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The Mole (CIE A Level Physics)

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Amount of substance

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

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

  • 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 space equals fraction numerator space N over denominator N subscript A end fraction

  • Where:
    • N = number of molecules
    • NA = Avogadro's constant

The Avogadro 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
  • 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 × 10-26 kg

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

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

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

  • One mole can be calculated as:

1 space mole space space equals space fraction numerator 0.012 space over denominator 1.99 space cross times space 10 to the power of negative 26 end exponent end fraction space equals space 6.02 space cross times 10 to the power of 23 space 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 NA, for example:

2.0 mol of nitrogen contains:  2.0 × NA = 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:

n space equals fraction numerator space m over denominator M subscript r end fraction

  • Where:
    • m = mass of the substance (g)
    • Mr = 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

6 over 24 space equals space 0.25 space 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

Examiner Tip

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

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Ashika

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Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.