M l and Moles d Numbers N b There are times when we want to deal with the actual number of atoms or molecules in a sample, p , not jjust in the total amount of moles. To do this you need the relationship 1 mole = 6.022x1023 things. This number seems a bit arbitrary and is called Avogadro’s number. You do not need to memorize this number because I include it on a sheet of constants I distribute with all of my tests. M l and Moles d Numbers N b Avogadro’s number is a very big number. It is useful for calculation involvingg atoms and molecules,, but it is a really y bad number to use for counting things that are any bigger that atoms or molecules. Let’s work a couple of problems to try to get a feel how big this number is. First, what is the volume of 1 mole or 6.022x1023 molecules of water? M l and Moles d Numbers N b What is the volume of 1 mole or 6.022x1023 molecules of water? Using the molar mass of water = 1(16) + 2(1.008) = 18.002g you can quickly come up with the fact that 1 mole of water x (18.002 g/1mole) = 18.002 g of water Remembering that water has a density of 1 or 1 g = 1 ml You can take this a bit farther 18.002 g of water x (1 ml/1g) = 18.002 ml of water (that is a little over a tablespoon!) M l and Moles d Numbers N b Now how many molecules of water are there in this 18 g of water? 18 g x (1 mole/18g) x (6.022x1023 molecules/mole) = 6.022x1023 molecules M l and Moles d Numbers N b Now let’s try it the other direction. How many atoms are there in a ngg of Mercury? y First do you remember how much a ng is? n = nanonano so this is 1 nanogram of Mercury a nano is 1x10-9 so 1 ng = 1x10-9 g or .000000001 g M l and Moles d Numbers N b How many atoms are there in a ng of Mercury? Mercury (Hg) has an atomic mass of 200.6g so that will convert grams to moles, and we have Avogadro’s number 6 022x1023 atoms = 1 mole, 6.022x10 mole so we have all the conversion factors we need to finish the problem. 1x10 − 9 g 1 mole Hg 6.022 x10 23 atoms 1 ng Hg × × × 1 ng 200.6 g Hg 1 mole = 3x1012 atoms t M l and Moles d Numbers N b How many atoms are there in a ng of Mercury? So even though we are dealing with only .000000001 g of Mercury still have 3x1012 or 3,000,000,000,000 atoms. Like I said earlier, 6.022x1023 is a BIG number.