Dipole Moment

To arrange the given compounds HBr, H₂S, NF₃, and CCl₃ in order of increasing dipole moment, we need to understand the concept of dipole moments first.

Dipole Moment: The dipole moment (μ) is a measure of the separation of opposite electrical charges. It is a vector quantity, having both magnitude and direction. The dipole moment is defined as:

where is the charge and is the distance between the charges. Molecules have a dipole moment due to the difference in electronegativity between atoms and the structural arrangement of the atoms in the molecule. The unit is Debye (D).

Let's analyze each compound:

1. HBr:

Hydrogen bromide is a diatomic molecule. Br is more electronegative than H, creating a dipole moment. However, it is relatively small because it is a simple diatomic molecule.

1. H₂S:

Due to the bent shape of water-like molecules and a small difference in electronegativity between H and S, the dipole moment is small.

1. NF₃:

Nitrogen trifluoride has a dipole moment because of both electronegativity differences and the pyramidal shape. However, the lone pair on nitrogen partially cancels the dipole moment.

1. CCl₃:

Although CCl₃ is commonly regarded as somewhat nonpolar due to symmetry concerns, in this context it is considered to polarize due to electronegative Cl atoms, leading to a higher dipole moment than the others.

Comparing these, we order them by increasing dipole moment:

1. H₂S - least dipole moment due to symmetrical structure and lower electronegativity difference.
2. HBr - a minor increase in dipole moment compared to H₂S.
3. NF₃ - due to its pyramidal structure, it has a moderate dipole moment.
4. CCl₃ - has the highest dipole moment among the given options due to the polarity of C-Cl bonds.

Thus, the increasing order of dipole moment is: H₂S < HBr < NF₃ < CCl₃.

The dipole moment of a molecule is determined by both the electronegativity difference between atoms and the molecular geometry.

: Chlorine is highly electronegative, but the molecule has a symmetric trigonal planar geometry, which results in a low dipole moment due to cancellation of individual dipoles.

: Nitrogen is more electronegative than fluorine, but due to the geometry of (a trigonal pyramidal shape), the dipole moment is moderate.

HBr: Bromine is less electronegative than fluorine or chlorine, but since HBr has a linear geometry, it results in a moderate dipole moment.

: Due to the bent geometry of and the significant electronegativity difference between sulfur and hydrogen, has the highest dipole moment among the given compounds.

Thus, the increasing order of dipole moments is: