The Mole

Avogadro’s Number

Define mole.
Define Avogadro’s number.

It is often convenient to have a unit for large amounts, such as a mole

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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.

Avogadro’s Number

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 every second for 50 years without stopping you would have counted only 1.6 × 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. Amedeo 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 (mol) is the amount of a substance that contains 6.02 × 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 × 10 ²³ water molecules in a mole of water molecules. There also would be 6.02 × 10 ²³ bananas in a mole of bananas, if such a huge number of bananas ever existed.

Figure 10.1

Italian scientist Amedeo Avogadro, whose work led to the concept of the mole as a counting unit in chemistry.

The number 6.02 × 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 H ₂ , N ₂ , O ₂ , F ₂ , Cl ₂ , Br ₂ , and I ₂ . The representative particle for these elements is the molecule. Likewise, all molecular compounds such as H ₂ O and CO ₂ exist as molecules and so the molecule is their representative particle. For ionic compounds such as NaCl and Ca(NO ₃ ) ₂ , the representative particle is the formula unit. A mole of any substance contains Avogadro’s number (6.02 × 10 ²³ ) of representative particles.

The animal mole is very different from the unit mole

Figure 10.2

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 23rd (10/23) of each year.

Summary

A mole of any substance contains Avogadro’s number (6.02 × 10 ²³ ) of representative particles.

Practice

Questions

Use the link below to answer the following questions:

http://www.scientificamerican.com/article.cfm?id=how-was-avogadros-number

What was Avogadro’s hypothesis?
Who first calculated this number?
Who coined the term “Avogadro’s number”?
What contribution did Robert Millikan make to the determination for the value for the number?

Review

Questions

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

Avogadro’s number: The number of representative particles in a mole, 6.02 × 10 ²³ .
mole (mol): The amount of a substance that contains 6.02 × 10 ²³ representative particles of that substance.
representative particle : The smallest unit in which a substance naturally exists.

Conversions Between Moles and Atoms

Perform calculations involving conversions between number of moles and number of atoms or molecules.

Using moles allows us to avoid superscripts and subscripts

Big numbers or little numbers?

Do you hate to type subscripts and superscripts? Even with a good word-processing program, having to click on an icon to get a superscript and then remembering to click off after you type the number can be a real hassle. If we did not know about moles and just knew about numbers of atoms or molecules (those big numbers that require lots of superscripts), life would be much more complicated and we would make many more typing errors.

Conversions Between Moles and Atoms

Conversions Between Moles and Number of Particles

Using our unit conversion techniques, we can use the mole label to convert back and forth between the number of particles and moles.

Sample Problem 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 × 10 ²⁴ atoms of carbon?

Step 1: List the known quantities and plan the problem.

Known

number of C atoms = 4.72 × 10 ²⁴
1 mole = 6.02 × 10 ²³ atoms

Unknown

4.72 × 10 ²⁴ = ? mol C

One conversion factor will allow us to convert from the number of C atoms to moles of C atoms.

Step 2: Calculate.

$4.72 times 10^{24} text{atoms C} times frac{1 text{mol C}}{6.02 times 10^{23} text{atoms C}}=7.84 text{mol C}$

Step 3: Think about your result.

The given number of carbon atoms was greater than Avogadro’s number, so the number of moles of 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.

Suppose that you wanted to know how many hydrogen atoms were in a mole of water molecules. First, you would need to know the chemical formula for water, which is H ₂ O. There are two atoms of hydrogen in each molecule of water. How many atoms of hydrogen would there be in two water molecules? There would be 2 × 2 = 4 hydrogen atoms. How about in a dozen? In that case a dozen is 12 so 12 × 2 = 24 hydrogen atoms in a dozen water molecules. To get the answers, (4 and 24) you had to multiply the given number of molecules by two atoms of hydrogen per molecule. So to find the number of hydrogen atoms in a mole of water molecules, the problem could be solved using conversion factors.

$1 text{mol} text{H}_2text{O} times frac{6.02 times 10^{23} text{molecules} text{H}_2text{O}}{1 text{mol} text{H}_2text{O}} times frac{2 text{atoms H}}{1 text{molecule} text{H}_2text{O}}=1.20 times 10^{24} text{atoms H}$

The first conversion factor converts from moles of particles to the number of particles. The second conversion factor reflects the number of atoms contained within each molecule.

Figure 10.3

Two water molecules contain 4 hydrogen atoms and 2 oxygen atoms. A mole of water molecules contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms.

Sample Problem 2: Atoms, Molecules, and Moles

Sulfuric acid has the chemical formula H ₂ SO ₄ . A certain quantity of sulfuric acid contains 4.89 × 10 ²⁵ atoms of oxygen. How many moles of sulfuric acid is the sample?

Step 1: List the known quantities and plan the problem.

Known

4.89 × 10 ²⁵ = O atoms
1 mole = 6.02 × 10 ²³ molecules H ₂ SO ₄

Unknown

mol of H ₂ SO ₄ molecules

Two conversion factors will be used. First, convert atoms of oxygen to molecules of sulfuric acid. Then, convert molecules of sulfuric acid to moles of sulfuric acid.

Step 2: Calculate.

$4.89 times 10^{25} text{atoms O} times frac{1 text{molecule} text{H}_2text{SO}_4}{4 text{atoms O}} times frac{1 text{mol} text{H}_2text{SO}_4}{6.02 times 10^{23} text{molecules} text{H}_2text{SO}4}=20.3 text{mol} text{H}_2text{SO}_4$

Step 3: Think about your result.

The original number of oxygen atoms was about 80 times larger than Avogadro’s number. Since each sulfuric acid molecule contains 4 oxygen atoms, there are about 20 moles of sulfuric acid molecules.