R2
How much, how fast and how far?
21 SL · +10 HL (sum of sub-topics)
Unverified
← View on the mapGuiding question
Official titleHow much, how fast and how far?
The one big idea
Every reaction has three governing questions: how much (stoichiometry), how fast (rate) and how far (equilibrium). Quantitative answers to all three separate a grade 5 from a grade 7.
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.
Prerequisites are recorded at the sub-topic level only. The list below aggregates the prerequisites of this topic’s sub-topics.
- EditorialS1.4 Counting particles by mass: The moleStoichiometric calculations are mole-ratio calculations. (via R2.1)
- EditorialS1.4 Counting particles by mass: The moleConcentration calculations for reaction rates are mole calculations. (via R2.2)
- EditorialS1.4 Counting particles by mass: The moleEquilibrium constant expressions use concentrations. (via R2.3)
- EditorialS1.5 Ideal gasesGas volumes in stoichiometry use the ideal gas model. (via R2.1)
- EditorialS3.1 The periodic table: Classification of elementsHL onlyTransition elements are useful as catalysts; their features come from periodic position (HL linking question R2.2.5). (via R2.2)
- EditorialS3.2 Functional groups: Classification of organic compoundsOrganic compounds appear in stoichiometry calculations such as combustion of hydrocarbons. (via R2.1)
- EditorialS1.1 Introduction to the particulate nature of matterCollision theory is kinetic molecular theory applied to reactions (explicit linking question). (via R2.2)
- EditorialR1.1 Measuring enthalpy changesEnergy profiles and activation energy extend the enthalpy-change energy profile. (via R2.2)
- EditorialR2.2 How fast? The rate of chemical changeDynamic equilibrium is defined as equal forward and backward rates. (via R2.3)
What rests on this
- EditorialS2.4 From models to materials
- EditorialR3.1 Proton transfer reactions
- EditorialR3.2 Electron transfer reactions
- EditorialR2.3 How far? The extent of chemical change
- EditorialR3.4 Electron-pair sharing reactions
- EditorialR1.4 Entropy and spontaneity
- EditorialR3.1 Proton transfer reactions
- EditorialR3.2 Electron transfer reactions
Core concepts that must be mastered
Reactivity 2 answers three questions about any reaction: how much product forms, how fast does it happen, and how far does it go? Three sub-topics — stoichiometry (2.1), rate (2.2) and equilibrium (2.3) — each quantitative, each with a significant HL extension. Together they are the calculation backbone of the course.
- How much — the amount of chemical change(2.1.1–2.1.5)Balanced chemical equations show reactant:product ratios in their simplest whole-number form (2.1.1). The mole ratio from the equation determines masses, volumes and concentrations for solution reactions (2.1.2) — this is Structure 1.4 applied to reactions, so every stoichiometry problem is a mole problem. The limiting reactant — the one that runs out first — determines the theoretical yield (2.1.3). Identifying the limiting reactant is where most stoichiometry errors happen: you cannot just use the moles given in the question, you must compare the mole ratio to the equation ratio to find which reactant is exhausted first. Percentage yield compares what you actually obtained (experimental yield) to what you should have obtained (theoretical yield) (2.1.4). Atom economy — the proportion of reactant atoms that end up in the desired product — is a green-chemistry metric of efficiency, with an inverse relationship to industrial wastage (2.1.5). The equation for atom economy is in the data booklet.
