The Mole (Cambridge International A-Level Physics)

Amount of Substance

• In physics, the amount of substance is an SI base quantity with the base unit mol
• The mole is a unit of substance (not mass) and is defined as:

The amount of substance containing as many particles (e.g. atoms or molecules) as there are atoms in 12 g of carbon-12

• When held under the same conditions (temperature and pressure), two different gases of equal volume will contain the same number of molecules
• The number of moles n can be calculated using the equation

$n=\frac{N}{N_{A}}$

• Where:

  • N = number of molecules
  • N_A = Avogadro's constant

The Avogadro Constant

Spec point — 15.1.2

• In AS Physics, the atomic mass unit (u) was introduced as approximately the mass of a proton or neutron = 1.66 × 10^-27 kg
• So an atom or molecule has a mass approximately equal to the number of protons and neutrons it contains
• A carbon-12 atom has a mass of:

12 u = 12 × 1.66 × 10^-27= 1.99 × 10^-26kg

• A mole contains 6.02 × 10²³molecules, this is known as Avogadro's constant

• Avogadro’s constant (N_A) is defined as:

The number of atoms in 12 g of carbon-12, equal to 6.02 × 10²³molecules per mol

• One mole can be calculated as:

$1\mathrm{mole}=\frac{0.012}{1.99\times10^{-26}}=6.02\times10^{23}\mathrm{molecules}$

• For example, 1 mole of sodium (Na) contains 6.02 × 10²³ atoms of sodium
• The number of atoms can be determined if the number of moles is known by multiplying by N_A, for example:

2.0 mol of nitrogen contains: 2.0 × N_A= 2.0 × 6.02 × 10²³= 1.20 × 10²⁴atoms

Mole and the atomic mass

• One mole of any element is equal to the relative atomic mass of that element in grams

  • E.g. Helium has an atomic mass of 4 - this means 1 mole of helium has a mass of 4 g

• If the substance is a compound, add up the relative atomic masses

• For example, water (H₂O) is made up of

  • 2 hydrogen atoms (each with atomic mass of 1) and 1 oxygen atom (atomic mass of 16)
  • So, 1 mole of water would have a mass of (2 × 1) + 16 = 18 g

Molar mass

• The molar mass of a substance is the mass, in grams, in one mole

  • Its unit is g mol^-1

• The number of moles n can also be calculated from the equation:

$n=\frac{m}{M_{r}}$

• Where:

  • m = mass of the substance (g)
  • M_r = molar mass of the substance (g mol^-1)

Worked Example How many molecules are there in 6 g of magnesium-24?

Answer:

Step 1: Calculate the mass of 1 mole of magnesium

• One mole of any element is equal to the relative atomic mass of that element in grams

1 mole = 24 g of magnesium

Step 2: Calculate the amount of moles in 6 g

$\frac{6}{24}=0.25\mathrm{moles}$

Step 3: Convert the moles to the number of molecules

1 mole = 6.02 × 10²³ molecules

0.25 moles = 0.25 × 6.02 × 10²³ = 1.51 × 10²³ molecules

Exam Hint If you want to find out more about the mole, check out the CIE IGCSE Chemistry revision notes