When our thinking is slanted toward atoms and molecules, it makes sense to measure the sizes of our samples in moles. If we do so, we can be certain that we are comparing samples that contain the same number of atoms or molecules. The mole is one of the seven SI base units and is defined as follows:
One mole is the number of atoms in a 12 g sample of carbon-12.
The obvious question now is: “How many atoms or molecules are there in a mole?” The answer is determined experimentally and, as you saw in Lesson 18, is
where mol–1 represents the inverse mole or “per mole,” and mol is the abbreviation for mole. The number NA is called Avogadro’s number after Italian scientist Amadeo Avogadro (1776–1856), who suggested that all gases occupying the same volume under the same conditions of temperature and pressure contain the same number of atoms or molecules.
The number of moles n contained in a sample of any substance is equal to the ratio of the number of molecules N in the sample to the number of molecules NA in 1 mol:
(Caution: The three symbols in this equation can easily be confused with one another, so you should sort them with their meanings now, before you end in “N-confusion.”) We can find the number of moles n in a sample from the mass Msam of the sample and either the molar mass M (the mass of 1 mol) or the molecular mass m (the mass of one molecule):
In Eq. 19-3, we used the fact that the mass M of 1 mol is the product of the mass m of one molecule and the number of molecules NA in 1 mol:
PROBLEM – SOLVING TACTICS
TACTIC 1 : Avogadro’s Number of What?
In Eq. 19-1, Avogadro’s number is expressed in terms of mol−1, which is the inverse mole, or 1/mol. We could instead explicitly state the elementary unit involved in a given situation. For example, if the elementary unit is an atom, we might write NA = 6.02 × 1023 atoms/mol. If, instead, the elementary unit is a molecule, then we might write NA = 6.02 × 1023 molecules/mol.
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