Under what circumstances would you expect the shared electron pair to be equal distances on the average from each of the atoms participating in a covalent bond?

In a covalent bond, when the shared electron pair is equally distant from each of the atoms participating in the bond, it is known as a nonpolar covalent bond. This occurs when the two atoms have the same or similar electronegativity values.

Electronegativity refers to the tendency of an atom to attract electrons towards itself in a chemical bond. When two atoms with similar electronegativity values bond together, they both exert similar levels of pull on the shared electron pair, resulting in an equal distribution of electron density between them.

To determine whether a covalent bond is nonpolar, you can look up the electronegativity values of the atoms involved in the bond. The most commonly used electronegativity scale is the Pauling scale, where the values range from 0.7 to 4.0 (approximately). If the electronegativity difference between the two atoms is very small (usually less than 0.5), the bond is considered nonpolar.

For example, in a diatomic molecule like nitrogen gas (N2), both nitrogen atoms have similar electronegativity values (3.04 on the Pauling scale). Since the electronegativity difference is negligible, the electron pair is shared equally, resulting in a nonpolar covalent bond.

In summary, a nonpolar covalent bond occurs when two atoms with similar electronegativity values share electrons equally. You can determine this by comparing the electronegativity values of the atoms involved in the bond.