12.7.1: Moles and Avogrado's Number
- Page ID
- 476600
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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.
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.
Conversions Between Moles and Atoms
Using our unit conversion techniques, we can use the mole label to convert back and forth between the number of particles and moles.
Example \(\PageIndex{1}\): Converting Number of Particles to Moles
The element carbon exists in two primary forms: graphite and diamond. How many moles of carbon atoms is \(4.72 \times 10^{24}\) atoms of carbon?
Solution
Step 1: List the known quantities and plan the problem.
Known
- number of \(\ce{C}\) atoms \(= 4.72 \times 10^{24}\)
- \(1\) mole \(= 6.02 \times 10^{23}\) atoms
Unknown
- 4.72 x 1024 = ? mol C
One conversion factor will allow us to convert from the number of \(\ce{C}\) atoms to moles of \(\ce{C}\) atoms.
Step 2: Calculate.
\[4.72 \times 10^{24} \: \text{atoms} \: \ce{C} \times \frac{1 \: \text{mol} \: \ce{C}}{6.02 \times 10^{23} \: \text{atoms} \: \ce{C}} = 7.84 \: \text{mol} \: \ce{C}\nonumber \]
Step 3: Think about your result.
The given number of carbon atoms was greater than Avogadro's number, so the number of moles of \(\ce{C}\) atoms is greater than 1 mole. Since Avogadro's number is a measured quantity with three significant figures, the result of the calculation is rounded to three significant figures.
Section Summary
- A mole of any substance contains Avogadro's number \(\left( 6.02 \times 10^{23} \right)\) of representative particles.
- Methods are described for conversions between moles, atoms, and molecules.