3.4 - The Mole
The mole and the mass of one mole
- Atoms are far too small to count individually, so chemists count by weighing.
- The counting unit is the mole (symbol mol) - a fixed number of particles, just as a dozen is a fixed number of items.
- The particles can be atoms, molecules, ions, electrons or formula units - whichever the substance is made from.
- The quantity measured is the amount of substance, measured in moles.
Working out the mass of one mole
The mass of one mole of a substance is its relative formula mass (or relative atomic mass) in grams.
| Substance | Relative atomic or formula mass | Mass of one mole |
|---|---|---|
| Carbon, C | 12 | 12 g |
| Nitrogen gas, N2 | 2 × 14 = 28 | 28 g |
| Carbon dioxide, CO2 | 12 + (2 × 16) = 44 | 44 g |
12 g of carbon, 28 g of nitrogen gas and 44 g of carbon dioxide each hold one mole of particles, even though their masses differ.
Relative formula mass vs molar mass
- Relative formula mass is a comparison, so it has no units (for CO2, it is 44).
- The mass of one mole is measured in grams - 44 g for CO2. The molar mass is the mass per mole, measured in g/mol - 44 g/mol for CO2.
- Its value is always numerically identical to the relative formula mass.
Formula for amount of substance
Where:
- Amount of substance is in moles (mol)
- Mass is in grams (g)
- (or ) = Relative formula mass (or relative atomic mass)
Convert masses in kilograms or tonnes to grams before calculating (1 kg = 1,000 g; 1 tonne = 1,000,000 g).
Worked example - Amount in a given mass
A sample of sodium chloride, NaCl, has a mass of 25 g. The relative atomic masses are Na 23 and Cl 35.5. What amount of sodium chloride, in moles, is this?
Step 1 - Find the relative formula mass
There's one sodium atom and one chlorine atom in NaCl, so:
Step 2 - Divide the mass by the relative formula mass
Amount of substance = 25 ÷ 58.5 = 0.4273... mol
Step 3 - Round the answer
The mass was given to two significant figures, so give the amount to two as well:
0.43 mol
The Avogadro constant and numbers of particles
- One mole of any substance contains the same number of particles: 6.02 × 1023 particles per mole.
- This value is called the Avogadro constant.
- One mole of carbon holds 6.02 × 1023 C atoms, one mole of nitrogen gas holds 6.02 × 1023 N2 molecules, and one mole of sodium chloride holds 6.02 × 1023 NaCl formula units.
Stating the particle type
- Be clear about which particle is being counted:
- Element made of single atoms - Count atoms
- Molecular substance - Count molecules
- Ionic compound - Count formula units
- One mole of CO2 contains 6.02 × 1023 CO2 molecules, which contains three times as many atoms (1.806 × 1024 atoms) because each molecule has three atoms.
Formula for number of particles
Number of particles = amount of substance × 6.02 × 1023
Where:
- Number of particles is the count of atoms, molecules, ions or formula units
- Amount of substance is in moles (mol)
- Avogadro constant is 6.02 × 1023 per mole
Worked example - Number of particles in a mass
A piece of calcium has a mass of 84 g. The relative atomic mass of calcium is 40, and the Avogadro constant is 6.02 × 1023 per mole. How many calcium atoms does the piece contain?
Step 1 - Convert the mass into an amount in moles
Calcium is an element made of single atoms, so use its relative atomic mass:
Amount of substance = 84 ÷ 40 = 2.1 mol
Step 2 - Multiply the amount by the Avogadro constant
Number of atoms = 2.1 × 6.02 × 1023 = 1.2642 × 1024
Step 3 - Round the answer
The mass was given to two significant figures, so give the answer to two as well:
1.3 × 1024 atoms