Which of the following molecules would be expected to be polar? (a) \(\mathrm{PBr}_{3},\) (b) \(\mathrm{SO}_{3},\) (c) \(\mathrm{AsCl}_{3},\) (d) \(\mathrm{ClF}_{3},\) (e) \(\mathrm{BCl}_{3}\).

The shape of a molecule, known as molecular geometry, is a fundamental factor in determining its polarity. At the most basic level, molecular geometry describes the three-dimensional arrangement of atoms within a molecule. Factors such as the number of bonds, the presence of lone pairs of electrons, and the types of atoms involved influence a molecule's geometry.

Let's consider a molecule of water (H₂O) as an example. The oxygen atom forms two bonds with hydrogen atoms and also has two lone pairs of electrons. These lone pairs repel the bonded hydrogen atoms, resulting in a bent molecular geometry. Due to this shape, water is polar because the distribution of electrons is uneven, leading to areas of negative (oxygen) and positive (hydrogen) charge.

For the exercise with molecules like PBr₃ and AsCl₃, their trigonal pyramidal geometry means there is an uneven distribution of electrons. This leads to molecular polarity. On the other hand, molecules with symmetrical shapes like SO₃ and BCl₃, which have a trigonal planar geometry, distribute charge more evenly and are typically nonpolar.

Electronegativity is a measure of how strongly an atom attracts electrons in a chemical bond. The scale ranges from 0.7 (least electronegative) to 4.0 (most electronegative). It's important to note that when two different atoms form a bond, the atom with higher electronegativity will pull the shared electrons closer to itself, creating a polar bond.

For instance, in hydrogen fluoride (HF), fluorine has a higher electronegativity compared to hydrogen. This causes the shared electrons to spend more time around the fluorine atom, giving it a partial negative charge and hydrogen a partial positive charge. Consequently, HF has a polar bond.

In the molecules listed in the exercise, if we compare the central atom to the surrounding atoms, differences in electronegativity can indicate which bonds are polar. Molecules with substantial differences in electronegativity between bonded atoms are more likely to have an overall polar character.

A dipole moment arises when there is a separation of charge within a molecule, leading to a molecule having a 'positive end' and a 'negative end', much like a magnet with a north and south pole. Mathematically, it is a product of the charge difference and the distance between the charges. It is measured in Debye units (D).

The presence of a dipole moment is a clear indicator of molecular polarity. For a molecule to possess a dipole moment, it must have polar bonds and an asymmetric geometry that does not cancel out these polarities.

How to Determine Dipole Moment?

By assessing the molecular geometry and the electronegativity of the atoms involved, we can predict the dipole moment. If a molecule like ClF₃ has an asymmetrical shape and polar bonds due to significant electronegativity differences, it will definitely have a net dipole moment, which confirms its polar nature.

In the given exercise, by combining molecular geometry and electronegativity, we can infer that molecules such as PBr₃ and AsCl₃ will have a net dipole moment and are thus polar, whereas symmetrical molecules like SO₃ and BCl₃ will not have a net dipole moment, thus being nonpolar.