- How fast — the rate of chemical change(2.2.1–2.2.13)Rate is the change in concentration of a reactant or product per unit time, read from tangents to concentration–time, volume–time or mass–time graphs (2.2.1). Reactions occur when particles collide with sufficient energy and proper orientation (2.2.2). The relationship between particle kinetic energy and temperature in kelvin, and the role of collision geometry, are both central. Rate is influenced by pressure, concentration, surface area, temperature and catalysts (2.2.3). Activation energy Eₐ is the minimum energy colliding particles need; the Maxwell–Boltzmann distribution shows that raising temperature increases the fraction of particles exceeding Eₐ — the area under the curve beyond Eₐ — not just the frequency of collisions (2.2.4). This is the dominant reason temperature speeds a reaction. Catalysts provide an alternative pathway with lower Eₐ, increasing the rate without being consumed (2.2.5); enzymes are biological catalysts. At HL, the mechanism comes into focus. Many reactions occur in elementary steps, and the slowest step — the rate-determining step (RDS) — governs the overall rate (2.2.6, 2.2.7). You must distinguish intermediates (species formed in one step and consumed in another) from transition states (momentary high-energy arrangements), and recognise both in energy profiles. The case where the RDS is not the first step is explicitly included. Molecularity counts the reacting particles in an elementary step: unimolecular, bimolecular, termolecular (2.2.8). Rate equations are determined experimentally, not from the balanced equation — the order with respect to a reactant is its exponent in the rate equation and is not necessarily its stoichiometric coefficient (2.2.9, 2.2.10). You must sketch and analyse concentration–time and rate–concentration graphs for zero, first and second order reactions (only integer orders assessed). The rate constant k is temperature-dependent, and its units follow from the overall order (2.2.11). The Arrhenius equation — k = Ae^(−Eₐ/RT) — and its linear form (ln k vs 1/T) determine Eₐ and the Arrhenius factor A, which accounts for the frequency of collisions with proper orientation (2.2.12, 2.2.13).
- How far — the extent of chemical change(2.3.1–2.3.7)Dynamic equilibrium is reached in a closed system when forward and backward rates are equal — the reaction has not stopped, the macroscopic concentrations have just stopped changing (2.3.1). The equilibrium law relates K to reaction stoichiometry (2.3.2); the magnitude of K tells you the extent — K≫1 means products dominate, K≪1 means reactants dominate — and K is temperature-dependent only (2.3.3). Changing concentration, pressure or adding a catalyst shifts the position but does not change K. Le Châtelier's principle predicts qualitative effects of changing concentration, temperature or pressure on equilibrium composition (2.3.4), and can be applied to heterogeneous equilibria such as X(g) ⇌ X(aq). It is a prediction tool, not the explanation — the explanation is Q vs K. At HL, the reaction quotient Q uses non-equilibrium concentrations to tell you which way the reaction will move: Q < K means forward, Q > K means reverse (2.3.5). Quantitative equilibrium calculations let you solve for equilibrium concentrations from initial data (2.3.6); the [reactant]_initial ≈ [reactant]_eqm approximation is valid when K is very small, and quadratic equations are not expected. The thermodynamic link ΔG⦵ = −RT lnK connects equilibrium to Gibbs energy from Reactivity 1.4 (2.3.7).
- Three questions, one networkThese three sub-topics are not independent. Rate and equilibrium share the collision model. Equilibrium and thermodynamics share ΔG⦵ = −RT lnK. The linking questions in §8 connect rate to the kinetic model (Structure 1.1), equilibrium to Gibbs energy (Reactivity 1.4), and stoichiometry to the mole (Structure 1.4) — the same edges that appear on the Spine Map.
Quantitative non-negotiables
- Calculate reacting masses, volumes and concentrations from balanced equations and mole ratios.
- Identify the limiting reactant; calculate theoretical, experimental and percentage yield, and atom economy.
- Determine reaction rates from tangents to concentration–time graphs.
- Deduce the equilibrium constant expression K for a homogeneous reaction; interpret the magnitude of K.
- Apply Le Châtelier's principle to predict the effect of changing concentration, temperature and pressure.
- Deduce rate equations from experimental data; solve for k including its units (HL).
- Apply the Arrhenius equation in linear form to determine Eₐ (HL).
- Calculate Q and determine the direction of change; solve quantitative equilibrium problems (HL).
- Use ΔG⦵ = −RT lnK (HL).
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.
M-32 — A catalyst changes ΔH.
Confidence: verified
Why it’s wrong: A catalyst lowers Ea by providing an alternative pathway; ΔH (a state function) is unchanged.
Correction: A catalyst does not change ΔH or the equilibrium position.
M-38 — The order of reaction is the coefficient in the balanced equation.
Confidence: verified
Why it’s wrong: Orders are determined only by experiment.
Correction: They reflect the mechanism up to and including the rate-determining step. They may be zero, fractional, or unrelated to the coefficients.
M-39 — Increasing temperature speeds a reaction mainly because particles move faster and collide more often.
Confidence: verified
Why it’s wrong: Collision frequency rises only modestly (roughly with √T).
