Understand that amount of substance is an SI base quantity with the base unit mol.
Definition of the Mole
The mole is defined as the amount of substance that contains exactly $N_{\mathrm A}=6.02214076\times10^{23}$ elementary entities (atoms, molecules, ions, electrons, …). This number is the Avogadro constant.
Why the Mole is a Base Quantity
It provides a bridge between the microscopic world (atoms, molecules) and the macroscopic quantities we can measure (mass, volume, pressure).
It is independent of any other physical quantity; it is defined by a fixed numerical value of $N_{\mathrm A}$.
It is one of the seven SI base quantities alongside metre, kilogram, second, ampere, kelvin, candela.
Relationship to Mass
For a pure substance the mass $m$ of one mole is called the molar mass $M$, expressed in $\mathrm{g\,mol^{-1}}$.
$$
n = \frac{m}{M}
$$
where $n$ is the amount of substance in moles.
Common Molar Masses
Substance
Formula
Molar Mass $M$ (g·mol⁻¹)
Hydrogen gas
H$_2$
2.016
Oxygen gas
O$_2$
31.998
Carbon dioxide
CO$_2$
44.009
Water
H$_2$O
18.015
Sodium chloride
NaCl
58.44
Example Calculations
How many molecules are in $5.00\ \mathrm{g}$ of water?
First calculate the number of moles:
$$
n = \frac{5.00\ \mathrm{g}}{18.015\ \mathrm{g\,mol^{-1}}}=0.277\ \mathrm{mol}
$$
Then multiply by Avogadro’s number:
$$
N = n\,N_{\mathrm A}=0.277\times6.022\times10^{23}=1.67\times10^{23}\ \text{molecules}
$$
What mass of carbon dioxide corresponds to $2.5\ \mathrm{mol}$?
$$
m = nM = 2.5\ \mathrm{mol}\times44.009\ \mathrm{g\,mol^{-1}}=110.0\ \mathrm{g}
$$
Using the Mole in Gas Laws
In the ideal‑gas equation $pV=nRT$, the variable $n$ is the amount of substance in moles. This demonstrates how the mole links pressure, volume, and temperature to a count of particles.
Suggested diagram: A schematic showing the relationship between number of particles, moles, and mass for a sample of a substance.
Key Points to Remember
The mole is an SI base unit: $1\ \text{mol}=6.02214076\times10^{23}$ entities.
Molar mass $M$ allows conversion between mass and amount of substance: $n=m/M$.
Avogadro’s constant provides the quantitative link between the microscopic and macroscopic worlds.
In equations, $n$ always represents the amount of substance in moles.