One mole of anything is Avogadro’s number of that thing. If we know the number we have of something, we can find out how many moles we have by dividing by the number in a mole—that is, by Avogadro’s number.

In chemistry, many of us like to set the problem up in a way that is mathematically equivalent but which emphasizes that we are talking about the same quantity expressed two different ways, in units and in number(s) of moles. We begin with an equation expressing that 1 mole of anything is equal to Avogadro’s number of that thing:

1 mol = 6.02 x 10^23

We note that since the two sides of the equation are equal, if we divide one side by the other side, we get 1. Thus

(1 mol)/(6.02 x 10^23) = 1

We can multiply anything by 1 without changing its value. We call this a “conversion factor” because it converts the units while leaving the value unchanged. We will start with the quantity we are * given*, and multiply by this conversion factor to express the same quantity in moles. We are given 16 oranges, so

(16 oranges) x ((1 mol)/(6.02x10^23)) = 2.66 x 10^-23 mol oranges

Now you can convert units, as long as you are talking about the same things on both sides. We can convert oranges to moles of oranges, but we cannot convert bananas to moles of persons. If you wanted to know how many moles of bananas you had, you would evaluate that very large number, then convert (as with the oranges), or else divide by Avogadro’s number to get moles.

27^14 bananas = 1.09 x 10^20 bananas. If you divide this by Avogadro’s number, you get 1.82x 10^-4 moles of bananas. Again, no mathematical operation will take you from bananas to humans.

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