Which of the following has the highest dipole moment?

\(CH_2Cl_2\)

The correct answer is option 4. \(CH_2Cl_2\).

Dipole moment (\(\mu\)) is a measure of the separation of positive and negative charges in a molecule and depends on both the magnitude of charge and the distance between charges. A molecule’s dipole moment is affected by:

Electronegativity differences between atoms: Greater the difference in electronegativity between atoms, the greater the dipole moment of the bond.

Molecular geometry: Symmetrical molecules have dipole moments that cancel out, resulting in a net dipole moment of zero.

Analysis of Each Compound:

1. \(CH_4\) (Methane):

Methane has a tetrahedral geometry with four hydrogen atoms symmetrically arranged around the central carbon. The electronegativity difference between carbon and hydrogen is very small, and the symmetry of the tetrahedral arrangement causes the dipole moments of the C-H bonds to cancel each other out.

Net Dipole Moment: Zero.

2. \(CCl_4\) (Carbon Tetrachloride):

\(CCl_4\) also has a tetrahedral geometry, but this time with four chlorine atoms symmetrically arranged around the central carbon. While chlorine is much more electronegative than carbon, the symmetrical arrangement of the C-Cl bonds means that the dipole moments cancel out.

Net Dipole Moment: Zero (due to symmetry).

3. \(CHCl_3\) (Chloroform):

Chloroform has a tetrahedral geometry with one hydrogen and three chlorine atoms around the central carbon. Chlorine is much more electronegative than hydrogen, so the C-Cl bonds create strong dipoles. The arrangement of three chlorine atoms on one side and a single hydrogen on the other causes the dipoles not to cancel out completely.

Net Dipole Moment: \(CHCl_3\) has a moderate dipole moment because the dipoles of the three chlorine atoms dominate but do not completely cancel out due to the presence of the hydrogen atom (1.08 D).

4. \(CH_2Cl_2\) (Dichloromethane):

Dichloromethane also has a tetrahedral geometry, with two chlorine atoms and two hydrogen atoms attached to the central carbon. Chlorine is significantly more electronegative than hydrogen, so the C-Cl bonds create strong dipoles. The molecule is asymmetrical because the two chlorine atoms are on one side of the molecule and the two hydrogen atoms are on the other.

Net Dipole Moment: The asymmetry of the dipoles, with chlorine pulling more electron density than hydrogen, results in a strong net dipole moment. The dipoles from the two C-Cl bonds add together, giving \(CH_2Cl_2\) a higher dipole moment than \(CHCl_3\) (1.60 D).

Why \(CH_2Cl_2\) Has the Highest Dipole Moment:

Asymmetry: In \(CH_2Cl_2\), the two electronegative chlorine atoms create significant dipoles, while the hydrogen atoms contribute very little to dipole cancellation. This asymmetry results in a higher overall dipole moment.

Comparison to Other Molecules:

\(CH_4\) and \(CCl_4\) are completely symmetrical, so they have no dipole moment.

\(CHCl_3\) has a dipole moment, but since it has three chlorine atoms and one hydrogen, the dipole cancellation is more significant than in \(CH_2Cl_2\), where the two chlorine atoms dominate and produce a higher net dipole.

Conclusion:

Highest dipole moment: \(CH_2Cl_2\) has the highest dipole moment because it is asymmetric and has two chlorine atoms pulling electron density more strongly than the two hydrogen atoms.

Thus, the correct answer is option 4: \(CH_2Cl_2\).