Which of the following molecules have zero dipole moment?
(I) gauche conformation of 1, 2 - dibromoethane.
(II) anti conformation of 1, 2 - dibromoethane.
(III) trans - 1, 4 - dibromocyclohexane
(IV) cis - 1, 4 - dibromocylohexane
(V) tetrabromomethane.
(VI) 1, 1- dibromocyclohexane

Options

A. I and II
B. II, III and V
C. II and V
D. I, IV and VI

Answer

To determine which of the given molecules have a zero dipole moment, we will analyze each molecule based on its structure and the arrangement of its polar bonds.

### Step-by-Step Solution:

1. **Gauche Conformation of 1,2-Dibromoethane (I)**:
- In this conformation, the two bromine atoms are positioned such that their dipole moments do not cancel each other out. The electronegative bromine atoms pull electron density towards themselves, resulting in a net dipole moment.
- **Conclusion**: This molecule has a dipole moment that is **not equal to zero**.

2. **Anti Conformation of 1,2-Dibromoethane (II)**:
- In this conformation, one bromine atom is positioned above the plane and the other below. The dipole moments of the two bromine atoms are equal in magnitude but opposite in direction, leading to cancellation.
- **Conclusion**: This molecule has a dipole moment that is **equal to zero**.

3. **Trans-1,4-Dibromocyclohexane (III)**:
- In the trans configuration, the bromine atoms are located on opposite sides of the cyclohexane ring. Similar to the anti conformation, the dipole moments of the two bromine atoms cancel each other out.
- **Conclusion**: This molecule has a dipole moment that is **equal to zero**.

4. **Cis-1,4-Dibromocyclohexane (IV)**:
- In this configuration, both bromine atoms are on the same side of the cyclohexane ring. The dipole moments do not cancel out, resulting in a net dipole moment directed downwards.
- **Conclusion**: This molecule has a dipole moment that is **not equal to zero**.

5. **Tetrabromomethane (V)**:
- This molecule has a tetrahedral geometry with four bromine atoms symmetrically arranged around the central carbon atom. The dipole moments of the bromine atoms cancel each other out perfectly.
- **Conclusion**: This molecule has a dipole moment that is **equal to zero**.

6. **1,1-Dibromocyclohexane (VI)**:
- In this molecule, both bromine atoms are attached to the same carbon atom. The dipole moments of the bromine atoms do not cancel out, resulting in a net dipole moment.
- **Conclusion**: This molecule has a dipole moment that is **not equal to zero**.

### Final Answer:
The molecules with zero dipole moment are:
- (II) Anti conformation of 1,2-dibromoethane
- (III) Trans-1,4-dibromocyclohexane
- (V) Tetrabromomethane