Mole calculations
This equation shows how relative formula massThe relative formula mass (Mr) of a compound is calculated by adding together the relative atomic masses (Ar) of the atoms present in the compound., number of moleThe amount of substance that contains the same number of particles as there are atoms in 12 g of carbon-12 (contains the Avogadro's constant 6.0 ×10²³ number of particles). and massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). are related:
Note that 1 mole of a substance contains 6.022 × 1023 atoms or molecules. 6.022 × 1023 is a constant number, known as Avogadro’s constant.
The equation can be rearranged to find the mass if the number of moles and molar mass (its relative formula mass in grams) are known. It can also be rearranged to find the molar mass if the mass and number of moles are known.
\(\text{mass} = {\text{number of moles}}\times{\text{relative formula mass}}\)
Finding the number of moles
Question
Calculate the number of moles of carbon dioxide molecules in 22 g of CO2.
Ar (relative atomic mass) of carbon, C = 12
Ar of oxygen, O = 16
Mr (relative formula mass) of carbon dioxide, CO2 = 12 + 16 + 16 = 44
number of moles = 22 ÷ 44 = 0.5 mol
Finding the mass
Question
Calculate the mass of 2 mol of carbon dioxide (CO2).
mass = number of moles × relative formula mass = 2 × 44 = 88 g
Finding the relative formula mass
Question
10 mol of carbon dioxide has a mass of 440 g. What is the relative formula mass of carbon dioxide?
relative formula mass = mass ÷ number of moles = 440 ÷ 10 = 44
Reacting masses using moles
You can calculate the mass of a productA substance formed in a chemical reaction. or reactantA substance that reacts together with another substance to form products during a chemical reaction. using the idea of moles, a balanced equation and relevant Ar values.
Example
Sulfuric acid and sodium hydroxide react together to make sodium sulfate and water:
H2SO4 + 2NaOH → Na2SO4 + 2H2O
Question
Calculate the mass of sodium sulfate made when 20 g of sodium hydroxide reacts with excess sulfuric acid.
- Ar of hydrogen, H = 1
- Ar of oxygen, O = 16
- Ar of sodium, Na = 23
- Ar of sulfur, S = 32
Mr of sodium hydroxide, NaOH = 23 + 16 + 1 = 40
Mr of sodium sulfate, Na2SO4 = 23 + 23 + 32 + 16 + 16 + 16 + 16 = 142
Number of moles of NaOH = mass ÷ relative formula mass = 20 ÷ 40 = 0.5 mol
From the equation, 2 mol of NaOH reacts with 1 mol of Na2SO4, so 0.5 mol of NaOH will react with 0.25 mol of Na2SO4.
mass of Na2SO4 = moles × relative formula mass = 0.25 × 142 = 35.5 g
The example above could also be tackled like this:
mass of Na2SO4 = \(\frac{20}{2 \times 40} \times 142\) = 35.5 g
