Number of Atoms in a Drop of Water

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Because atoms and molecules are extremely small, there are a great many of them in any macroscopic sample. The 15.9994 g of oxygen referred to in Moles: the Number of Water molecules would contain 6.022 × 10²³ oxygen atoms, for example, and the 2.016 g of hydrogen that reacts with it would contain twice as many (12.044 × 10²³) hydrogen atoms. The very large numbers involved in counting microscopic particles are inconvenient to think about or to write down. Therefore chemists have chosen to count atoms and molecules using a unit called the mole. One mole (abbreviated mol) is 6.022 × 10²³ of the microscopic particles which make up the substance in question. Thus 6.022 × 10²³ O atoms is referred to as 1 mol O.

The idea of using a large number as a unit with which to measure how many objects we have is not unique to chemists. Eggs, doughnuts, and many other things are sold by the dozen—a unit of twelve items. Smaller objects, such as pencils, may be ordered in units of 144, that is, by the gross, and paper is packaged in reams, each of which contains 500 sheets. A chemist who refers to 1 mol O is very much like a bookstore manager who orders 2½ dozen sweat shirts, 20 gross of pencils, or 62 reams of paper.

There is a difference in degree, however, because the chemist’s unit, 6.022 × 10²³, is so large. A stack of paper containing a mole of sheets would extend more than a million times the distance from the earth to the sun, and 6.022 × 10²³ grains of sand would cover all the land in the world to a depth of nearly 2 ft. A student may contain 10²⁷ water molecules (about 10⁴ mol), and would need to accumulate about 10¹⁸ (ten million million million, but only 0.00001 mol) water molecules per second over 18 years to attain that amount. The proof is given soon in Using the Molar Mass of Water. Obviously there are a great many particles in a mole of anything.

Why have chemists chosen such an unusual number as 6.022 × 10²³ as the unit with which to count the number of atoms or molecules? Surely some nice round number would be easier to remember. The answer is that the number of grams in the mass of 1 mol of atoms of any element is the atomic weight of that element. For example, 1 mol of oxygen atoms not only contains 6.022 × 10²³ atoms, but its mass of 15.9994 g is conveniently obtained by adding the unit gram to the Table of Atomic Weights. Some other examples are

1mol H contains 6.022 × 10²³ H atoms; its mass is 1.008 g.

1 mol C contains 6.022 × 10²³ C atoms; its mass is 12.01 g.

1 mol O contains 6.022 × 10²³ O atoms; its mass is 15.994 or 16.00 g.

1 mol Br contains 6.022 × 10²³ Br atoms; its mass is 79.90 g.

(Here and in subsequent calculations atomic weights are rounded to two decimal places, unless, as in the case of H, fewer than four significant figures would remain.)

The mass of a mole of molecules can also be obtained from atomic weights. Just as a dozen eggs will have a dozen whites and a dozen yolks, a mole of CO molecules will contain a mole of C atoms and a mole of O atoms.

The mass of a mole of CO is thus

\[\text{Mass of 1 mol C} + \text{mass of 1 mol O} = \text{mass of 1 mol CO}\nonumber\]

\[\text{12.01 g} + \text{16.00 g} = \text{28.01 g}\nonumber\]

The molecular weight of CO(28.01) expressed in grams is the mass of a mole of CO. Some other examples are

Table \(\PageIndex{1}\) Molecular Weights

Molecule	Molecular Weight	Mass of 1 Mol of Molecules
Br₂	2(79.90) = 159.80	159.80 g
O₂	2(16.00) = 32.00	32.00 g
H₂O	2(1.008) + 16 = 18.02	18.02 g
H₂O₂	2(1.008) + 2(16) = 34.016	34.016 g
HgBr₂	200.59 + 2(79.90) = 360.39	360.39 g

It is important to specify to what kind of particle a mole refers. A mole of O atoms, for example, has only half as many atoms (and half as great a mass) as a mole of O₂ molecules. It is best not to talk about a mole of oxygen without specifying whether you mean 1 mol O or 1 mol O₂.

From ChemPRIME: 2.7: The Mole

Contributors and Attributions

Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.