(a) Cis-1,2-cylopentanediol reacts with acetone in the presence of dry HCl to yield compound K, `C_(8)H_(14)O_2`, which is resistant to boiling alkali, but which readily forms the starting material by aqueous acids. What is structure of K ?
(b) Trans-1,2-Cyclopentanediol does not form an analogous compound. explain why.

Answer

### Step-by-Step Solution:

#### (a) Structure of Compound K

1. **Understanding the Reactants**:
- We have cis-1,2-cyclopentanediol and acetone. The formula for cis-1,2-cyclopentanediol is C5H10O2, and for acetone, it is C3H6O.
- The overall reaction will yield a compound K with the formula C8H14O2.

2. **Reaction Mechanism**:
- The reaction occurs in the presence of dry HCl, which acts as a catalyst. HCl provides protons (H⁺) that activate the hydroxyl (OH) groups of the diol.
- The hydroxyl group of cis-1,2-cyclopentanediol can attack the carbonyl carbon of acetone, leading to the formation of an acetal.

3. **Formation of Compound K**:
- The cis-1,2-cyclopentanediol has both hydroxyl groups in a position that allows them to interact with the carbonyl of acetone.
- The reaction leads to the formation of a cyclic acetal, where the two hydroxyl groups from the diol form bonds with the carbonyl carbon of acetone.
- The resulting structure of compound K is a cyclic acetal, which is stable and has the formula C8H14O2.

4. **Properties of Compound K**:
- Compound K is resistant to boiling alkali, indicating that it is stable under basic conditions.
- However, it can be hydrolyzed back to the starting materials (cis-1,2-cyclopentanediol and acetone) in the presence of aqueous acids, which is characteristic of acetals.

5. **Final Structure**:
- The structure of compound K can be represented as follows:
```
O
/ \
C C
/ \
C C
| |
C C
\ /
C---C
```

#### (b) Why Trans-1,2-Cyclopentanediol Does Not Form an Analogous Compound

1. **Understanding the Structure of Trans-1,2-Cyclopentanediol**:
- In trans-1,2-cyclopentanediol, the two hydroxyl groups are positioned such that one is axial and the other is equatorial in the chair conformation.
- This spatial arrangement creates steric hindrance and prevents effective overlap with the carbonyl group of acetone.

2. **Lack of Reactivity**:
- The axial hydroxyl group in trans-1,2-cyclopentanediol cannot effectively approach the carbonyl carbon of acetone due to steric hindrance.
- Because of this, the trans isomer cannot undergo the acetal formation reaction that occurs with the cis isomer.

3. **Conclusion**:
- Therefore, trans-1,2-cyclopentanediol does not form an analogous compound because the spatial arrangement of the hydroxyl groups prevents the necessary interaction with the carbonyl group of acetone.