A critical concept in chemistry is the idea of a mole. A mole is a method of counting collections of discrete chemical objects such as atoms or molecules. Often people say a mole is just like a dozen. While technically this is true as they are both simply a new name for a particular number of objects, this misses the key point that the mole comes about not simply from counting but from the fact that chemical units such as these are much too small for us to see and count. **This means that we need a method that links the macroscopic world in which we operate to the microscopic world of atoms.** Thus we arrive at the mole.

The IUPAC has pretty much now made all fundamental physical constants and quantities to be based on some physical phenomenon and the numbers are SET and exact. As of May 20, 2019, the Avogadro number, which is shown symbolically as \(N_{\rm A}\), is *exactly* equal to 6.02214076 × 10^{23}. No longer is the mole based on the number of atoms in 0.012 kg of carbon-12 which happens to depend on the kilogram. Now, the Avogadro number is an exact number with no plus or minus anything. An exact number! Infinitely precise.

the *exact definition* of a **mole** is based on the Avogadro Number which is

*N*_{A} = 6.02214076 × 10^{23}

That many elementary particles, be they atoms, molecules, ions, photons, etc., is known as a mole of that substance or entity.

IUPAC's wording: One mole contains exactly 6.02214076 × 10^{23} elementary entities.

No need to recalibrate your brain though. The number was chosen such that is happens to still equal the number of atoms in 0.012 kilograms of carbon-12. Plus to help out even more, the kilogram is now based on Planck's constant and not on an object stashed away somewhere on earth (an artefact). So we still might reference the old definition at times, but know that the mole is an *exact* number of things now. Preferably, those things are atoms, ions, or molecules - which is what we deal with in chemistry.

Hey, just for fun, lets write Avogadro's number as an integer and not in scientific notation:

602,214,076,000,000,000,000,000

Wow! Now you see why we use scientific numbers. And we say stuff like "a mole of carbon"... which is leaps and bounds better than saying the equivalent statement, "six hundred two sextillion two hundred fourteen quintillion seventy-six quadrillion atoms of carbon". Let's hear it for the mole and Avogadro's number... woo hoo!

The following information is here for historic purposes. So do understand, the following is NOT the definition of the mole anymore.

Old Definition: **The mole is the number of carbon atoms in 12 grams of C-12** (a particular isotope of carbon with a particular mass). We pick this number to allow for simple conversions between numbers of atoms (which are really, really hard to count) and the mass of the sample in grams (which is really easy to measure with a balance). Since different atoms have different masses, if we know the mass of the atom relative to that of C-12, we can know the mass of one mole of that atom. This is true for any atom or compound. For example since H_{2} has a mass which is about 6 times less than that of C, then any sample in which we have an equal mass of H_{2} and C must have 6 times as many H_{2} molecules as C atoms (and consequently six times as many moles) since each H_{2} molecule has a mass that is 6 times smaller. The choice of grams and C-12 as a reference is simply that “a choice”. If you are interested in the history of these choices you can research this topic online. Just be happy that we are no longer using the *pound mole* which is defined as the number of atoms is one pound of C-12 (except the engineers who refuse to change) or that we use O-16 as a standard.

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