Correction: The dominant effect is the exponential increase in the fraction of collisions with energy ≥ Ea, visible as the area under the tail of the Maxwell–Boltzmann curve.
M-40 — A catalyst lowers the activation energy of the reaction.
Confidence: verified
Why it’s wrong: A catalyst provides an alternative pathway with a lower Ea; the uncatalysed pathway still exists.
Correction: Say 'provides an alternative pathway with lower Ea', not 'lowers the activation energy'.
M-41 — The rate constant k changes when you change the concentration.
Confidence: verified
Why it’s wrong: k depends on temperature (and the catalyst/pathway) only.
Correction: Changing concentration changes the rate, not k.
M-42 — The Maxwell–Boltzmann curve shifts up as well as right when temperature increases.
Confidence: verified
Why it’s wrong: The total area (total number of particles) is constant.
Correction: The peak moves right and down, and the curve broadens.
M-43 — The rate-determining step is the one with the biggest activation energy in the profile, so it must be the first step.
Confidence: likely
Why it’s wrong: The RDS is the slowest step, which is the one with the highest activation energy barrier from its preceding intermediate.
Correction: It can be anywhere in the sequence.
M-26 — Concentration and amount are the same thing.
Confidence: likely
Why it’s wrong: Diluting a solution changes the concentration but not the amount of solute.
Correction: This matters enormously in equilibrium and titration calculations.
M-44 — At equilibrium the reaction has stopped.
Confidence: verified
Why it’s wrong: Forward and reverse reactions continue at equal, non-zero rates — dynamic, not static.
Correction: The RSC's escalator analogy: walking up a down-escalator at matching speed looks static.
M-45 — At equilibrium the concentrations of reactants and products are equal.
Confidence: verified
Why it’s wrong: Stems from confusing rate equality with concentration equality.
Correction: The concentrations are constant, not equal; their ratio is fixed by K, which can be enormous or tiny.
M-46 — Adding more reactant increases K.
Confidence: verified
Why it’s wrong: K depends only on temperature.
Correction: Adding reactant changes Q, so the system shifts to restore Q = K, but K itself is unchanged.
M-47 — A catalyst increases the yield at equilibrium.
Confidence: verified
Why it’s wrong: It speeds the approach to equilibrium in both directions equally.
Correction: The position of equilibrium and K are unaffected.
M-48 — If I add reactant, the forward reaction just keeps going until the extra is consumed.
Confidence: verified
Why it’s wrong: Treating forward and reverse reactions as isolated.
Correction: Both rates respond; the system reaches a new equilibrium with a different composition but the same K.
M-49 — Increasing pressure always shifts the equilibrium to the right.
Confidence: verified
Why it’s wrong: It shifts toward the side with fewer moles of gas.
Correction: If the moles of gas are equal on both sides, pressure has no effect. Adding an inert gas at constant volume has no effect either.
M-50 — Le Châtelier's principle explains why the shift happens.
Confidence: likely
Why it’s wrong: It predicts, it does not explain.
Correction: The explanation is that the disturbance makes Q ≠ K, and the system responds until Q = K again.
What "HL standard" actually looks like
HL adds reaction mechanisms (elementary steps, rate-determining step, molecularity), experimentally-determined rate equations and orders (0, 1, 2), the Arrhenius equation and factor A, the reaction quotient Q with direction-of-change analysis, quantitative equilibrium calculations (including the small-K approximation), and the thermodynamic link ΔG⦵ = −RT lnK.
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.
Linking questions are recorded at the sub-topic level only. The list below aggregates the linking questions of this topic’s sub-topics.
- Official IB
What is the graphical distribution of kinetic energy values of particles in a sample at a fixed temperature?
(via R2.2)
- Official IB
What must happen to particles for a chemical reaction to occur?
(via R2.2)
- Official IB
How can molar masses be used with chemical equations to determine the masses of the products of a reaction?
(via R2.1)
- Official IBwording unverified against the guide
Graphs can be presented as sketches or as accurately plotted data points. What are the advantages and limitations of each representation?
(via R2.2)
- Official IB
How does the presence of double and triple bonds in molecules influence their reactivity?
(via R2.2)
- Official IB
How does the resonance energy in benzene explain its relative unreactivity?
(via R2.1)
- Official IB
Why is the atom economy 100% for an addition polymerization reaction?
