# How should I study about moles and how they relate to things like Avogadro's number and molar mass?

Nov 6, 2016

Warning! Long answer, but here is my revisionist view of chemical history.

#### Explanation:

Since the early days of chemistry, chemists could figure out the relative masses of atoms.

For example, they knew that a $\text{C}$ atom had a mass 12 times that of an $\text{H}$ atom, an $\text{O}$ atom had 16 times the mass of an $\text{H}$ atom, and so on.

For argument's sake, let's assume that they could put a "pile" of atoms on a balance and determine their total mass.

Then, if they measured out say, 1 g of hydrogen, 12 g of carbon, and 16 g of oxygen, they knew they had the same number of atoms in each pile, even if they didn’t know how many atoms or their individual masses.

They decided to use $\text{H}$ as their standard pile with a mass of 1 g. The pile became a mole, after the Latin word for a pile of rocks.

Even today in England, which was occupied by the Romans, a pile of stones used as a breakwater is called a "mole".

It was natural to assign to each atom an atomic mass that had the same number as the mass of its mole.

Thus, the atomic masses became 1 unit for $\text{H}$, 12 units for $\text{C}$, and 16 units for $\text{H}$.

Eventually, chemists figured out how many atoms there are in a mole of atoms, and they called it Avogadro's Number (${N}_{\text{A}}$).

${N}_{\text{A" = 6.022 × 10^"23"color(white)(l) "per mole}}$

Then, if one mole of $\text{H}$ atoms had a mass of 1 g, one atom must have had a mass of

$\text{1 g"/(6.022 × 10^"23" "atoms") ≈ 1.6 × 10^"-24" color(white)(l)"g}$

Today, we use carbon-12 atoms as our standard, and we define a mole (symbol mol) of carbon-12 as exactly 12 g of carbon-12.

We say that the molar mass of carbon-12 is exactly 12 g.

Since it contains Avogadro's number of atoms,

A mole of anything (atoms, molecules, ions, people, etc.) is Avogadro's number of those things.

The mass of an atom of carbon-12 is defined as exactly 12 unified atomic mass units (symbol u).

Thus the atomic mass of a carbon-12 atom is exactly 12 u (not amu).

Summary: The mole is a convenient way to measure a desired number of atoms or molecules.