GCSEChemistry: Combined ScienceAQARevision Notes3. Quantitative Chemistry3.1 Measurement, Mass & EquationsCalculate Relative Formula Mass

Calculate Relative Formula Mass (AQA GCSE Chemistry: Combined Science)

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Relative formula (molecular) mass

How to calculate relative formula mass

  • The symbol for the relative atomic mass is Ar
  • This is calculated from the mass number and relative abundances of all the isotopes of a particular element
  • The symbol for the relative formula mass is Mr and it refers to the total mass of the molecule
  • To calculate the Mr of a substance, you have to add up the relative atomic masses of all the atoms present in the formula

Relative formula mass calculations table

Substance Atoms present Calculation Mr 
Hydrogen
H2 		 2 x H (2 x 1) 2
Water
H2O		 (2 x H) + (1 x O) (2 x 1) + (1 x 16) 18
Potassium carbonate
K2CO3 		 (2 x K) + (1 x C) + (3 x O) (2 x 39) + (1 x 12) + (3 x 16) 138
Calcium hydroxide
Ca(OH)2 		 (1 x Ca) + (2 x O) + (2 x H) (1 x 40) + (2 x 16) + (2 x 1) 74
Ammonium sulfate
(NH4)2SO4		 (2 x N) + (8 x H) + (1 x S) + (4 x O) (2 x 14) + (8 x 1) + (1 x 32) + (4 x 16) 132

  • In accordance with the Law of Conservation of Mass, the sum of the relative molecular masses of the reactants will be the same as the sum of the relative molecular masses of the products

Worked example

Calculate the relative formula mass of:

  1. Sodium chloride, NaCl

  2. Copper oxide, CuO

  3. Magnesium nitrate, Mg(NO3)2

Answers:

  1. Sodium chloride

    • NaCl = 23 + 35.5 = 58.5

  2. Copper oxide

    • CuO = 63.5 + 16 = 79.5

  3. Magnesium nitrate

    • Mg(NO3)2 = 24 + (14 x 1 x 2) + (16 x 3 x 2) = 148

Examiner Tip

The relative atomic mass of every element is given on the Periodic Table. It is the larger of the two numbers.

Calculating % mass of an element in a compound

  • The percentage by mass of an element in a compound can be calculated using the following equation:

percent sign space mass space of space an space element equals fraction numerator A subscript straight r cross times number space of space atoms space of space the space element over denominator M subscript straight r space of space the space compound end fraction cross times 100

  • For example, in water:
    • Water is a simple molecule with the chemical formula H2O
    • So, water is made of two hydrogen (H) atoms and one oxygen (O) atom
    • From the Periodic Table, the relative atomic mass of:
      • Hydrogen = 1
      • Oxygen = 16
    • Therefore, the total mass of water is:
      • (2 × 1) + 16 = 18
  • To find the percentage by mass of hydrogen:
    • Percentage of hydrogen = open parentheses fraction numerator 2 cross times 1 over denominator 18 end fraction close parentheses × 100 = 11.1%
  • Similarly, the percentage by mass of oxygen is:
    • Percentage of oxygen = open parentheses fraction numerator 1 cross times 16 over denominator 18 end fraction close parentheses × 100 = 88.9%
  • Note: The total percentage by mass of all the elements should add up to 100%, e.g. 11.1% + 89.9% = 100%

Examiner Tip

  • The most common incorrect answer for percentage composition are values above 100%
  • This is not possible and usually happens when the numbers in the calculation are "upside down"
    • For example, the percentage composition of hydrogen in water:
      • CORRECT = open parentheses fraction numerator 2 cross times 1 over denominator 18 end fraction close parentheses x 100 = 11.1%
      • INCORRECT = stretchy left parenthesis fraction numerator 18 over denominator 2 cross times 1 end fraction stretchy right parenthesis x 100 = 900%

Worked example

Calculate the percentage of carbon in the formula of glucose, C6H12O6.

Answer:

  • From the Periodic Table, the relative atomic masses are:
    • Carbon = 12
    • Hydrogen = 1
    • Oxygen = 16 
  • The total mass of glucose is:
    • (6 × 12) + (12 × 1) + (6 × 16) = 180
  • The equation for percentage composition is:
    • Percentage composition = stretchy left parenthesis fraction numerator total space mass space of space element over denominator total space space mass space of space compound end fraction stretchy right parenthesis × 100
  • So, the percentage composition of carbon in glucose is:
    • Percentage of carbon = open parentheses fraction numerator 6 cross times 12 over denominator 180 end fraction close parentheses × 100 = 40%

Worked example

The chemical formula of the fertiliser ammonium nitrate is NH4NO3. Calculate the percentage by mass of nitrogen in ammonium nitrate.

Answer:

  • From the Periodic Table, the relative atomic masses are:
    • Nitrogen = 14
    • Hydrogen = 1
    • Oxygen = 16 
  • The total mass of ammonium nitrate is:
    • (1 x 14) + (4 × 1) + (1 x 14) + (3 × 16) = 80
  • The equation for percentage composition is:
    • Percentage Composition = stretchy left parenthesis fraction numerator total space mass space of space element over denominator total space space mass space of space compound end fraction stretchy right parenthesis × 100
  • So, the percentage composition of nitrogen in ammonium nitrate is:
    • Careful: There are two nitrogen atoms in ammonium nitrate
    • Percentage of nitrogen = open parentheses fraction numerator 2 cross times 14 over denominator 80 end fraction close parentheses × 100 = 35%

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