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 alkanes, we will analyze the three compounds based on their structure and the factors affecting boiling points.

### Given Compounds:
1. **(I)** Pentane: \( CH_3CH_2CH_2CH_2CH_3 \) (5 carbon straight chain)
2. **(II)** 2-Methylbutane: \( (CH_3)_2CHCH_2CH_3 \) (branched structure with 5 carbons)
3. **(III)** 2,2-Dimethylpropane: \( (CH_3)_4C \) (highly branched structure with 5 carbons)

### Step-by-Step Analysis:

1. **Identify the Structure and Surface Area**:
- **Pentane (I)**: This is a straight-chain alkane with a larger surface area compared to the branched ones.
- **2-Methylbutane (II)**: This is a branched alkane, which reduces the surface area compared to pentane.
- **2,2-Dimethylpropane (III)**: This is the most branched structure, having the least surface area among the three.

2. **Understanding Boiling Point Trends**:
- Boiling points of alkanes generally increase with increasing molecular weight and surface area due to stronger Van der Waals forces.
- Branched alkanes tend to have lower boiling points than their straight-chain isomers because branching decreases the surface area available for intermolecular interactions.

3. **Comparing the Boiling Points**:
- **Pentane (I)** will have the highest boiling point due to its straight-chain structure and larger surface area.
- **2-Methylbutane (II)** will have a lower boiling point than pentane but higher than 2,2-dimethylpropane due to its moderate branching.
- **2,2-Dimethylpropane (III)** will have the lowest boiling point because it is the most branched and has the smallest surface area.

### Conclusion:
Based on the analysis, we can arrange the compounds in order of increasing boiling point as follows:
- **Increasing Order**: \( (III) < (II) < (I) \)
- **Decreasing Order**: \( (I) > (II) > (III) \)

### Final Answer:
- Increasing Order: **(III) < (II) < (I)**
- Decreasing Order: **(I) > (II) > (III)**