What you'll learn
Quantitative chemistry is the unit of AQA GCSE Combined Science: Trilogy that puts numbers to chemical reactions. It starts from the law of conservation of mass — that no atoms are created or destroyed in a chemical reaction — and builds from there to balanced equations, relative formula masses, concentrations and, for Higher Tier students, the mole. It is the unit students most often lose marks on through arithmetic slips rather than misunderstanding, so method and presentation matter as much as chemistry. By the end you should be able to state and apply conservation of mass, explain apparent mass changes when a gas is lost or gained, balance equations, calculate relative formula mass, calculate the concentration of a solution in grams per cubic decimetre, comment on uncertainty in measurements, and, at Higher Tier, use moles to calculate reacting masses and identify a limiting reactant. This unit is assessed on Chemistry Paper 1.
Key terms and definitions
Law of conservation of mass — no atoms are lost or made during a chemical reaction, so the total mass of the products equals the total mass of the reactants
Relative formula mass — the sum of the relative atomic masses of all the atoms shown in a formula, given the symbol Mr
Mole — the amount of a substance containing 6.02 times 10 to the power 23 particles, with a mass in grams equal to the relative formula mass
Avogadro constant — the number of atoms, molecules or ions in one mole of a substance, 6.02 times 10 to the power 23
Concentration — the amount of solute dissolved in a given volume of solution, measured in grams per cubic decimetre
Limiting reactant — the reactant that is completely used up and therefore determines the amount of product formed
Reactant in excess — a reactant of which some remains unreacted when the reaction has finished
Uncertainty — the range within which the true value of a measurement lies, often estimated as half the range of repeated results
Precision — how close repeated measurements are to one another
Resolution — the smallest change in value that a measuring instrument can detect
Core concepts
Conservation of mass and balanced equations
In a chemical reaction, atoms are rearranged but never created or destroyed. It follows that the total mass of the products equals the total mass of the reactants, and that a symbol equation must have the same number of atoms of each element on both sides.
Balancing is done by placing numbers in front of formulae, never by changing a formula itself. Changing a subscript changes the substance, which is why altering water to something else to make an equation balance is always wrong. Work through one element at a time, leaving oxygen and hydrogen until last as they often appear in several compounds.
Apparent changes in mass
Sometimes a reaction appears to gain or lose mass, and explaining this is a standard question.
Mass appears to decrease when one of the products is a gas that escapes into the air. Heating a metal carbonate releases carbon dioxide, so the solid left behind weighs less than the carbonate did. No mass has actually been lost; it has simply left the container.
Mass appears to increase when one of the reactants is a gas taken from the air. When a metal is heated in air it combines with oxygen, and the oxygen atoms add to the mass of the solid product.
In both cases the answer must state where the gas went or came from. Saying only that a gas was involved does not earn the mark.
Relative formula mass
The relative formula mass of a compound is the sum of the relative atomic masses of all the atoms in its formula. For water, two hydrogens at 1 plus one oxygen at 16 gives 18. For calcium carbonate, calcium at 40 plus carbon at 12 plus three oxygens at 16 gives 100.
Where brackets appear, multiply everything inside them by the number outside. Calcium hydroxide, written with a hydroxide group in brackets and a subscript 2, has one calcium at 40 plus two oxygens at 16 plus two hydrogens at 1, giving 74.
A useful check follows from conservation of mass: in a balanced equation, the sum of the relative formula masses of the reactants, each multiplied by its balancing number, equals the same sum for the products.
Chemical measurements, uncertainty and precision
Whenever a measurement is repeated, the results vary a little. The mean is the best estimate of the true value, and the spread of results indicates the precision.
Uncertainty is often estimated as half the range of the repeated results. If four titres are 24.8, 25.0, 25.2 and 25.0 cubic centimetres, the range is 0.4, so the uncertainty is plus or minus 0.2 cubic centimetres.
Resolution is a property of the instrument rather than of the results: a balance reading to two decimal places has a higher resolution than one reading to one. Choosing an instrument of appropriate resolution is part of good experimental design, and questions often ask which of two instruments is better and why.
Concentration of solutions
Many chemicals are used in solution. The concentration in grams per cubic decimetre is the mass of solute in grams divided by the volume of solution in cubic decimetres.
The conversion trips students up constantly: one cubic decimetre is 1,000 cubic centimetres, and it is the same volume as one litre. A volume given in cubic centimetres must be divided by 1,000 before use.
Concentration increases if more solute is dissolved in the same volume, or if the same mass of solute is dissolved in a smaller volume.
Moles at Higher Tier
Chemical amounts are measured in moles. One mole of any substance contains 6.02 times 10 to the power 23 particles, and has a mass in grams numerically equal to its relative formula mass. So one mole of carbon dioxide, with a relative formula mass of 44, has a mass of 44 grams.
The relationship to learn is that the number of moles equals the mass in grams divided by the relative formula mass. It rearranges to give mass equals moles multiplied by relative formula mass, and relative formula mass equals mass divided by moles.
