The Mole (CIE A Level Physics)

• In thermodynamics, the amount of substance is measured in the SI unit ‘mole’
• This has the symbol mol
• The mole is a unit of substance, not a unit of mass
  • The mole is defined as:

The SI base unit of an ‘amount of substance’. It is the amount containing as many particles (e.g. atoms or molecules) as there are atoms in 12 g of carbon-12

• The mole is an important unit in thermodynamics
• If we consider the number of moles of two different gases under the same conditions, their physical properties are the same
• 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

• In AS Physics, the atomic mass unit (u) was introduced as approximately the mass of a proton or neutron = 1.66 × 10^-27 kg
• This means that 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^-26 kg

• The exact number for a mole is defined as the number of molecules in exactly 12 g of carbon:

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

The number of atoms of carbon-12 in 12 g of carbon-12; equal to 6.02 × 10²³ mol^-1

• 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 × 10²⁴ atoms

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 therefore can also be calculated from the equation:

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