10.1: Avogadro's Number

Figure $\PageIndex{1}$ (Public Domain; User:OSX/Wikimedia Commons via Wikipedia)

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Avogadro's Number

It certainly is easy to count objects such as bananas, or something as large as elephants (as long as you stay out of their way). However, counting grains of sugar from a sugar canister would take 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 every 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 of the past needed a name that could stand for a very large number of items. Amadeo Avogadro (1776-1856), an Italian scientist, provided 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 $\PageIndex{2}$: Italian scientist Amadeo Avogadro, whose work led to the concept of the mole as a counting unit in chemistry. (Public Domain; C. Sentier via Wikipedia)

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 $\PageIndex{3}$: 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^rd (10/23) of each year. ((left; Left: Michael David Hill, 2005 (Mikiwikipikidikipedia); Right: [e-mail];(left) Michael David Hill, 2005 (Mikiwikipikidikipedia); (right) [e-mail] via Left: http://commons.wikimedia.org/wiki/File:Close-up_of_mole.jpg; Right: http://www.flickr.com/photos/chrisbrenschmidt/436990097;(left) http://commons.wikimedia.org/wiki/File:Close-up_of_mole.jpg; (right) http://www.flickr.com/photos/chrisbrenschmidt/436990097) CC-BY 2.5; (right) CC-BY 2.0)

Summary

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

Review

1. What is the SI unit for amount of a substance?
2. What is the representative particle for an element?
3. The formula unit is the representative particle for what?