The increasing order of the boiling points for the following compound is :
`underset((I))(C_(2)H_(5))OH " " underset((II))(C_(2)H_(5))Cl " " underset((III))(C_(2)H_(5))CH_(3) " " underset((IV))(C_(2)H_(5))OCH_(3)`

Options

A. `(III)lt(IV)lt(II)lt(I)`
B. `(IV)lt(III)lt(I)lt(II)`
C. `(II)lt(II)lt(IV)lt(I)`
D. `(III)lt(II)lt(I)lt(IV)`

Answer

To determine the increasing order of boiling points for the given compounds, we need to analyze the types of intermolecular forces present in each compound. The compounds given are:

1. (I) Ethanol, \( C_2H_5OH \)
2. (II) Ethyl chloride, \( C_2H_5Cl \)
3. (III) Ethane, \( C_2H_6 \)
4. (IV) Ethyl methyl ether, \( C_2H_5OCH_3 \)

### Step-by-Step Solution:

**Step 1: Identify the types of intermolecular forces in each compound.**

- **Ethanol (I)**: Ethanol can form hydrogen bonds due to the presence of the -OH group. Hydrogen bonding is a strong intermolecular force, which leads to a higher boiling point.

- **Ethyl chloride (II)**: Ethyl chloride has dipole-dipole interactions due to the electronegativity difference between carbon and chlorine. This results in a moderate boiling point.

- **Ethane (III)**: Ethane is a non-polar molecule and primarily exhibits London dispersion forces (weakest type of intermolecular force). Therefore, it has the lowest boiling point among the given compounds.

- **Ethyl methyl ether (IV)**: Ethyl methyl ether can also form hydrogen bonds, but they are weaker than those in ethanol because it lacks an -OH group. It has a moderate boiling point, likely higher than ethyl chloride but lower than ethanol.

**Step 2: Compare the boiling points based on the strength of intermolecular forces.**

- Ethanol (I) has the highest boiling point due to strong hydrogen bonding.
- Ethyl methyl ether (IV) has a lower boiling point than ethanol but higher than ethyl chloride due to weaker hydrogen bonding.
- Ethyl chloride (II) has a boiling point lower than ethyl methyl ether due to dipole-dipole interactions.
- Ethane (III) has the lowest boiling point due to weak London dispersion forces.

**Step 3: Arrange the compounds in increasing order of boiling points.**

Based on the analysis, the increasing order of boiling points is:

**(III) Ethane < (II) Ethyl chloride < (IV) Ethyl methyl ether < (I) Ethanol**

### Final Answer:
The increasing order of the boiling points for the compounds is:
**(III) < (II) < (IV) < (I)**