In chemistry, what is a mole? A mole is how much 6.02 x 10(23) atoms weighs. (The 23 is to the power of as in 10(2) is 10 x 10. So 10(23) is 10 x 10 x 10 x and so on up to 23 times. It's a big freakin' number!) When you look at the periodic table, that number at the bottom is how a mole of that stuff weighs.
So if I have a mole of sodium, I have 23.0 grams of sodium. If I have a mole of carbon, I have 12.01 grams of carbon.
It isn't all about the pure elements! You can break anything down into moles; just add the components together. If I have a mole of water, I have 18.02 grams of water (hydrogen is 1.01 grams per mole and oxygen is 16.00 grams per mole, so H20 is 1.01 + 1.01 +16.00 grams). If I wanted to figure out a mole of oleic acid, I would multiply all the carbons by their atomic weight (18 x 12.01), all the oxygen by their atomic weight (2 x 16.00) and all the hydrogen by their atomic weight (17 x 1.01) and all them together to get the molar weight of 265.35 grams per mole.
Why do we care? Because molarity is all about the moles, and molarity will help us figure out the concentration of something! Concentration is defined as how much stuff is dissolved into the solvent, and that is something really vital to know! It can determine the strength of something - 10% salicylic acid, for instance, or 2 mole SLeS - or it can help us figure out how much we can dissolve into the solvent - for instance, 2 moles of salicylic acid or a 0.25 moles of Vitamin C at 25˚C. And concentration's all about the solublity!
Molarity works out to the number of moles divided by the number of litres, and this gives us the concentration of something. If we have 1 mole of sodium and 1 litre of water, the molarity of that solution is 1M. If we have 3 moles of sodium and one litre of water, it is 3M. 0.5 moles of sodium and one litre of water is 0.5 M.
If we have more or less than a litre, we would do the math. So 1 mole of sodium in 0.5 litres of water (1/0.5) would be 2M. 1 mole of sodium in 3 litres of water, would be 0.33M. And so on.
Molarity is always done in litres, so when you see 0.5M, you know that means 0.5 moles of something in 1 litre. We always get it back to 1 litre by doing some math on the numbers.
So when we look at a chart like this one on dissolving salicylic acid, we can figure out how much salicylic acid will dissolve into how much solvent by using molarity. First, figure out how much a mole of salicylic acid weighs - 138.12 grams per mole according to online sources. Then figure out how much we can use. If we look at line 17, it says that a mix of 25% PEG-400 and 75% water (to make a total of a litre) will result in 0.067M or molarity of 0.067 moles per litre. If we do a little math - 0.067 moles/litre x 138.12 grams = 9.25 grams per litre.
If we look at line 19, we see that a mix of 75% PEG-400 and 25% water results in 2.094 moles of salicylic acid dissolved in one litre of this solution, which means we can dissolve 289.22 grams per litre salicylic acid in this mixture. (2.094 moles/litre x 138.12 grams = 289.22 grams per litre)
Try doing a few of these calculations on your own. If we have 1 litre of ethanol and we have a molarity of 2.087 M, how much salicylic acid do we have?
2.087 M = 2.087 moles salicylic acid =
1 litre ethanol
2.087 M = 2.087 moles x 138.12 grams per mole = 285.25644 grams dissolved.
Try the next few on your own!
Knowing molarity helps you figure out how much of something can be dissolved in something else, and we all know how important that becomes when we're trying to make lovely things like toners and lotions and other things that we want to keep more liquid-y and less powdery!
Related links on molarity: