R2.1
How much? The amount of chemical change
7 SL (SL 2.1.1-2.1.5)
Unverified
← View on the mapParent topic: How much, how fast and how far?
Guiding question
Guiding questionHow are chemical equations used to calculate reacting ratios?
The one big idea
A balanced equation is a recipe: the coefficients tell you the mole ratios, and the mole ratio tells you how much product you can make. The limiting reactant sets the ceiling; atom economy tells you how green the recipe is.
What this rests on
Our editorial judgement.The dependencies in this section are this site’s own assessment of what a sub-topic rests on. They have notbeen verified by a chemistry teacher and are not part of the official IB guide. By contrast, section 8 (Linking questions) reproduces the IB’s own wording verbatim.
- EditorialS1.4 Counting particles by mass: The moleStoichiometric calculations are mole-ratio calculations.
- EditorialS1.5 Ideal gasesGas volumes in stoichiometry use the ideal gas model.
- EditorialS3.2 Functional groups: Classification of organic compoundsOrganic compounds appear in stoichiometry calculations such as combustion of hydrocarbons.
What rests on this
- EditorialS2.4 From models to materials
- EditorialR3.1 Proton transfer reactions
- EditorialR3.2 Electron transfer reactions
Core concepts that must be mastered
- Chemical equations and mole ratios(2.1.1, 2.1.2)A balanced chemical equation shows the reactant:product ratios in moles. You must deduce equations when reactants and products are specified, including state symbols — (s), (l), (g), (aq). The coefficients are the mole ratios: 2H₂(g) + O₂(g) → 2H₂O(g) means 2 mol of H₂ reacts with 1 mol of O₂ to give 2 mol of H₂O. These ratios let you convert between masses, volumes of gases, and concentrations for solution reactions. Use data-booklet Ar values to 2 d.p. The calculation chain always follows the same pattern: write the balanced equation → identify the mole ratio from the coefficients → convert the given quantity to moles → use the ratio to find moles of the unknown → convert moles of the unknown to whatever quantity the question asks for (mass, volume, concentration). For gas reactions, Avogadro's law (S1.4) lets you use volume ratios directly as mole ratios without converting to moles first. For solution reactions, use n = cV to interconvert amount and concentration.
- The limiting reactant(2.1.3)The limiting reactant determines the theoretical yield — the maximum amount of product possible. When amounts of two or more reactants are given, one will run out first. To find it: divide each reactant's moles by its stoichiometric coefficient; the smallest value is the limiting reactant. The excess reactant is left over. The theoretical yield is calculated from the limiting reactant, not from whichever reactant was given first. If you skip this step and use the wrong reactant, you will calculate a yield that is physically impossible. For example, if 5 mol of H₂ reacts with 2 mol of O₂ in 2H₂ + O₂ → 2H₂O, divide each by its coefficient: H₂ gives 5/2 = 2.5, O₂ gives 2/1 = 2 — O₂ is limiting, so the maximum product is 4 mol of H₂O, not 5 mol.
- Percentage yield(2.1.4)Percentage yield compares what you actually got to what you could theoretically get: percentage yield = (experimental yield ÷ theoretical yield) × 100%. You must solve problems involving reacting quantities, limiting and excess reactants, and theoretical, experimental and percentage yields. A yield above 100% is not a chemical triumph — it signals experimental error such as incomplete drying, impurity, or a side product being weighed as the product. Distinguish theoretical yield (from stoichiometry) from experimental yield (from the lab).
- Atom economy and green chemistry(2.1.5)Atom economy measures how efficiently a reaction uses its atoms: atom economy = (mass of desired product ÷ total mass of products) × 100%. Unlike percentage yield, atom economy is a theoretical property of the equation — it does not depend on how the reaction went. A reaction can have 100% yield and 40% atom economy (the rest is waste by-product). There is an inverse relationship between atom economy and industrial wastage: high atom economy reactions are greener because they produce less waste per unit of product. Addition reactions (all reactant atoms end up in the product) have 100% atom economy; substitution reactions necessarily have less because the leaving group becomes waste. For example, the Haber process N₂ + 3H₂ → 2NH₃ has 100% atom economy, while the fermentation of glucose C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ has only 51% atom economy because the CO₂ is waste (unless it is captured and sold). The equation for atom economy is in the data booklet.
