4.2Unit 4. Rates, Equilibria and Further Organic Chemistry

Entropy — IAL Edexcel Linear (Chemistry) Revision Notes & Topical Questions

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4.2 Entropy — disorder, entropy changes, total entropy and feasibility — IAL EDEXCEL LINEAR (CHEMISTRY) notes: Explain entropy in terms of arrangements of particles and energy, calculate system, surroundings and total entropy changes, and use them to judge feasibility and kinetic…

Entropy, S
Melting increases entropy
Boiling increases entropy greatly
Condensing and freezing decrease entropy
Second law
Entropy (S)

Part 1 of 11Why entropy is needed

Enthalpy change alone cannot explain why endothermic reactions occur, because the products end in a higher-energy state.

Entropy, S

Entropy, S a measure of the number of possible arrangements of the particles and their energy in a system;
- in effect, how disordered the system is.

An increase in entropy makes a system energetically more favourable, because its energy is more spread out.

Units

J K⁻¹ mol⁻¹.

Part 2 of 11Arrangements of particles and energy

Distribution of molecules

Five molecules that can be in either of two jars have W = 2⁵ = 32 arrangements; 100 molecules have 2¹⁰⁰.
The number of arrangements rises rapidly with the number of particles.
S = k ln W, where k is the Boltzmann constant.

Distribution of energy

Energy exists in packets called quanta, shared among particles.
More quanta or more particles give more ways of arranging the energy, so entropy increases with temperature.

Diffusion and spreading of heat both increase entropy.

A perfect crystal at 0 K has S = 0; elements have non-zero standard entropies, unlike Δ_fH.

Part 3 of 11Entropy and changes of state

1Melting increases entropy

Melting increases entropy particles in a regular lattice become a more random arrangement and can slide past one another.

2Boiling increases entropy greatly

Boiling increases entropy greatly gas particles move freely and are far apart.

3Condensing and freezing decrease entropy

Condensing and freezing decrease entropy particles become more ordered, so there are fewer ways to arrange the energy.

Order of entropy: solid < liquid < gas.

Entropy rises when temperature is raised because particles become more disordered.

Complex molecules have higher entropy than simple ones.

Part 4 of 11Reactions and dissolving

Producing a gas increases entropy.

CaCO₃(s) → CaO(s) + CO₂(g) forms a gas from a solid.
(NH₄)₂CO₃ reacting with ethanoic acid forms a solution and CO₂, so entropy rises although the reaction is endothermic.

Dissolving ammonium nitrate is endothermic (Δ_solH = +25.7 kJ mol⁻¹) but the ions are free to move, so entropy increases.

For ionic solids, breaking the lattice raises disorder while solvent bonding lowers it, so the sign of ΔH is hard to predict.

Two solids reacting, e.g. Ba(OH)₂·8H₂O with NH₄Cl, form NH₃ gas and a liquid, so entropy rises even though the reaction is endothermic.

When two solids react, the entropy change depends on the physical states of the products.

Part 5 of 11Entropy change of the system

ΔS_system = ΣS⦵(products) − ΣS⦵(reactants).

Multiply each S⦵ by its balancing number and use data-book values, which are never zero for elements.

Entropy changes are much smaller than enthalpy changes, so they are quoted in J K⁻¹ mol⁻¹.

An increase in the number of moles of gas almost always gives a positive ΔS_system.

Change	Sign of ΔS system	Reason
Solid to liquid to gas	Positive	Particles more free to move
More moles of gas formed	Positive	More possible arrangements
Dissolving a solid	Usually positive	Ions spread through solvent
Gas to solid	Negative	Particles become ordered
Increase in temperature	Positive	More energy quanta to distribute

Part 6 of 11Entropy change of the surroundings

Entropy change of the surroundings

ΔS_surroundings = −ΔH ÷ T, with T in kelvin and ΔH converted from kJ mol⁻¹ to J mol⁻¹ (× 1000).

An exothermic reaction passes energy to the surroundings, so ΔS_surroundings is positive.

The same amount of energy transferred to cooler surroundings gives a larger entropy change than to hotter ones.

Part 7 of 11Total entropy and feasibility

ΔS_total = ΔS_system + ΔS_surroundings.

Second law

Second law in any spontaneous change the total entropy increases, so a reaction is feasible if ΔS_total > 0.

ΔS_total is positive when:

both ΔS_system and ΔS_surroundings are positive,
ΔS_surroundings is positive and ΔS_system is negative, but ΔS_surroundings is larger,
ΔS_surroundings is negative and ΔS_system is positive, but ΔS_system is larger.

Na + Cl₂ → NaCl has negative ΔS_system but a large exothermic ΔS_surroundings, so it is feasible.

Ethanoic acid with ammonium carbonate is endothermic, but a gas forms, so ΔS_system outweighs ΔS_surroundings.

ΔH	ΔS system	Feasible?
Negative	Positive	At all temperatures
Positive	Negative	Never
Negative	Negative	Only at low temperature
Positive	Positive	Only at high temperature

Part 8 of 11Gibbs energy and the temperature of feasibility

ΔG = ΔH − TΔS_system, with ΔS in kJ K⁻¹ mol⁻¹; a reaction is feasible when ΔG ≤ 0.

Exothermic with positive ΔS is feasible at all temperatures; endothermic with negative ΔS is never feasible.

Endothermic with positive ΔS becomes feasible at high temperature, e.g. metal extraction in the blast furnace at about 1500 °C.

The minimum temperature is where ΔG = 0: T = ΔH ÷ ΔS_system.

ΔS_total = R ln K links entropy to the equilibrium constant: a large positive value gives a large K.

Part 9 of 11Thermodynamic and kinetic stability

Thermodynamic and kinetic stability

Thermodynamic feasibility says whether a reaction can happen, not how fast.

A reaction with a high activation energy is kinetically stable and may not occur at room temperature.

Methane and oxygen do not react until ignited.
H₂O₂ → H₂O + ½O₂ is feasible but needs MnO₂, which gives a lower E_a route.
Diamond to graphite is feasible but extremely slow.

ΔH and ΔS vary slightly with temperature, and non-standard conditions change the values.

Part 10 of 11More from the specification

Substance
- A material with only one type of particle.

Part 11 of 11More on this topic

Key terms

Term	Meaning
Entropy (S)	A measure of the number of ways particles and their energy can be arranged, in J K⁻¹ mol⁻¹.
Standard molar entropy	The entropy of one mole of a substance under standard conditions.
Entropy change of surroundings	ΔS surroundings = −ΔH/T.
Total entropy change	ΔS total = ΔS system + ΔS surroundings.
Feasible reaction	A reaction with a positive total entropy change (ΔG ≤ 0).
Gibbs energy change	ΔG = ΔH − TΔS system; feasible when ΔG ≤ 0.
Kinetic stability	A feasible reaction that does not occur at a noticeable rate because of a high activation energy.

Avoid these mistakes

Giving ΔS in kJ — use J K⁻¹ mol⁻¹ and convert ΔH to J mol⁻¹ before ΔS surroundings = −ΔH/T.

Using the wrong sign in ΔS surroundings — it is −ΔH/T.

Assuming elements have zero standard entropy — only ΔfH of elements is zero.

Assuming a feasible reaction is fast — a high activation energy can make it very slow.

Saying a decrease in system entropy means no reaction — the surroundings may compensate.

Last updated: 18 October 2026