understand that amount of substance is an SI base quantity with the base unit mol

The Mole

Learning Objective

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

Example Calculations

1. 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}

   \$\$

2. 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.

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.