Using moles in equations at Higher Tier
The balancing numbers in a symbol equation give the ratio in which substances react, measured in moles. This makes reacting mass calculations a three-step routine that works every time.
First, convert the mass you are given into moles by dividing by the relative formula mass. Second, use the ratio from the balanced equation to find the moles of the substance you want. Third, convert those moles back into a mass by multiplying by the relative formula mass.
The same three steps, run in reverse, allow a balanced equation to be deduced from the masses of reactants and products: convert each mass to moles, then simplify the ratio to the smallest whole numbers.
Limiting reactants at Higher Tier
When two reactants are mixed, one is usually completely used up before the other. That one is the limiting reactant, and it determines how much product can form; the other is in excess.
To identify it, convert the mass of each reactant to moles, then divide each by its balancing number in the equation. The smaller result identifies the limiting reactant. All subsequent calculations must be based on the limiting reactant, because once it has run out the reaction stops however much of the other remains.
Worked examples
Example 1: Explaining an apparent mass increase (3 marks)
A student heats 2.4 grams of magnesium in an open crucible and finds the solid afterwards has a mass of 4.0 grams. Explain the increase.
The magnesium has reacted with oxygen from the air to form magnesium oxide. The oxygen atoms that have combined with the magnesium are now part of the solid product, so the mass of the solid increases. Mass has not been created: the total mass of magnesium plus oxygen used equals the mass of magnesium oxide formed, so conservation of mass still holds.
Example 2: Calculating a concentration (3 marks)
25 grams of sodium chloride is dissolved in water to make 500 cubic centimetres of solution. Calculate the concentration in grams per cubic decimetre.
First convert the volume: 500 cubic centimetres divided by 1,000 gives 0.5 cubic decimetres. Then divide the mass by the volume: 25 divided by 0.5 gives 50. The concentration is 50 grams per cubic decimetre. As a check, the volume is half a cubic decimetre, so the concentration must be double the mass dissolved, which it is.
Example 3: A reacting mass calculation at Higher Tier (4 marks)
Calculate the mass of calcium oxide produced when 50 grams of calcium carbonate is completely decomposed. The relative formula mass of calcium carbonate is 100 and of calcium oxide is 56, and one mole of calcium carbonate produces one mole of calcium oxide.
Convert the mass to moles: 50 divided by 100 gives 0.5 moles of calcium carbonate. The equation ratio is one to one, so 0.5 moles of calcium oxide are produced. Convert back to mass: 0.5 multiplied by 56 gives 28 grams of calcium oxide. As a sense check, the remaining 22 grams is the carbon dioxide released, and 28 plus 22 equals the original 50 grams.
Common mistakes and how to avoid them
The most costly error in this unit is changing a formula while balancing an equation. Only the large numbers in front may be altered. If an equation will not balance, check the formulae are right rather than adjusting them.
In concentration calculations, forgetting to convert cubic centimetres to cubic decimetres is by far the most common slip, and it produces an answer 1,000 times too small. Convert first, before any other step.
Students often round partway through a multi-step mole calculation and then carry the rounded value forward. Keep full precision until the final answer, then round.
Another regular error is treating the balancing numbers as mass ratios. They are mole ratios. A one to one ratio does not mean equal masses unless the relative formula masses happen to be the same.
Finally, in apparent mass change questions, many answers say mass was lost or gained. State explicitly that the gas escaped into the air, or was taken from the air, so conservation of mass is not broken.
Exam technique for "Chemistry: Quantitative Chemistry"
Set calculations out in labelled steps. Method marks are available even when the final number is wrong, but only if the examiner can see what you did.
Always write the unit. A concentration without grams per cubic decimetre, or a mass without grams, is an incomplete answer.
Give a sense check on every calculation where one is available. If a question asks for the mass of a product and your answer exceeds the total mass of the reactants, something has gone wrong.
For Higher Tier mole questions, write the balanced equation first, underneath it the moles of each substance, and only then convert to masses. Laying it out this way makes ratio errors visible immediately.
Pay attention to significant figures when the question specifies them, and never give more figures than the least precise measurement in the question justifies.
Quick revision summary
No atoms are created or destroyed, so mass is conserved and equations must balance by adjusting only the numbers in front of formulae. Apparent mass losses occur when a gas escapes and apparent gains when a gas is taken from the air. Relative formula mass is the sum of the relative atomic masses in a formula, multiplying out any brackets. Repeated measurements give a mean, with uncertainty often taken as half the range, while resolution describes the instrument. Concentration in grams per cubic decimetre is mass divided by volume, with cubic centimetres divided by 1,000 first. At Higher Tier, moles equal mass divided by relative formula mass, one mole containing 6.02 times 10 to the power 23 particles, and the balancing numbers give the mole ratio used to convert between substances. The limiting reactant is the one used up first and determines the yield.