Atomic Weight

Early work on atomic weights used naturally occurring oxygen, with an assigned atomic weight of exactly 16 as the basis for the scale of atomic weights. All other atomic weights were found in relation to it. Confusion arose when, in 1929, the three isotopes of oxygen were discovered. In 1961, it was finally decided to adopt carbon-12 as the basis for all other atomic weights. Under this system still in use today, the atomic weight of carbon-12 is taken to be exactly 12 and the atomic mass unit is defined as exactly one-twelfth the mass of carbon-12. All other atomic weights are measured in relation to this unit.

When examining the table of atomic weights, it is found that the weight of carbon is not given as exactly 12 as would be expected, but rather 12.01. The reason is that the weights used in the table represent the average weight of the isotopes of carbon that are found in a naturally occurring sample. For example, most of the carbon found in nature, 98.89% of it to be exact, is carbon-12 and has a weight of exactly 12. The rest of it (1.11%) is carbon-13 (with an atomic weight of 13.00) and carbon-14 (which exists in quantities too minute to affect this calculation). The atomic weight of carbon is calculated by taking 98.89% of the weight of carbon-12 and 1.11% of the weight of carbon-13 to give 12.0112. All weights in the table of atomic weights are calculated by using the percentage of each isotope in a naturally occurring sample.

Because atoms are so small, making it impossible for chemists to observe or weigh them, the weights of individual atoms are not very useful for experimentation. Very large numbers of atoms are involved in even the tiniest samples of matter. It is important to match the unit that is used to make a measurement to the size of the thing being measured. For example, it is useful to measure the length of a room in feet rather than miles because the unit, foot, corresponds to the length of a room. One would not measure the distance to London or Paris or to the sun in inches or feet because the distance is so large in relation to the size of the unit. Miles would be a much more appropriate unit.

A new unit, called a mole, was created as a more useful unit for working with atoms. A mole is a counting number much like a dozen. A dozen involves 12 of anything, 12 books, 12 cookies, 12 pencils, etc. Similarly, a mole involves 6.02 × 10²³ (602 with 21 zeros after it) particles of anything. The mole is such a large number that it is not a useful measurement for anything except counting very, very small particles, too small to even imagine. For example, if a mole of dollars were divided evenly among all the people of the world (5.5 billion), every single person alive would receive 1.09 × 10¹⁴ dollars! That is enough money to last nearly 300 years if a billion dollars were spent every single day of the year. Yet a mole of carbon atoms is contained in a chunk of coal about as big as a marble.

Needless to say, atoms cannot be counted in the same way that cookies or books are counted. But they can be counted by weighing, and the mole is the unit that can express this quantity. If a ping-pong ball weighs one ounce, then 12 ounces of ping-pong balls would contain 12 balls. Twenty ounces would contain 20 balls. If golf balls weigh four ounces each, then 48 ounces are needed in order to obtain 12 balls, and 80 ounces are needed in order to obtain 20 balls. Since the golf ball weighs four times as much as the ping-pong ball, it is easy to obtain equal numbers of these two balls by weighing four times as much for the golf balls as you weigh for the ping-pong balls. Actually, it is easier to count small numbers of ping-pong balls or golf balls than to weigh them. But if 10 or 20 or 30 thousand of them were needed, it would be much easier figure the weight of the balls and weigh them than it would be to count them.

Likewise, the weighing method is more useful and, in fact, is the only method by which atoms can be counted. It was discovered in the early 1800s, mostly through the work of Amadeo Avogadro, that when the atomic weight of an atom is interpreted in grams rather than atomic mass units, the number of atoms in the sample is always 6.02 × 10²³ atoms or a mole of atoms. Thus, 12 grams of carbon contain one mole of carbon atoms and 16 grams of oxygen contain one mole of oxygen atoms. One mole of the lightest atom, hydrogen, weighs just one gram and one mole of the heaviest of the naturally occurring elements, uranium, weighs 238 grams.

Molecules are particles made up of more than one atom. The weight of the molecule, called the molecular weight, can be found by adding the atomic weights of each of the atoms that make up the molecule. Water is a molecule with a formula, H₂O. It is composed of two atoms of hydrogen, with an atomic weight of one, and one atom of oxygen with an atomic weight of 16. Water, therefore has a molecular weight of 18. When this molecular weight is interpreted as 18 atomic mass units, it represents the weight of one molecule in relation to one-twelfth of carbon-12. When the molecular weight is interpreted as 18 grams (less than 400 drops of water), it represents the weight of one mole or 6.02 × 10²³ molecules of water. Similarly, the molecular weight of carbon dioxide (CO₂) is 44 atomic mass units or 44 grams. A chunk of solid carbon dioxide (known as dry ice) about the size of a baseball contains one mole of molecules. If this chunk were allowed to change to a gas at room conditions of temperature and pressure, this mole of carbon dioxide would take up slightly over a cubic foot.