Atoms and molecules are far too small to be weighed or counted individually. To solve this problem, chemists use a standardized unit called the mole to bridge the gap between subatomic particles and laboratory scale masses.
Key Principle
The mole is a counting unit, much like a dozen represents 12 items. Under the SI definition, one mole contains exactly 6.02214076 × 10²³ elementary entities (commonly rounded to 6.022 × 10²³ in A-Level calculations). This definition ensures that the mass of one mole of an element in grams is numerically equal to its relative atomic mass.
Relative Atomic and Molecular Mass
Because atoms have extremely small masses, we measure their mass relative to a standard reference: the carbon-12 isotope.
The weighted mean mass of an atom of an element compared to one twelfth of the mass of an atom of carbon-12.
The weighted mean mass of a molecule compared to one twelfth of the mass of an atom of carbon-12. This is calculated by adding up the relative atomic masses of all the atoms in the molecular formula.
For ionic compounds (such as NaCl), which do not exist as simple molecules, we use the term relative formula mass instead of relative molecular mass. However, both use the symbol \( M_r \) and are calculated in the same way, by summing the \( A_r \) values of the constituent atoms.
What is the Mole?
The mole (symbol mol) is the SI unit for amount of substance. One mole contains exactly 6.02214076 × 10²³ elementary entities (atoms, molecules, or ions). In A-Level chemistry, it has traditionally been referenced to the carbon-12 standard:
The amount of substance that contains the same number of particles as there are atoms in exactly 12 grams of carbon-12.
This number of particles per mole is known as Avogadro's constant (symbol \( L \) or \( N_A \)):
Avogadro's Constant (L)
\( L = 6.022 \times 10^{23} \text{ mol}^{-1} \)
The exact SI defined value is 6.02214076 × 10²³ mol⁻¹; rounded to 6.022 × 10²³ mol⁻¹ on the AQA Periodic Table Data Sheet.
Molar Mass
The mass of one mole of a substance is called its molar mass (symbol \( M \)) and is measured in units of g mol⁻¹.
- The molar mass of an element is its \( A_r \) in g mol⁻¹
- The molar mass of a compound is its \( M_r \) in g mol⁻¹
Use the relative atomic masses from the periodic table:
\( A_r(\text{H}) = 1.0 \), \( A_r(\text{S}) = 32.1 \), \( A_r(\text{O}) = 16.0 \)
Calculate the molar mass by summing the masses:
\[ M = (2 \times 1.0) + 32.1 + (4 \times 16.0) = 2.0 + 32.1 + 64.0 = 98.1 \text{ g mol}^{-1} \]
Mass-Mole Calculations
You can convert between the mass of a substance, the amount of substance in moles, and its molar mass using the following relationship:
Where:
- \( n \) = amount of substance in moles (mol)
- \( m \) = mass of the substance in grams (g)
- \( M \) = molar mass in grams per mole (g mol⁻¹)
Step 1: Find the molar mass of NaCl.
\( A_r(\text{Na}) = 23.0 \), \( A_r(\text{Cl}) = 35.5 \)
\[ M = 23.0 + 35.5 = 58.5 \text{ g mol}^{-1} \]
Step 2: Apply the equation \( n = \frac{m}{M} \).
\[ n = \frac{5.85}{58.5} = 0.100 \text{ mol} \]
Step 1: Find the molar mass of H₂O.
\( A_r(\text{H}) = 1.0 \), \( A_r(\text{O}) = 16.0 \)
\[ M = (2 \times 1.0) + 16.0 = 18.0 \text{ g mol}^{-1} \]
Step 2: Rearrange the equation to find mass: \( m = n \times M \).
\[ m = 0.250 \times 18.0 = 4.50 \text{ g} \]
To practise these conversions or check your answers, use our interactive Moles Calculator to explore relationships between mass, moles, and particle counts with step-by-step working.
Using Avogadro's Constant
You can calculate the total number of atoms, ions, or molecules in a given sample by multiplying the amount of substance in moles by Avogadro's constant.
Step 1: Calculate the moles of H₂O.
Molar mass of H₂O = 18.0 g mol⁻¹
\[ n = \frac{4.50}{18.0} = 0.250 \text{ mol} \]
Step 2: Calculate the number of H₂O molecules.
\[ N_{\text{molecules}} = 0.250 \times 6.022 \times 10^{23} = 1.506 \times 10^{23} \text{ molecules} \]
Step 3: Calculate the number of oxygen atoms.
Each molecule of H₂O contains exactly 1 atom of oxygen, so the number of oxygen atoms is equal to the number of molecules:
\[ N_{\text{atoms of O}} = 1.506 \times 10^{23} \text{ atoms} \]
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