(via R2.1)
- Official IB
Why is high activation energy often considered to be a useful property of a fuel?
(via R2.2)
- Official IB
How does limiting the supply of oxygen in combustion affect the products and increase health risks?
(via R2.1)
- Official IB
What is the likely composition of an equilibrium mixture when ΔG⦵ is positive?
(via R2.3)
- Official IB
When is it useful to use half-equations?
(via R2.1)
- Official IB
How does the molar volume of a gas vary with changes in temperature and pressure?
(via R2.1)
- Official IB
In what ways does Avogadro's law help us to describe, but not explain, the behaviour of gases?
(via R2.1)
- 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?
(via R2.1)
- Official IB
What is the relationship between the kinetic molecular theory and collision theory?
(via R2.2)
- Official IB
What is the relative effect of a catalyst on the rate of the forward and backward reactions?
(via R2.3)
- Official IB
What are the features of transition elements that make them useful as catalysts?
(via R2.2)
- Official IB
Which mechanism in the hydrolysis of halogenoalkanes involves an intermediate?
(via R2.2)
- Official IB
What are the rate equations and units of k for the reactions of primary and tertiary halogenoalkanes with aqueous alkali?
(via R2.2)
- Official IB
How does the value of K for the dissociation of an acid convey information about its strength?
(via R2.3)
- Official IB
Why do catalysts have no effect on the value of K or on the equilibrium composition?
(via R2.2)
- Official IB
How does the equilibrium law help us to determine the pH of a weak acid, weak base or a buffer solution?
(via R2.3)
- Official IB
How can Gibbs energy be used to explain which of the forward or backward reaction is favoured before reaching equilibrium?
(via R2.3)
- Official IB
Why does the extent of ionization of water increase as temperature increases?
(via R2.3)
- Official IB
How would you expect the equilibrium constants of strong and weak acids to compare?
(via R2.3)
- Official IB
How can we simplify calculations when equilibrium constants Ka and Kb are very small?
(via R2.3)
- Official IB
Why must buffer solutions be composed of weak acid or base conjugate systems, not of strong acids or bases?
(via R2.3)
- Official IB
How does Le Châtelier's principle enable us to interpret the behaviour of indicators and buffer solutions?
(via R2.3)
- Official IB
Secondary cells rely on electrode reactions that are reversible. What are the common features of these reactions?
(via R2.3)
- Official IB
Why are alkanes described as kinetically stable but thermodynamically unstable?
(via R2.2)
- Official IB
What differences would be expected between the energy profiles for SN1 and SN2 reactions?
(via R2.2)
- Official IB
What are the rate equations for these SN1 and SN2 reactions?
(via R2.2)
- Official IB
How useful are mechanistic models such as SN1 and SN2?
(via R2.2)
7 further official linking questions target Tool, Inquiry or Nature of Science strands 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?
(via R2.1)
- Official IB
Concentration changes in reactions are not usually measured directly. What methods are used to provide data to determine the rate of reactions?
(via R2.2)
- Official IB
What experiments measuring reaction rates might use time as i) a dependent variable ii) an independent variable?
(via R2.2)
- Official IB
What variables must be controlled in studying the effect of a factor on the rate of a reaction?
(via R2.2)
- Official IB
How can graphs provide evidence of systematic and random error?
(via R2.2)
- Official IB
What measurements are needed to deduce the order of reaction for a specific reactant?
(via R2.2)
- Official IB
Why are reaction mechanisms only considered as "possible mechanisms"?
(via R2.2)
Bridge: GCSE → IB HL
Derived. These are the bridge items tagged to this topic— places where the GCSE model gets redefined, genuinely new territory, or carry-over strengths. The tagging is this site’s editorial judgement.
- K-01 — Writing and balancing chemical equations, and state symbolsCarry-over
- R-11 — The mole stops being a formula triangleRedefined
- K-05 — Collision theory and the qualitative rate factorsCarry-over
- N-08 — Rate laws and the Arrhenius equation — kinetic data as evidence for mechanismNew
- R-10 — Rate stops being "how fast" and becomes a rate lawRedefined
- K-06 — Le Châtelier's principle, qualitativelyCarry-over
- R-03 — Reactions stop going to completionRedefined
- R-06 — "Exothermic = happens" becomes ΔG = ΔH − TΔSRedefined