Importantly, in science (mostly chemistry), one mole (shortened to mol) is a number: approximated to 6.02x1023. A mole can be used to measure anything: a mole of trees is 6.02x1023 trees; a mole of people is 6.02x1023 people, half a mole of dust mites is 3.01x1023 dust mites.
This magical figure of 6.02x1023, also called Avogadro's Constant, was arrived at when experiments found that, in exactly 12 grams of the element carbon (or more, correctly, the isotope carbon-12), there were 6.02x1023 carbon atoms.
The symbol for amount is n. Using this number is quite useful in stoichiometry, taught to Year 11 (or equivalent) students in secondary school. The mole can be used in several equations to allow counting by weighing. The equations are
- Solid matter: n=m/M
- Matter in solutions: n=cv
- Gases with certain conditions: n=V/Vm
- General gases: PV=nRT
with m being mass (in grams, not kilograms); M being molar mass, c being concentration, v being volume, Vm being molar volume, P being atmospheric pressure, R being a gas constant and T being temperature.
The molar mass, relative atomic mass, or relative molecular mass of a chemical compound is equal to all the atomic masses of the respective elements. For example, H2O, water, has a molar mass of 18 g mol-1, since oxygen's is 16 and hydrogen's is 1. Other values can be found on any periodic table.
Concentration is in mol L-1 (or M), volume is in L, pressure is in Pa, temperature is in K, and the gas constant R has a value of 8.31. Vm has a value of 24.5 at SLC (pressure 1 atm, temperature approx. 298K) and 22.4 at STP (pressure 1 atm, temperature approx. 273K).
So, say you have weighed out 20g of pure sulfur, with the formula S. It's easy to work out 'M', and you already have 'm', so just substitute these values into the appropriate equation. Thus: n=20/32=5/8, which is five-eighths of a mole. How many particles of sulfur are there? 6.02x1023*5/8. Easy. Try it yourself one day: weigh out a small amount of table salt, substitute that into the first equation, and use 63 as the value for M. Or, weigh out some baking soda (NaHCO3, with the value of M being 84).
It's the same with solutions: weigh some sugar, and calculate n from the first formula (taking M to be 342), then stir it into some water that you know the volume of, in litres. Take the value for n you found in the first formula, rearrange the second formula to give c=n/v, then divide accordingly. You'll end up with a concentration in M.
What do you get as a reward for all this hard effort? You get to drink the sugar water.