Find the molecule with the maximum dipole moment

The correct option is NH₃.

To determine which molecule has the maximum dipole moment, let's analyze each of the given options step-by-step:

1. Methane (CH₄):
Methane has a regular tetrahedral geometry with the carbon atom at the center. The individual C-H bond dipoles point towards the carbon atom (since carbon is slightly more electronegative than hydrogen). Because of the symmetrical tetrahedral arrangement, these four bond dipoles vectorially cancel each other out completely. Therefore, the net dipole moment ($\mu$) of CH₄ is 0 D.

2. Carbon Dioxide (CO₂):
Carbon dioxide is a linear molecule (O=C=O). Oxygen is more electronegative than carbon, so the individual C=O bond dipoles point outwards in opposite directions from the central carbon atom. Since they are equal in magnitude and point in exactly opposite directions ($180°$ angle), they cancel each other out. Thus, the net dipole moment ($\mu$) of CO₂ is 0 D.

3. Nitrogen Trifluoride (NF₃) vs. Ammonia (NH₃):
Both NH₃ and NF₃ have a pyramidal geometry due to the presence of three bond pairs and one lone pair on the central nitrogen atom. However, their net dipole moments differ significantly because of the direction of the bond dipoles relative to the lone pair dipole:

In NH₃, nitrogen is more electronegative than hydrogen. The C-N (or in this case, H-N) bond dipoles point towards the nitrogen atom. The lone pair dipole also points away from the nitrogen atom in the same direction. Consequently, the bond dipoles and the lone pair dipole reinforce each other, resulting in a large net dipole moment ($\mu \approx 1.47\text{D}$).

In NF₃, fluorine is much more electronegative than nitrogen. The N-F bond dipoles point away from the nitrogen atom towards the fluorine atoms. However, the lone pair dipole points away from the nitrogen atom in the opposite direction. Thus, the lone pair dipole opposes the vector sum of the N-F bond dipoles, partially cancelling them out and resulting in a very low net dipole moment ($\mu \approx 0.23\text{D}$).

Comparing all the options, ammonia (NH₃) has the highest net dipole moment.