehydration, it forms propene (CH3-CH=CH2), which does not have different groups on the double bond. **No geometric isomers**.
- **2-methylpropan-1-ol**:
- Structure: (CH3)2-CHOH-CH2
- Dehydration leads to isobutylene (CH2=C(CH3)2), which has identical groups on one carbon. **No geometric isomers**.
- **Pentan-2-ol**:
- Structure: CH3-CHOH-CH2-CH2-CH3
- Dehydration can yield 2-pentene, which has different groups on the double bond. **Geometric isomers possible** (cis/trans).
- **Ethanol**:
- Structure: CH3-CH2OH
- Dehydration yields ethene (CH2=CH2), which has identical groups. **No geometric isomers**.
- **Propan-1-ol**:
- Structure: CH3-CH2-CHOH
- Dehydration yields propene (CH2=CH-CH3), which does not have different groups. **No geometric isomers**.
- **2-methylpropan-2-ol**:
- Structure: (CH3)3COH
- Dehydration yields no double bond as all groups are identical. **No geometric isomers**.
- **Butan-1-ol**:
- Structure: CH3-CH2-CH2-CHOH
- Dehydration yields butene (CH2=CH-CH2-CH3), which does not have different groups. **No geometric isomers**.
- **Butan-2-ol**:
- Structure: CH3-CHOH-CH2-CH3
- Dehydration can yield 2-butene, which has different groups on the double bond. **Geometric isomers possible** (cis/trans).
- **Hexan-3-ol**:
- Structure: CH3-CH2-CHOH-CH2-CH2-CH3
- Dehydration can yield 3-hexene, which has different groups on the double bond. **Geometric isomers possible** (cis/trans).

3. **Count the Alcohols Yielding Geometric Isomers**:
- From the analysis, the alcohols that yield geometric isomers upon dehydration are:
- Pentan-2-ol
- Butan-2-ol
- Hexan-3-ol

### Final Answer:
**Total number of alcohols that yield geometric isomers upon dehydration: 3**