- How this sub-topic connectsStoichiometry is the quantitative backbone of the entire course. Mole ratios from balanced equations underpin every titration (R3.1), every redox calculation (R3.2), and every gas-volume problem. Concentration (from S1.4) is the currency of equilibrium (R2.3) and kinetics (R2.2). The limiting-reactant concept explains why incomplete combustion (R1.3) happens when oxygen is limited. Percentage yield connects to Tool 1 (experimental error analysis) and the equilibrium concept (R2.3: a reaction that does not go to completion has a yield below 100% for thermodynamic, not experimental, reasons). Atom economy links to green chemistry and to the Nature of Science theme of sustainable design.
Quantitative non-negotiables
- Deduce balanced chemical equations with state symbols from specified reactants and products.
- Calculate reacting masses, volumes and concentrations from mole ratios.
- Identify the limiting reactant from data and calculate the theoretical yield.
- Calculate percentage yield = (experimental ÷ theoretical) × 100%.
- Calculate atom economy = (mass of desired product ÷ total mass of products) × 100%.
Common failure modes
M-25 — You can just use the moles of the reactant given in the question.
Confidence: verified
Why it’s wrong: If amounts of two or more reactants are given, one may be limiting.
Correction: Identify the limiting reactant by dividing moles by stoichiometric coefficient and taking the smallest; theoretical yield comes from that one.
M-27 — Percentage yield can exceed 100% if the reaction goes well.
Confidence: verified
Why it’s wrong: Above 100% indicates impurity or incomplete drying.
Correction: Above 100% is an experimental error, not a chemical triumph.
M-28 — Atom economy and percentage yield are the same.
Confidence: verified
Why it’s wrong: They measure different things.
Correction: Atom economy is a theoretical property of the equation (mass of desired product ÷ total mass of products); percentage yield is an experimental property of the run. A reaction can have 100% yield and 40% atom economy.
What "HL standard" actually looks like
No HL extension. Reactivity 2.1 is entirely SL and shared — stoichiometry is the most leveraged quantitative skill in the course, and every subsequent calculation (equilibrium, electrochemistry, titration) rests on it.
Linking questions
Official IB.The questions in this section are the IB’s own linking questions, reproduced verbatim from the guide. They are not this site’s editorial judgement — see section 3 for that distinction.
- Official IB
How can molar masses be used with chemical equations to determine the masses of the products of a reaction?
- Official IB
How does the resonance energy in benzene explain its relative unreactivity?
- Official IB
Why is the atom economy 100% for an addition polymerization reaction?
- Official IB
How does limiting the supply of oxygen in combustion affect the products and increase health risks?
- Official IB
When is it useful to use half-equations?
- Official IB
How does the molar volume of a gas vary with changes in temperature and pressure?
- Official IB
In what ways does Avogadro's law help us to describe, but not explain, the behaviour of gases?
- Official IB
The atom economy and the percentage yield both give important information about the "efficiency" of a chemical process. What other factors should be considered in this assessment?
1 further official linking question target a Tool, Inquiry or Nature of Science strand and are not drawn as edges on the map:
Editorial The decision to surface these off-graph questions here is our editorial judgement — the IB does not prescribe where they should appear.
- Official IB
What errors may cause the experimental yield to be i) higher and ii) lower than the theoretical yield?
Bridge: GCSE → IB HL
Derived. These are the bridge items tagged to this sub-topic— places where the GCSE model gets redefined, genuinely new territory, or carry-over strengths. The tagging is this site’s editorial judgement.