Formula Mass: The Mass of a Molecule or Formula Unit

One skill needed in future chapters is the ability to determine the mass of the formula of an ionic compound. This quantity is called the formula mass. The formula mass is obtained by adding the masses of each individual atom in the formula of the compound. Because a proper formula is electrically neutral (with no net electrons gained or lost), the ions can be considered atoms for the purpose of calculating the formula mass.

Let us start by calculating the formula mass of sodium chloride (NaCl). This formula mass is the sum of the atomic masses of one sodium atom and one chlorine atom, which we find from the periodic table; here, we use the masses to two decimal places:

Na: 22.99 amu

Cl: +35.34 amu

Total: 58.44 amu

To two decimal places, the formula mass of NaCl is 58.44 amu.

When an ionic compound has more than one anion or cation, you must remember to use the proper multiple of the atomic mass for the element in question. For the formula mass of calcium fluoride (CaF₂), we must multiply the mass of the fluorine atom by 2 to account for the two fluorine atoms in the chemical formula:

Ca: 1 x 40.08 = 40.08 amu

F: 2 x 19.00 = +38.00 amu

Total = 78.08 amu

The formula mass of CaF₂ is 78.08 amu.

For ionic compounds with polyatomic ions, the sum must include the number and mass of each atom in the formula for the polyatomic ion. For example, potassium nitrate (KNO₃) has one potassium atom, one nitrogen atom, and three oxygen atoms:

K: 1 x 39.10 = 39.10 amu

N: 1 x 14.00 = +14.00 amu

O: 3 x 16.00 = +48.00 amu

Total = 101.10 amu

The formula mass of KNO₃ is 101.10 amu.

Potassium nitrate is a key ingredient in gunpowder and has been used clinically as a diuretic.

When a formula contains more than one polyatomic unit in the chemical formula, as in Ca(NO₃)₂, do not forget to multiply the atomic mass of every atom inside the parentheses by the subscript outside the parentheses. This is necessary because the subscript refers to the entire polyatomic ion. Thus, for Ca(NO₃)₂, the subscript 2 implies two complete nitrate ions, so we must sum the masses of two (1 × 2) nitrogen atoms and six (3 × 2) oxygen atoms, along with the mass of a single calcium atom:

Ca: 1 x 40.08 = 40.08 amu

N: 2 x 14.00 = +28.00 amu

O: 6 x 16.00 = +96.00 amu

Total = 164.08 amu

The key to calculating the formula mass of an ionic compound is to correctly count each atom in the formula and multiply the atomic masses of its atoms accordingly.