Mole Calculations
The Mole
- The mole is one of the seven SI base units
- It is used to measure the amount of substance
- One mole is defined as follows:
The amount of substance that contains as many elementary entities as the number of atoms in 12 g of carbon-12
- This amount of substance is exactly 6.02214076 × 1023 elementary entities (i.e. particles, atoms, molecules)
- At IB level, this number can be rounded to 6.02 × 1023
- One mole of gas contains a number of particles (atoms or molecules) equal to the Avogadro constant
- Therefore, to calculate the number of particles N in a gas, knowing the number of moles n, the following relationship must be used:
N = nNA
- Where:
- N = number of gas particles
- n = number of moles of gas (mol)
- NA = 6.02 × 1023 mol–1 (Avogadro constant)
Molar Mass
- The molar mass M of a substance is defined as the mass m of the substance divided by the amount (in moles) of that substance
- The molar mass is calculated as follows:
- Where:
- M = molar mass in g mol–1
- m = mass in grams (g)
- n = number of moles (mol)
Worked example
Nitrogen is normally found in nature as a diatomic molecule, N2. The molar mass of nitrogen is 28.02 g mol–1.
Determine the mass of a nitrogen atom.
Step 1: Write down the relationship between the molar mass M and the mass m
Step 2: Rearrange the equation to find the mass m of n = 1 mol of nitrogen
m = Mn
m = 28.02 g mol–1 × 1 mol
m = 28.02 g
Step 3: Identify the number of nitrogen atoms in 1 mol of nitrogen
- n = 1 mol of nitrogen contains a number of molecules equal to the Avogadro constant
- From the data booklet, NA = 6.02 × 1023
Nmolecules = nNA
Nmolecules = 6.02 × 1023
- Each nitrogen molecule contains 2 atoms of nitrogen
- n = 1 mol of nitrogen contains a number of atoms equal to twice the number of molecules
Natoms = 2 × Nmolecules = 2 × (6.02 × 1023)
Natoms = 1.2 × 1024
Step 4: Divide the mass of 1 mol of nitrogen m by the number of atoms in 1 mol of nitrogen Natoms in order to find the mass of a nitrogen atom
Mass of a nitrogen atom = 2.3 × 10–23 g