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 need to analyze the molecular geometry and the arrangement of polar bonds in each case. A molecule will have a zero dipole moment if the individual bond dipoles cancel each other out due to symmetry.

### Step-by-Step Solution:

1. **Gauche Conformation of 1,2-Dibromoethane (I)**:
- In the gauche conformation, the bromine atoms are positioned at an angle to each other, leading to a net dipole moment. The dipoles do not cancel out completely.
- **Conclusion**: This molecule does not have a zero dipole moment.

2. **Anti Conformation of 1,2-Dibromoethane (II)**:
- In the anti conformation, the two bromine atoms are positioned opposite each other. The dipole moments from the bromine atoms will cancel each other out.
- **Conclusion**: This molecule has a zero dipole moment.

3. **Trans-1,4-Dibromocyclohexane (III)**:
- In the trans configuration, the bromine atoms are on opposite sides of the cyclohexane ring. The dipole moments cancel each other out due to symmetry.
- **Conclusion**: This molecule has a zero dipole moment.

4. **Cis-1,4-Dibromocyclohexane (IV)**:
- In the cis configuration, both bromine atoms are on the same side of the cyclohexane ring. The dipole moments do not cancel out completely.
- **Conclusion**: This molecule does not have a zero dipole moment.

5. **Tetrabromomethane (V)**:
- Tetrabromomethane (CBr₄) has a tetrahedral geometry with bromine atoms symmetrically arranged around the central carbon atom. The dipole moments from the four bromine atoms cancel each other out.
- **Conclusion**: This molecule has a zero dipole moment.

6. **1,1-Dibromocyclohexane (VI)**:
- In 1,1-dibromocyclohexane, both bromine atoms are attached to the same carbon. The dipole moments from the two bromine atoms do not cancel out due to their arrangement.
- **Conclusion**: This molecule does not have a zero dipole moment.

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