Mole Calculations

Molecules and atoms are so small that we need to count them in larger quantities than one at a time. People rarely cook only one egg, so they are sold in quantities of 12 at a time. Paper clips are sold in boxes of 100. Paper is sold in reams. In chemistry, everything is measured in moles. A mole is 6.022 x 10^23 just like a dozen is 12.

Calculating the number of things:

You could have a dozen roses or a dozen doughnuts or a dozen eggs. Similarly, you could have a mole of water or a mole of hydrogen or a mole of doughnuts or a mole of eggs. It's just a number of things (a big number!).

Example: How many doughnuts are in 4.0 moles of doughnuts?

4.0 moles * 6.022 x 10^23 doughnuts/1 mole = 2.4 x 10^24 doughnuts

Notice that this is simply a unit conversion. All mole calculations are. 6.022 x 10^23 is an identity of the number of doughnuts in one mole. The identity was positioned so that the moles would cancel. In the following example, the identity will be upside down to cancel the things instead.

Example: If you have 8.9 x 10^25 paper clips, how many moles of clips is this?

8.9 x 10^25 clips * 1 mole/6.022 x 10^23 clips = 150 moles

Calculating the mass of things:

We can't see one water molecule, much less find it's mass. We need to use the mass of a mole of water molecules instead. The identity that we used in the previous examples was how many things were in a mole of that thing. Now we will use the identity of how much mass a mole of things has. For instance, a mole of water has a mass of 18.0 g. A mole of carbon dioxide has a mass of 44.0 g.

Example: What is the mass of 2.6 moles of carbon dioxide?

2.6 moles * 44.0 g/1 mole = 110 g

Example: How many moles of water have a mass of 6.43 g?

6.43 g * 1 mole/18.0 g = .357 mole

Example: How many molecules of water have a mass of 5.4 g?

5.4 g * 1 mole/18.0 g * 6.022 x 10^23 molecules/ 1 mole = 1.8 x 10^23 molecules

Ready for a quiz? Answers are on the answer page as usual.

Mole Quiz:

1. How many roses do you have if you have .25 mole?
2. How many moles of hydrogen atoms is 4.5 x 10^36 atoms?
3. How many years would it take you to count 3 moles of pennies at a speed of 2 pennies every second?
4. Every water molecule has 2 hydrogen atoms in it. How many hydrogen atoms are in 5 moles of water?
5. What is the mass of 7.5 moles of carbon dioxide (44.0 g/1 mole)?
6. How many molecules of carbon dioxide have a mass of 72.0 g?

Mole calculations are just like converting from inches to feet or counting piles of ten and then multiplying by ten. If this still seems foreign to you, read back through the examples above. If you are still having trouble, feel free to contact me at 651-486-9697 or jcaskey@ties.k12.mn.us

Also, for more information, visit Mr. Logan's page on mole calculations.

Return to introduction page here.