Arrange the following compound in order of increasing dipole moment :
(I) 1, 3, 5-Trichloro benzene
(II) 1, 2, 4-Trichloro benzene
(III) 1, 2, 3, 4-Tetrachloro benzene
(IV) P-dichloro benzene

Options

A. `I=IV lt II lt III`
B. `IV lt I lt II lt III`
C. `IV = I lt III lt II`
D. `IV lt II lt I lt III`

Explanation

To determine the order of increasing dipole moment for the given compounds, we need to analyze the molecular structure and the arrangement of the chlorine substituents on the benzene ring. The dipole moment of a molecule depends on both the magnitude of the individual dipoles and their directions.

### Step-by-Step Solution:

1. **Identify the Structures**:
- (I) 1, 3, 5-Trichlorobenzene: Chlorine atoms are at positions 1, 3, and 5.
- (II) 1, 2, 4-Trichlorobenzene: Chlorine atoms are at positions 1, 2, and 4.
- (III) 1, 2, 3, 4-Tetrachlorobenzene: Chlorine atoms are at positions 1, 2, 3, and 4.
- (IV) P-Dichlorobenzene: Chlorine atoms are at positions 1 and 4.

2. **Analyze Dipole Moments**:
- For **1, 3, 5-Trichlorobenzene**: The dipole moments of the chlorine atoms at positions 1 and 5 will partially cancel each other out, leading to a relatively low dipole moment.
- For **1, 2, 4-Trichlorobenzene**: The dipole moments from the chlorine atoms at positions 1 and 2 will add up, while the one at position 4 will create a net dipole moment in a specific direction, resulting in a moderate dipole moment.
- For **1, 2, 3, 4-Tetrachlorobenzene**: The presence of four chlorine atoms will create a significant dipole moment as there are no opposing dipoles to cancel out the overall effect.
- For **P-Dichlorobenzene**: The dipole moments from the chlorine atoms at positions 1 and 4 will cancel each other out to some extent, resulting in a lower dipole moment compared to the other structures.

3. **Order of Increasing Dipole Moment**:
- From the analysis, we can conclude the following order based on the strength of the dipole moments:
- (IV) P-Dichlorobenzene < (I) 1, 3, 5-Trichlorobenzene < (II) 1, 2, 4-Trichlorobenzene < (III) 1, 2, 3, 4-Tetrachlorobenzene.

### Final Answer:
The order of increasing dipole moment is:
**P-Dichlorobenzene < 1, 3, 5-Trichlorobenzene < 1, 2, 4-Trichlorobenzene < 1, 2, 3, 4-Tetrachlorobenzene.**