R1.4
Entropy and spontaneity
0 SL · +5 HL · HL only (HL 1.4.1-1.4.4)
Unverified
← View on the mapParent topic: What drives chemical reactions?
Guiding question
Guiding questionWhat determines the direction of chemical change?
The one big idea
Enthalpy alone does not decide whether a reaction happens — entropy does too. Gibbs energy unites them: ΔG = ΔH − TΔS. A change is spontaneous when ΔG < 0, and at equilibrium ΔG = 0.
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.
- EditorialS1.1 Introduction to the particulate nature of matterHL onlyEntropy of states is the particulate model applied to dispersal of matter and energy.
- EditorialR1.1 Measuring enthalpy changesHL onlyΔG = ΔH − TΔS needs both enthalpy and entropy.
- EditorialR1.2 Energy cycles in reactionsHL onlyHess's law and energy cycles are needed before Gibbs energy; ΔG builds on ΔH pathways.
- EditorialR2.3 How far? The extent of chemical changeHL onlyΔG⦵ = −RT lnK appears in both sub-topics; equilibrium is a prerequisite for the Gibbs capstone (reciprocal linking questions).
- EditorialR3.2 Electron transfer reactionsHL onlyΔG⦵ = −nFE⦵cell links thermodynamics to electrochemistry; electrochemistry is a prerequisite for the Gibbs capstone (reciprocal linking questions).
What rests on this
No dependents recorded.
Core concepts that must be mastered
- Entropy: the dispersal of matter and energy(1.4.1)Entropy S measures the dispersal or distribution of matter and/or energy. More ways of distributing the system's energy means higher entropy. Under the same conditions, S(gas) > S(liquid) > S(solid), because gases have the most ways to distribute their particles and energy. You can predict whether a change increases or decreases entropy from two rules of thumb: a change to a more disperse phase (solid → liquid → gas) increases entropy, and an increase in the number of gaseous moles on the product side increases entropy. You must also calculate ΔS⦵ from standard entropy values S⦵ using ΔS⦵ = ΣS⦵(products) − ΣS⦵(reactants). S⦵ values are in the data booklet. Entropy is not "disorder" or "messiness" — the tidy-bedroom analogy misleads. It is a quantitative measure of how many ways the system's energy can be distributed. A block of ice melting at 0 °C increases entropy not because the liquid is "messier" but because the molecules have more ways to arrange themselves and distribute their energy.
- Gibbs energy(1.4.2)Gibbs energy G relates obtainable energy to ΔH, ΔS and absolute temperature T: ΔG⦵ = ΔH⦵ − TΔS⦵. Watch the units carefully: ΔH is in kJ mol⁻¹, S⦵ is in J K⁻¹ mol⁻¹, so ΔS⦵ is in J K⁻¹ mol⁻¹. Divide ΔS⦵ by 1000 before using it in the equation, and always use T in kelvin. Getting the units wrong — adding kJ mol⁻¹ directly to J K⁻¹ mol⁻¹ — is the most common error here. ΔG comes out in kJ mol⁻¹.
- Spontaneity and the temperature of spontaneity(1.4.3)At constant pressure, a change is spontaneous if ΔG < 0. You must interpret the sign of ΔG from thermodynamic data and determine the temperature at which a reaction becomes spontaneous. At that temperature ΔG = 0, so T = ΔH⦵/ΔS⦵ (both in the same units). The four cases: ΔH < 0, ΔS > 0 → ΔG always negative → spontaneous at all T; ΔH > 0, ΔS < 0 → ΔG always positive → never spontaneous; ΔH < 0, ΔS < 0 → spontaneous at low T (enthalpy dominates); ΔH > 0, ΔS > 0 → spontaneous at high T (entropy dominates). Spontaneous does not mean fast — it is a thermodynamic statement about direction, not rate. Diamond → graphite has ΔG < 0 but takes geological time. Endothermic reactions can be spontaneous when the entropy increase is large enough: dissolving NH₄NO₃ in water is endothermic (the solution gets cold) yet spontaneous, because the increase in entropy from the dissolved ions overcomes the positive ΔH at room temperature. ΔG accounts for the direct entropy change of the chemicals and the indirect entropy change of the surroundings from heat transfer.
