Arrange the following in order of increase/decrease in boiling point,
`underset(I)(CH_3CH_2CH_2CH_2CH_3),underset(II)((CH_3)_2CHCH_2CH_3),underset(III)((CH_3)_4C)`
Which of the folllowing is/are correct?

Options

A. `I gt II gt III`
B. `II gt I gt III`
C. `III gt I gt II`
D. `III lt II lt I`

Answer

To determine the order of boiling points for the given hydrocarbons, we need to analyze their structures and how they affect boiling point based on molecular interactions, particularly van der Waals forces.

### Step-by-Step Solution:

1. **Identify the Compounds**:
- (I) Pentane: \( CH_3CH_2CH_2CH_2CH_3 \)
- (II) 2-Methylbutane: \( (CH_3)_2CHCH_2CH_3 \)
- (III) 2,2-Dimethylpropane: \( (CH_3)_4C \)

2. **Understand Boiling Points**:
- Boiling points are influenced by the strength of intermolecular forces. In hydrocarbons, van der Waals forces (dispersion forces) play a significant role.
- The strength of these forces is generally greater in straight-chain alkanes compared to branched alkanes because straight-chain alkanes have a larger surface area for intermolecular interactions.

3. **Analyze Each Compound**:
- **Pentane (I)**: This is a straight-chain alkane with five carbon atoms. It has the highest surface area among the three compounds, leading to stronger van der Waals forces.
- **2-Methylbutane (II)**: This compound is branched, which reduces its surface area compared to pentane. Therefore, it has a lower boiling point than pentane.
- **2,2-Dimethylpropane (III)**: This is more branched than 2-methylbutane, resulting in an even smaller surface area and weaker van der Waals forces, leading to the lowest boiling point among the three.

4. **Order of Boiling Points**:
- Based on the analysis:
- Pentane (I) has the highest boiling point.
- 2-Methylbutane (II) has a lower boiling point than pentane but higher than 2,2-dimethylpropane.
- 2,2-Dimethylpropane (III) has the lowest boiling point.
- Therefore, the order of boiling points from highest to lowest is:
\[ I > II > III \]

5. **Conclusion**:
- The correct answer for the order of boiling points is:
- Option A: \( I > II > III \)
- Option D: \( I > II > III \)