Hello, Ian,
Remember Avogadro's number: 6.02 ×1023 atoms. It will come in handy for a future social encounter. [Just kidding - it is used in most science classes at some point.]
The important feature about this number is that it is a crucial conversion factor in the sciences. Avogadro's number is defined as one mole, of anything. It is most often used in measuring out chemicals for a reaction, but it is a generic term that can apply to anything, just like a "dozen" may mean eggs, coffees, people, etc. If I told you I have one mole of paperclips, you will understand I have 6.02 ×1023 paperclips. It's just a convenient shorthand for "I have exactly a lot of something."
The special value of the mole in science is that it can be used to count out numbers of molecules by using their atomic masses, instead of doing it by hand with an extremely small set of tweezers and enough time to bore Rip van Winkle. Reactions are written as individual molecules. 2H2 + O2 = H2O means two molecules of H2 and one of O2 combine to make one H2O. Fun, but impractical when you actually want to make some.
Avogadro's number and the concept of mole allows one to determine the numbers of molecules based on their mass. That's because it was discovered that 6.02 x 1023 atoms or molecules is equal to the AMU of that material, but expressed as grams, instead. Carbon has a mass of 12 AMU. If you measure out 12 grams of C, you'll have one mole of carbons. Water has an AMU of 18. Again, if you measure out 18 grams of H2O, you have one mole of water molecules. Amazing! You'll use this knowledge a lot in science, so think it through and internalize it.
In this problem, you are asked how much mass do you have in 6.27 x 1023 atoms of Cl. I'll assume you mean Cl and not Cl2 (chlorine naturally exists in a diatomic state). Be aware if it is Cl2, the calculation would be different because it's mass is twice that of Cl.
The mass of a single Cl is 35.45 AMU. I can state that one mole of Cl has a mass of 35.45 grams. So the relevant conversion factor is 35.45 g Cl/1 mole Cl.
Change "mole" to actual numbers of atoms and you can then determine the mass of the collection you brought:
(35.45 grams Cl)/(6.02x1023 atoms Cl) * (6.27x1023 atoms Cl)
((
The "atoms Cl" unit cancels, leaving just grams Cl. : (35.45 grams Cl) *(6.27x1023)/6.02x1023)
This equals 35.45 grams Cl times 1.04 [3 sig figs] = 36.9 grams Cl.
This makes sense. It is slightly larger than 1 mole. We had slightly more than one mole of Cl atoms.
I hope this helps. Again, check on whether the molecule was Cl or Cl2, just to be sure. If it is Cl2, everything is the same except the conversion is then 70.9 g/mole.
Bob