- Gibbs energy and equilibrium(1.4.4)As a reaction approaches equilibrium, ΔG becomes less negative and finally reaches zero. ΔG = 0 is the condition for equilibrium — both directions proceed at equal rate and the system is dynamic, not static. You must use: ΔG = ΔG⦵ + RT lnQ where Q is the reaction quotient. At equilibrium, Q = K and ΔG = 0, giving: ΔG⦵ = −RT lnK. This is the thermodynamic link between equilibrium (R2.3) and Gibbs energy. A large positive ΔG⦵ means K is very small (reaction hardly proceeds); a large negative ΔG⦵ means K is very large (reaction goes essentially to completion). When ΔG⦵ = 0, K = 1 and the equilibrium lies in the middle.
- How this sub-topic connectsR1.4 is the conceptual capstone of Reactivity 1 and one of the most unifying ideas in the syllabus. It sits at tier 6 (the deepest dependency tier) because it requires enthalpy (R1.1, R1.2), entropy, and the equilibrium concept (R2.3). The equation ΔG⦵ = −RT lnK connects thermodynamics to the equilibrium constant directly. ΔG⦵ = −nFE⦵cell connects to electrochemistry (R3.2): a positive E⦵cell means a negative ΔG⦵, which means a spontaneous reaction. This is why the map places R1.4 late in dependency order but early in syllabus order — it is numbered early but conceptually depends on everything below it.
Quantitative non-negotiables
- Predict whether a physical or chemical change increases or decreases entropy from the phase and the change in the number of gaseous moles.
- Calculate ΔS⦵ from standard entropy values S⦵ (in the data booklet).
- Apply ΔG⦵ = ΔH⦵ − TΔS⦵ — mind the units (ΔH in kJ mol⁻¹, ΔS in J K⁻¹ mol⁻¹, T in kelvin).
- Determine the temperature at which a reaction becomes spontaneous from the condition ΔG = 0.
- Use ΔG = ΔG⦵ + RT lnQ and at equilibrium ΔG⦵ = −RT lnK.
Common failure modes
M-33 — Exothermic reactions are the ones that happen.
Confidence: verified
Why it’s wrong: Spontaneity is governed by ΔG = ΔH − TΔS.
Correction: Endothermic reactions with a large positive ΔS (e.g. dissolving NH₄NO₃, thermal decomposition of CaCO₃ at high T) are spontaneous.
M-34 — Spontaneous means fast.
Confidence: verified
Why it’s wrong: Spontaneous is a thermodynamic statement about direction, not rate.
Correction: Diamond → graphite has ΔG < 0 and takes geological time.
M-35 — Entropy is disorder / messiness.
Confidence: likely
Why it’s wrong: The tidy-bedroom analogy misleads.
Correction: Entropy is a measure of the dispersal of matter and energy — the number of ways the system's energy can be distributed. Use the state-change ranking (gas ≫ liquid > solid) and the change in number of gaseous moles, not 'mess'.
M-36 — ΔS and ΔH can be added directly.
Confidence: verified
Why it’s wrong: ΔH is in kJ mol⁻¹, S⦵ in J K⁻¹ mol⁻¹ — different units.
Correction: Divide ΔS by 1000 before using ΔG = ΔH − TΔS, and use T in kelvin.
M-37 — ΔG⦵ = 0 means nothing is happening.
Confidence: verified
Why it’s wrong: ΔG = 0 is the condition for equilibrium.
Correction: Both directions proceed at equal rate; the system is dynamic, not static.
What "HL standard" actually looks like
HLThis sub-topic is wholly HL (hlOnly: true) — there is no SL version. Every statement (1.4.1–1.4.4) is HL. You must handle entropy, Gibbs energy, the temperature of spontaneity, and the thermodynamic link to equilibrium via ΔG⦵ = −RT lnK. This is the conceptual capstone of Reactivity 1: it unifies enthalpy (R1.1–R1.2), equilibrium (R2.3) and electrochemistry (R3.2) through ΔG.
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
Why is the entropy of a perfect crystal at 0 K predicted to be zero?
- Official IB
How can electrochemical data also be used to predict the spontaneity of a reaction?
- Official IB
What is the likely composition of an equilibrium mixture when ΔG⦵ is positive?
- Official IB
How can Gibbs energy be used to explain which of the forward or backward reaction is favoured before reaching equilibrium?
- Official IB
How can thermodynamic data also be used to predict the spontaneity of a reaction?
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.