# Moles

Overview: In this module, we introduce the mole, a unit of measure that is used extensively in chemistry. The interconversion between mass, moles, number of atoms or molecules, and volume is described.

### Skills:

• Determining the number of moles in a given mass of a sample
• Converting sample mass to the number of molecules or atoms
• Using the density to relate volume to number of moles

### New terms:

• Mole
• molecular mass
• molar mass
• density (r)

#### Moles

What is a mole? Basically a mole is defined as Avogadro's number of anything. Avogadro's number, denoted by the symbol NA is 6.022 x 1023.

Fine, but what does this have to do with chemistry? That's a fair question. Maybe this will help. Imagine that you are a chemist and you would like to measure out 6.022 x 1023 molecules of ethanol. If you didn't know better, you might think that you had to somehow count out all of these molecules individually. But this is far too time consuming and expensive. Besides you probably wouldn't live long enough to finish. (It would take almost 2 x 1016 years to do this. Even if a billion people worked together to count out the molecules you wouldn't be able to finish even close to within your lifetime.)

Since 6.022 x 1023 ethanol molecules are needed, we simply need to measure out one mole of ethanol, but how do we do that? Let's redefine a mole. A mole is any item that contains the same number of that item as the number of atoms in exactly 12 g of 12C. This means that in 12 g of C there are exactly 6.022 x 1023 atoms of carbon. Each atom of C has a mass of 12 amu's, which means that:

Now we are getting somewhere. Ethanol is CH3CH2OH. Its total mass is 46 u:

How does this help us measure out 6.022 x 1023 molecules of ethanol? As we said before, 1 g = 6.022 x 1023 u.

Therefore we only need to measure 46 g of ethanol to get 6.022 x 1023 molecules or 1 mol of ethanol. This is a lot easier than counting out all those molecules.

The molecular mass of a molecule is measured in g/mol. In this case, ethanol's molecular mass is 46 g/mol. This means that in 1 mol of ethanol, there are 46 g, thus the term molecular mass and molar mass are often used interchangeably.

When thinking about a mole, think of it like a dozen. A dozen of anything is 12 of that item:

a dozen eggs = 12 eggs
a dozen N atoms = 12 N atoms
a dozen ethanol molecules = 12 ethanol molecules

The same is true of a mole. A mole of anything is 6.022 x 1023 of that item.

a mol of ethanol molecules = 6.022 x 1023 ethanol molecules
a mol of N atoms = 6.022 x 1023 N atoms
a mol of eggs = 6.022 x 1023 eggs

#### Example 1.

How many molecules of ethanol are in 89.0 g of ethanol?

Here are a few hints to use in solving this type of problem:

1. Start by writing the given information, including the units.
2. Next determine what you are trying to solve and what units it will be in.
3. Use conversion factors to cancel out units and get to your final units.

So in this example 89.0 g of ehtanol are given. We want molecules of ethanol to answer the question. Now we need to come up with conversion factors to cancel units and get to the desired set of units. Molecular mass is g/mol. This can be used to cancel out the given number's units. In order to cancel units, multiply by the reciprocal of the molecular mass. Avogadro's number can be used to cancel out the moles and leaves molecules of ethanol units. This is why using units is very imporatant. Also, remember to use the correct number of significant figures.

#### Example 2.

How many carbon atoms are in 89.0 g of ethanol (CH3CH2OH)?

Again, we used the same gram to mole conversion factor, the molecular mass, and also Avogadro's number to go from moles to atoms. Notice that there is an extra conversion in this equation. In each molecule of ethanol there are two carbon atoms. This also means that for each mole of ethanol there are two moles of carbon.

#### Example 3.

How many molecules of ethanol are in 1.0 L of ethanol at 1 atm and 25oC?

To answer this we will need a volume to mass conversion factor. This is defined as density (denoted by the Greek letter rho, r) and is in units of g/mL. Density is both temperature and pressure dependent; both need to be specified to know the density for a given substance. At 25oC and 1 atm pressure, the density of ethanol is r = 0.789 g/mL.
So back to the question:

#### Summary

Now you should see how moles are related to mass, density, and number of molecules or atoms. You should now understand what a mole is and how it is associated with Avogadro's number.

#### Practice Quiz: Moles

Note: You will need a pencil, scratch paper, calculator, periodic table and equation sheet to work the practice quiz. Quizzes are timed (approximately 4 minutes per question).

We suggest that you print out the periodic table and the constants/equations page before starting the quizzes.

Open Periodic Table in a separate browser window.

Open Equations/Constants Page in a separate browser window.