In calculations, do the molar masses of diatomic elements ever need to be doubled to account for this?

Yes. Diatomic elements exist as molecules with the basic formula ##"X"_2"##, where ##"X"## represents the element, and ##"X"_2"## represents a molecule consisting of two ##"X"## atoms covalently bonded. Therefore, the molar mass for one ##"X"## atom is doubled when determining the molar mass of the molecule ##"X"_2##.

For example, a molecule of hydrogen gas has the formula ##"H"_2"##, which means it consists of two hydrogen atoms covalently bonded. The molar mass of a single hydrogen atom is 1 g/mol. The molar mass of a hydrogen molecule is 2 x 1 g/mol = 2 g/mol.

Likewise, a molecule of oxygen gas has the formula ##"O"_2##. The molar mass of a single oxygen atom is 16 g/mol. The molar mass of an ##"O"_2## molecule is 2 x 16g/mol = 32 g/mol.

Note: Given molar masses have been rounded to a whole number.