When the weather is nice, many people begin to work on their yards and homes. For many projects, sand is needed as a foundation for a walk or to add to other materials. You could order up twenty million grains of sand and have people really stare at you. You could order by the pound, but that takes a lot of time weighing out. The best bet is to order by the yard, meaning a cubic yard. The loader can easily scoop up what you need and put it directly in your truck.

It certainly is easy to count bananas or to count elephants (as long as you stay out of their way). However, you would be counting grains of sugar from your sugar canister for a long, long time. Atoms and molecules are extremely small - far, far smaller than grains of sugar. Counting atoms or molecules is not only unwise, it is absolutely impossible. One drop of water contains about $$10^{22}$$ molecules of water. If you counted 10 molecules very second for 50 years without stopping you would have counted only $$1.6 \times 10^{10}$$ molecules. Put another way, at that counting rate, it would take you over 30 trillion years to count the water molecules in one tiny drop.

Chemists needed a name that can stand for a very large number of items. Amadeo Avogadro (1776 - 1856), an Italian scientist, provided just such a number. He is responsible for the counting unit of measure called the mole. A mole $$\left( \text{mol} \right)$$ is the amount of a substance that contains $$6.02 \times 10^{23}$$ representative particles of that substance. The mole is the SI unit for amount of a substance. Just like the dozen and the gross, it is a name that stands for a number. There are therefore $$6.02 \times 10^{23}$$ water molecules in a mole of water molecules. There also would be $$6.02 \times 10^{23}$$ bananas in a mole of bananas, if such a huge number of bananas ever existed.

Figure 10.1.1: Italian scientist Amadeo Avogadro, whose work led to the concept of the mole as a counting unit in chemistry.

The number $$6.02 \times 10^{23}$$ is called Avogadro's number, the number of representative particles in a mole. It is an experimentally determined number. A representative particle is the smallest unit in which a substance naturally exists. For the majority of elements, the representative particle is the atom. Iron, carbon, and helium consist of iron atoms, carbon atoms, and helium atoms, respectively. Seven elements exist in nature as diatomic molecules and they are $$\ce{H_2}$$, $$\ce{N_2}$$, $$\ce{O_2}$$, $$\ce{F_2}$$, $$\ce{Cl_2}$$, $$\ce{Br_2}$$, and $$\ce{I_2}$$. The representative particle for these elements is the molecule. Likewise, all molecular compounds such as $$\ce{H_2O}$$ and $$\ce{CO_2}$$ exist as molecules and so the molecule is their representative particle. For ionic compounds such as $$\ce{NaCl}$$ and $$\ce{Ca(NO_3)_2}$$, the representative particle is the formula unit. A mole of any substance contains Avogadro's number $$\left( 6.02 \times 10^{23} \right)$$ of representative particles.

Figure 10.1.2: The animal mole is very different than the counting unit of the mole. Chemists nonetheless have adopted the mole as their unofficial mascot. National Mole Day is a celebration of chemistry that occurs on October 23 (10/23) of each year.

### Summary

• A mole of any substance contains Avogadro's number $$\left( 6.02 \times 10^{23} \right)$$ of representative particles.

### Contributors

• CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.