A mole is a number representing an amount of a substance (like a dozen or a six-pack) and is equal to the number of atoms in exactly 12 grams of the ¹²C isotope of carbon.

How many would that be? 6.022 x 10²³, a number determined experimentally based on a gas law proposed by Amedeo Avogadro and thus named for him - Avogadro's number. A mole of anything, atoms, molecules, etc., is 6.022 x 10²³ atoms, or molecules or whatever you're talking about.

So what? What's the big deal about a mole? Well, if you were weigh an amount of any element equal to its atomic weight in grams and then you were to measure the number of atoms in that amount it would be equal to Avogadro's number of atoms. That's a fairly cool deal - 1 gram of ¹H contains 6.022 x 10²³ atoms of the ¹H isotope of hydrogen, 23 grams of Na contains 6.022 x 10²³ atoms of the ²³Na isotope of sodium, etc.

The molarity of a solution is the number of moles of solute per liter of solution. To show that the number represents molarity it is followed by M. A one molar solution (1 M) contains one mole of solute per liter of solvent.

Let me give you an example.

Suppose you want to know how to make that fine old southern beverage sweet tea.

Adjusting the amount of tea you brew and the intricacies of the brewing method (the "bring the water almost to a boil, remove from heat, pour over tea bags" vs. the "boil the tea bags repeatedly until you extract every last molecule of anything in them" schools of thought along with the proper steeping time and vessel) until you are happy can go on for a lifetime, but it should be fairly easy to at least get some information on the amount of sugar to add.

That depends. When I ask I usually get answers like "Well I add about two cups". Hmmm... Two cups of sugar to how much tea? Then I'll get a response like "Two cups of sugar to a pitcher, what else?".

Great, I was thinking two cups of sugar to a 55 gallon drum - What sized pitcher?!?!?

"Oh, well, I don't know, I guess one about this big" indicating the volume of the pitcher with their hands. You couldn't protect state secrets from spies any better.

Well, I'm going to have you give it away: Homework assignment - calculate the molarity of sweet tea.

Hint: Table sugar, or sucrose, is a disaccharide consisting of one glucose molecule joined to one fructose molecule. The monosaccharides glucose and fructose are isomers and have the same chemical formula (more on this later): C₆H₁₂O₆ .

All you have to do is figure out the molecular weight of sucrose in grams (add the atomic mass of all the atoms), which gives you the weight of a mole of sucrose. Then figure out how many grams of sugar you'll add to your pitcher (another hint - one cup dry measure is 8 ounces, or 1/2 lb. and there are 454 grams in 1 lb.) and convert the number of grams you want to moles.

Then figure out how many liters that pitcher holds, divide moles by liters and there you have it, the molarity of sweet tea.

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