2.7: Molar Mass

The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. For example, water, H₂O, and hydrogen peroxide, H₂O₂, are alike in that their respective molecules are composed of hydrogen and oxygen atoms. However, because a hydrogen peroxide molecule contains two oxygen atoms, as opposed to the water molecule, which has only one, the two substances exhibit very different properties.

Atoms and molecules are extremely small. Therefore, for measuring their macroscopic amounts, a standard scientific unit is needed. The mole is an amount unit similar to familiar units like pair, dozen, gross, etc. It provides a specific measure of the number of atoms or molecules in a sample of matter. The Latin connotation for the word “mole” is “large mass” or “bulk,” which is consistent with its use as the name for this unit. The mole provides a link between an easily measured macroscopic property, bulk mass, and an extremely important fundamental property, number of atoms, molecules, and so forth.

A mole of a substance is that amount in which there are 6.02214076 × 10²³ discrete entities (atoms or molecules). This large number conveniently rounded to 6.022 × 10²³, is a fundamental constant known as Avogadro’s number (N_A) or the Avogadro constant in honor of Italian scientist Amedeo Avogadro. This constant is properly reported with an explicit unit of “per mole”.

Consistent with its definition as an amount unit, 1 mole of any element contains the same number of atoms as 1 mole of any other element. The masses of 1 mole of different elements, however, are different, since the masses of the individual atoms are drastically different. The molar mass of an element (or compound) is the mass in grams of 1 mole of that substance, a property expressed in units of grams per mole (g/mol).

The molar mass of any substance is numerically equivalent to its atomic or formula weight in amu. Per the amu definition, a single carbon atom weighs 12 amu (its atomic mass is 12 amu). A mole of carbon weighs 12 g (12 g C = 1 mol C atoms = 6.022 × 10²³ C atoms), and the molar mass of carbon is 12 g/mol. This relationship holds for all elements since their atomic masses are measured relative to that of the amu-reference substance, carbon-12. Extending this principle, the molar mass of a compound in grams is likewise numerically equivalent to its formula mass in amu. For example, helium has an atomic mass of 4.002 amu and a molar mass of 4.002 g/mol.

While atomic mass and molar mass are numerically equivalent, keep in mind that they are vastly different in terms of scale. To appreciate the enormity of the mole, consider a small drop of water weighing about 0.03 g. Although this represents just a tiny fraction of 1 mole of water (~18 g), it contains more water molecules than can be imagined. If the molecules were distributed equally among the roughly seven billion people on earth, each person would receive more than 100 billion molecules of water.

The mole defines the relationship between mass and the number of atoms. This allows the number of atoms to be calculated based using suitable forms of the conversion factor: 1 mole of atoms = 6.022 × 10²³ atoms. To convert between the mass of an element (in grams) and the number of moles, the molar mass of the element (g/mol) is used as a conversion factor.

Text adapted from Openstax Chemistry 2e, Section 3.1: Formula Mass and the Mole Concept.

The periodic table gives the average atomic mass of each atom. However, macroscopic samples contain extremely large numbers of atoms. Therefore, it is essential to use a counting unit called Avogadro's number.

Avogadro’s number, expressed as the symbol N_A, is usually rounded to 6.022 × 10²³. Its value is equal to the number of atoms in exactly 12 grams of pure carbon-12 isotope.

The term mole, abbreviated mol, is used to describe Avogadro's number, just as the familiar term, dozen, is used to describe an amount of 12.

Nonetheless, a dozen of different items can weigh differently despite having the same number of items. Similarly, moles of different elements have different masses but always contain the same number of atoms. 

The mass in grams of one mole of an element is called the molar mass, expressed in grams per mole. Its value is numerically equivalent to the element’s atomic mass. Hence, the definition of the mole lets us count particles by weighing them. The molar mass and Avogadro's number can be used as conversion factors.

This can be used to calculate the number of atoms in a 5 gram bar of gold. The average molar mass of gold is 196.96 g/mol. So, to convert the mass into moles, divide the mass of the bar by the average molar mass. Then, multiply the number of moles by Avogadro's number to get the number of total atoms in the sample. So, this bar of gold contains 1.529 × 10²² atoms.