GCSE / Chemistry
Quantitative Chemistry
Learn GCSE Quantitative Chemistry including conservation of mass, balancing chemical equations, relative formula mass, moles, limiting reactants, concentration, percentage yield, atom economy and gas volume calculations.
Conservation of mass states that mass is not created or destroyed during a chemical reaction because atoms are only rearranged. In a closed system, the total mass of the reactants therefore equals the total mass of the products. Chemical equations must be balanced so that the number of atoms of each element is the same on both sides of the equation. Only coefficients placed before chemical formulae should be changed when balancing equations; subscripts within formulae must not be altered.
The relative formula mass, Mr, of a compound is calculated by adding together the relative atomic masses, Ar, of all the atoms shown in its chemical formula. For example, for MgCl₂, . Relative formula mass has no unit because it is a relative value. In a balanced equation, the total relative formula mass of the reactants in the quantities shown equals the total relative formula mass of the products.
Percentage by mass shows what fraction of the total mass of a compound is contributed by a particular element. It is calculated using: percentage by . The number of atoms of the element in the formula must be taken into account before calculating its contribution.
An apparent change in mass can occur when a reaction involves a gas in an open system. If a gaseous product escapes, the measured mass decreases even though mass is still conserved overall. If a reactant gas from the atmosphere enters the reaction, the measured mass of the products may be greater than the starting solid. These observations can be explained using the conservation of mass and the particle model.
Every chemical measurement has some uncertainty. A set of repeated measurements can be analysed by calculating the range, which is the highest value minus the lowest value. The spread of results around the mean provides information about uncertainty and repeatability. Smaller ranges generally indicate more consistent measurements, although measurement uncertainty can never be completely eliminated.
A mole is the unit used to measure amount of substance and has the symbol mol. One mole contains the Avogadro constant, approximately 6.02 × 10²³ particles. These particles may be atoms, molecules, ions or formula units depending on the substance. The mass in grams of one mole of a substance is numerically equal to its relative atomic mass or relative formula mass.
The number of moles in a substance can be calculated using: . The equation can be rearranged to give . These calculations connect measurable masses in the laboratory with the number of particles involved in chemical reactions.
Balanced chemical equations show the mole ratio between reactants and products. For example, Mg + 2HCl → MgCl₂ + H₂ shows that one mole of magnesium reacts with two moles of hydrochloric acid to produce one mole of magnesium chloride and one mole of hydrogen. These ratios can be used to calculate unknown masses or amounts of reactants and products.
For Higher Tier calculations, the coefficients in an unknown chemical equation can be determined from experimental masses. The mass of each substance is converted into moles using . The calculated mole amounts are then divided by the smallest value to obtain the simplest whole-number ratio, which provides the balancing numbers for the equation.
A limiting reactant is the reactant that is completely used up first and therefore determines the maximum amount of product that can be formed. Other reactants may be present in excess. To identify the limiting reactant, the available amounts must be compared with the mole ratio in the balanced equation rather than simply comparing their masses.
The concentration of a solution expresses how much solute is present in a given volume of solution. When concentration is measured in g/dm³, . This can be rearranged to calculate mass or volume. Volumes given in cm³ must be converted to dm³ by dividing by 1000.
Percentage yield compares the actual amount of product obtained experimentally with the maximum theoretical amount that could be produced. Percentage . Yields below 100% may occur because reactions are reversible, reactions may not go to completion, unwanted side reactions can occur, or some product may be lost during separation and purification.
Atom economy measures the proportion of reactant atoms that become part of the desired product. Percentage atom . High atom economy reduces waste, conserves raw materials and can make industrial processes more sustainable and economical.
For Higher Tier Chemistry, concentration may also be measured in mol/dm³. Concentration in mol/dm³ = moles of solute ÷ volume of solution in dm³. Therefore . This relationship can be combined with balanced equation ratios to calculate the concentration of an unknown reacting solution when the concentration and volume of another solution are known.
At room temperature and pressure, one mole of any gas occupies approximately 24 dm³. Therefore gas volume in dm³ = moles × 24, and . Balanced equations can be used with this relationship to calculate volumes of gaseous reactants and products. The same mole ratio shown by the equation applies to reacting gas volumes when the gases are measured under the same conditions.