A molecule has a zero dipole moment if it is nonpolar. For a molecule to be nonpolar, two conditions must generally be met:

1. The individual bond dipoles must be zero, or
2. The individual bond dipoles must cancel each other out due to the molecule's symmetrical geometry.

Let's analyze each option:

A) BF₃:

Boron trifluoride (BF₃) has a central boron atom bonded to three fluorine atoms. Boron has 3 valence electrons, and it forms three single bonds with fluorine atoms. There are no lone pairs on the central boron atom. According to VSEPR theory, this leads to a trigonal planar geometry. The B-F bonds are polar, but due to the symmetrical trigonal planar arrangement (bond angles of 120°), the three bond dipoles cancel each other out. Therefore, BF₃ has a zero dipole moment.

B) XeF₂:

Xenon difluoride (XeF₂) has a central xenon atom. Xenon has 8 valence electrons. It forms two single bonds with fluorine atoms and has three lone pairs of electrons. According to VSEPR theory, the steric number is 2 (bonds) + 3 (lone pairs) = 5. This corresponds to a trigonal bipyramidal electron geometry. To minimize repulsion, the lone pairs occupy the equatorial positions, and the fluorine atoms occupy the axial positions, resulting in a linear molecular geometry. The Xe-F bonds are polar, but due to the symmetrical linear arrangement, the two bond dipoles cancel each other out. Therefore, XeF₂ has a zero dipole moment.

C) SO₃:

Sulfur trioxide (SO₃) has a central sulfur atom bonded to three oxygen atoms. Sulfur has 6 valence electrons. It forms three double bonds with oxygen atoms (or resonance structures with single and double bonds). There are no lone pairs on the central sulfur atom. According to VSEPR theory, this leads to a trigonal planar geometry. The S-O bonds are polar, but due to the symmetrical trigonal planar arrangement (bond angles of 120°), the three bond dipoles cancel each other out. Therefore, SO₃ has a zero dipole moment.

Since BF₃, XeF₂, and SO₃ all have zero dipole moments, option D is the correct answer.

Correct Answer: (D)