Atoms in the RDA of Iodine

As we have seen, the RDA for iodine is only 150 µg per day, or 0.000150 g per day. That seems like a miniscule amount, but it represents 7 x 10¹⁷, or 700 000 000 000 000 000 iodine atoms (about 10 million million atoms in each cm³ of our body). Our requirements for other nutrients are even smaller; for example, the RDA for vitamine B12 is only 2.4 µg/day, which represents about 1 x 10¹⁵ cobalt atoms. See the future section The Avogadro Constant for sample calculations. 

Because atoms and molecules are extremely small, there are a great many of them in any macroscopic sample. 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 I atoms is referred to as 1 mol I. The 7 × 10¹⁷ atoms of iodine in the RDA we have been discussing would be (7 × 10¹⁷)/(6.022 × 10²³) mol Br, or 0.0000012 mol iodine.

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 0.0000012 mol iodine 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. 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 iodine atoms not only contains 6.022 × 10²³ atoms, but its mass of 126.9 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 16.00 g.
• 1 mol Br contains 6.022 × 10²³ Br atoms; its mass is 79.90 g.
• 1 mol Cu contains 6.022 × 10²³ Cu atoms; its mass is 63.55 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 CuI is thus

\[\text{Mass of 1 mol Cu} + \text{mass of 1 mol I} = \text{mass of 1 mol CuI}\nonumber\]

\[\text{63.55 g} + \text{126.9 g} = \text{190.45 g}\nonumber\]

The molecular weight of CuI(190.45) expressed in grams is the mass of a mole of CuI. 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
CuI	63.55 + 126.9 = 190.45	190.45 g
CuI2	1(63.55) + 2(126.9) = 317.35	317.35 g

It is important to specify to what kind of particle a mole refers. A mole of I atoms, for example, has only half as many atoms (and half as great a mass) as a mole of I₂ molecules. It is best not to talk about a mole of iodine without specifying whether you mean 1 mol I or 1 mol I₂. This is especially confusing with the nutrient "iodine", because the name is a misnomer. "Iodine" means the element I₂, but the nutrient is really iodide, as in KI or CuI. So it takes two moles of KI to contain one mole of I₂.

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.