# How do you work out moles? I need an explanation. My teacher isn't helping me on it...

A mole (otherwise known as "Avogadro's Number," first determined by Italian scientist Amadeo Avogadro (1776-1856) ) is a specific, extremely large number, like a million (1 * 10^6) or a billion (1* 10^9).  If you count atoms, molecules, marbles, or cars, and have 6.02 * 10^23 of them, you've got a mole. Consider it just like any ordinary number with which you can add, subtract, multiply, or divide. If you take the atomic mass of an element, which is unitless, and specify that atomic mass as a number of grams, by definition, you've got 1 mole of that element. If you've got a solid of so many grams, you can calculate the number of moles by remembering that grams / grams per mole = # of moles. If you've got a gas, the constant to remember is 22.4 liters / mole.

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How many moles of silicon are in 4.60 g of Si? This is the first venture into one of the most common chemical calculations, finding the number of moles present in a given mass of substance. Restate it: 4.60 g Si <=> ? mol Si                         The atomic mass (you need this for each element in your problems, too) of silicon, 28.09 (rounded from 28.0855), gives us the needed tool, because we know from the definition of the mole that the following is true about silicon.            28.09 g Si <=> 1 mol Si     Like any equivalency, this one makes available two conversion factors.  One will be the tool we need for our grams-to-mole conversion.  28.09 g Si/1 mol of Si and 1 mol Si/28.09 g Si or:

28.09 g Si  and   1 mol Si

1 mol Si           28.09 g Si

Thus if we multiply the given, 4.60 g Si, by the second conversion factor, we will obtain the answer. Solution:  We carry out the following calculation.  Notice how the units, g Si, cancel to leave the correct unit, mol Si (Draw in the cancel lines yourself).

4.60 g Si x  1 mol Si/28.09 g Si  = 0.164 mol Si

In other words, 4.60 g Si <=> 0.164 mol Si.  Now, check to see if the answer makes sense.  Is its numerical size in the right range?  Yes, because we began with 4.60 g Si, clearly less than a whole mole of silicon, so the answer has to reflect this obvious fact. The atomic mass=1 mole.

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