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What is a mole and why are moles used?
A mole is a way of counting things. In the early days of chemistry, scientists realized that atoms and molecules react with each other in whole number ratios. That is one atom of something would react with 1 atom or 2 atoms or 3 atoms of something else, but never with, say, 1.33 atoms. Thus, they needed some way to count these atoms and/or molecules when they measured them out for their reactions.
Eventually, they figured out the relative masses of atoms. They knew, for example, that an atom of oxygen has sixteen times the mass of a hydrogen atom. Thus, if they measured out 1 g of H atoms and 16 g of O atoms, they knew they had the same number of atoms of each, even if they didn’t know what that number was. Here begins the concept of . Eventually, they decided to use exactly 12 g of carbon-12 as their standard. It would contain a fixed number of atoms (now called a mole of atoms). If they then measured out 16 g of O atoms, which have a mass ¹⁶/₁₂ times that of a carbon-12 atom, they knew that they had the same number of atoms (a mole of each).
So a mole is simply a way of counting atoms and molecules. We now know the relative masses of all the compared with carbon-12, so by measuring masses in the right proportions, we can make sure that the numbers of atoms and molecules are in the desired proportions as well.
The number of grams in a mole is different from substance to substance. If you're new to chemistry, you may find this confusing. Picture it this way: a dozen elephants have a different mass than a dozen rabbits but, in each case, you have the same number of each (a dozen). Similarly, a mole of oxygen gas has a different mass than a mole of hydrogen gas but, in each case, you have the same number (a mole) of molecules of each.
For many years, chemists worked happily without knowing exactly how many particles there were in a mole. All they had to know was the relative numbers of the molecules.
The problem was that individual molecules are so tiny that it is impossible to count them individually. Moles were devised to solve the problem of counting large numbers of molecules. With moles, you count the number of molecules in a sample by determining the mass of the sample.
We now know how many particles there are in a mole. That number is Avogadro's Number, which is roughly 6.022 × 10²³. A mole of carbon atoms is 6.022 × 10²³ carbon atoms. A mole of chemistry teachers is 6.022 × 10²³ chemistry teachers. It's a lot easier to write the word “mole” than to write “6.022 × 10²³” anytime you want to refer to a large number of things! Basically, that's why this particular unit was invented.
Why don't we simply stick with units like grams (and nanograms and kilograms, etc.)? The answer is that moles give us a consistent method for converting between atoms/molecules and grams. It's simply a convenient unit to use when performing calculations. You may not find it too convenient when you are first learning how to use it, but once you become familiar with it, a mole will be as normal a unit as, say, a dozen.
Here's a video which summarizes how to complete a mole calculation.