For any diatomic molecule \(\mathrm{A}-\mathrm{B}\), what is the following sum: \(\delta_{\mathrm{A}}+\delta_{\mathrm{B}}\) ?

Covalent bonding is the type of chemical bond where atoms share pairs of electrons. The ultimate aim of this sharing is to provide each atom in the molecule with a stable electronic configuration, usually that of a noble gas. In the case of diatomic molecules, which consist of two atoms, this sharing can be visualized by a simple straight line between the atoms, such as in hydrogen (H-H).

However, not every covalent bond is created equal. When two identical atoms are bonded together, the shared electrons experience equal attraction from both atomic nuclei, leading to a purely covalent bond with equal sharing. But when different types of atoms form a bond, the story changes. One atom might hog the electrons more than the other. That's where partial charges come into play, and it's crucial for students to remember that the existence of covalent bonds doesn't always mean that electrons are being shared equally between atoms. This inequality is what leads us to concepts like electronegativity and chemical polarity.

Electronegativity is an atom's ability to attract and hold onto electrons in a chemical bond. It is a relative scale where different elements have different values. The higher an element's electronegativity, the more it pulls shared electrons towards itself in a bond.

Thinking about our A-B diatomic molecule, if atom A is more electronegative than atom B, then A will have a greater share of the electron cloud or 'density' between them. This results in a partial negative charge \(\delta_{\mathrm{A}}\) on A, and conversely, B will have a partial positive charge \(\delta_{\mathrm{B}}\). The degree of electronegativity difference will determine how polarized the bond is. For instance, in a molecule of fluorine (F-F), both atoms have the same electronegativity, meaning there's no partial charge. However, in a hydrochloric acid molecule (HCl), chlorine has a higher electronegativity than hydrogen, leading to a partial negative charge on the chlorine atom.

Chemical polarity is a concept that arises when there is an unequal distribution of electrons in a molecule. This inequality creates a dipole, with a positive end and a negative end, much like a magnet. In diatomic molecules, if there is a substantial difference in electronegativity between the two atoms, a polar bond is formed.

A classic example is the water molecule (H2O), though not a diatomic molecule, it illustrates polarity well. Oxygen is more electronegative than hydrogen, pulling the shared electrons towards itself and away from hydrogen, creating a dipole moment. In simpler diatomic molecules, such as those in our exercise with A and B, if \(\delta_{\mathrm{A}}\) is not equal to \(\delta_{\mathrm{B}}\) in magnitude but opposite in sign, the molecule is polar. To deepen the students' understanding, it's important to connect this polarity back to physical properties. Polar molecules often have higher boiling points and solubilities in polar solvents compared to nonpolar molecules, due to the strong intermolecular forces between polar molecules.