Polar covalent molecules exhibit dipole moment. Dipole moment is equal to the product of charge separation , q and the bond length d for the bond. Unit of dipole moment is debye. One debye is equal to `10^(-18)` esu cm.
Dipole moments is a vector quantity. It has both magnitude and direction. Hence, dipole moment of a molecule depends upon the relative orientation of the bond dipoles, but not on the polarity of bonds alone. A symmetrical structure shows zero dipole moment. Thus, dipole moment helps to predict the geometry of a molecules. Dipole moment values can be distinguish between cis- and trans- isomers, ortho, meta and pare-forms of a substance, etc.
Q. Arrange the following compounds in increasing order of dipole moments, toluene (I), o-dichlorobenzene (II), m-dichlorobenzene (III) and p-dichlorobenzene (IV) :

Options

A. `IVltIltIIltIII`
B. `IltIVltIIltIII`
C. `IVltIltIIIltII`
D. `IVltIIltIltIII`

Explanation

To solve the problem of arranging toluene (I), o-dichlorobenzene (II), m-dichlorobenzene (III), and p-dichlorobenzene (IV) in increasing order of dipole moments, we need to analyze the molecular structures and the effects of substituents on the dipole moments.

### Step-by-Step Solution:

1. **Understanding Dipole Moment**:
- The dipole moment (μ) is a vector quantity defined as the product of charge separation (q) and bond length (d). It can be expressed as:
\[ \mu = q \cdot d \]
- The unit of dipole moment is the Debye (D), where \(1 \text{ D} = 10^{-18} \text{ esu cm}\).

2. **Analyzing Toluene (I)**:
- Toluene has a methyl group (–CH₃) attached to a benzene ring. The dipole moment is relatively low because the methyl group is less electronegative compared to chlorine and does not create a significant dipole.

3. **Analyzing o-Dichlorobenzene (II)**:
- In o-dichlorobenzene, two chlorine atoms are positioned adjacent to each other on the benzene ring. The dipole moments of the two C-Cl bonds do not cancel out completely, resulting in a moderate dipole moment.

4. **Analyzing m-Dichlorobenzene (III)**:
- In m-dichlorobenzene, the chlorine atoms are separated by one carbon atom. The dipole moments of the two C-Cl bonds add up vectorially, resulting in a larger dipole moment than that of o-dichlorobenzene.

5. **Analyzing p-Dichlorobenzene (IV)**:
- In p-dichlorobenzene, the two chlorine atoms are opposite each other on the benzene ring. The dipole moments of the two C-Cl bonds cancel each other out, leading to a net dipole moment of zero.

6. **Arranging in Increasing Order**:
- Based on the analysis:
- **p-Dichlorobenzene (IV)** has the lowest dipole moment (0 D).
- **Toluene (I)** has a low dipole moment, higher than p-dichlorobenzene.
- **o-Dichlorobenzene (II)** has a moderate dipole moment.
- **m-Dichlorobenzene (III)** has the highest dipole moment among the four.

Thus, the increasing order of dipole moments is:
\[ \text{p-Dichlorobenzene (IV)} < \text{Toluene (I)} < \text{o-Dichlorobenzene (II)} < \text{m-Dichlorobenzene (III)} \]

### Final Answer:
**Increasing order of dipole moments**: IV < I < II < III

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