Fundamentals of Chemistry

The mole is the amount of a substance that contains as many elementary entities as there are atoms in $\text{12 g}$ of carbon-12. Those entities are not always atoms; they can be molecules, formula units, ions or electrons, and the number of them in one mole is fixed at Avogadro's number, $N_A = 6.02 \times 10^{23}$ (the exact value is $6.02214179 \times 10^{23}\ \text{mol}^{-1}$, and papers almost always use the rounded form). Carbon-12 is the reference standard against which relative masses are measured, so one mole of $\text{CCl}_4$ carries $6.02 \times 10^{23}$ molecules while one mole of $\text{Na}^+$ carries $6.02 \times 10^{23}$ ions. The identity of the particle changes; the count never does.

Molar mass, written $M$, is the mass of one mole expressed in grams, and its unit is $\text{g mol}^{-1}$. It is built by adding the atomic masses of the component atoms, so the molar mass of $\text{CCl}_4$ is $12.0 + 4(35.5) = 154.0\ \text{g mol}^{-1}$. Because the same single number is shared by every mole of every substance, the amount of a sample follows directly from its mass: $n = m/M$. This is the conversion that opens every calculation in the rest of the chapter. A single atom weighs its molar mass divided by $N_A$, which is why one atom of sodium is $1/N_A$ mole and not $23\ \text{g}$.

Be careful with the mass unit itself. The atomic mass unit is $1.66 \times 10^{-27}\ \text{kg}$, not a mass of hydrogen and not a multiple of the electron mass. The mass shown on the periodic table is an average over the isotopes, so no individual neon atom in a sample weighs 20.18 amu; that figure is the average atomic mass and it belongs to the bulk, not to any one atom.