Entropy Change, ΔS

· Entropy, S = the number of possible arrangements of particles and their energy in a given system.
· Higher entropy means more possible arrangements / greater dispersal of particles or energy.
· ΔS = entropy change of a process or reaction.
· ΔS > 0 = entropy increases; products/system are more disordered or have more possible arrangements.
· ΔS < 0 = entropy decreases; products/system are more ordered or have fewer possible arrangements.
· Main exam idea: predict whether particles and/or energy become more spread out or less spread out.

This diagram shows that entropy increases from solid to liquid to gas because particles gain more freedom of movement. It is useful for remembering the sign of ΔS during melting, boiling, freezing and condensation. Source

Entropy Changes During Changes of State

· Solid → liquid: ΔS > 0 because particles become more mobile.
· Liquid → gas: ΔS > 0 because particles become much more spread out.
· Solid → gas: ΔS > 0, usually a large increase in entropy.
· Gas → liquid: ΔS < 0 because particles become less spread out.
· Liquid → solid: ΔS < 0 because particles become fixed in a more ordered arrangement.
· Entropy usually follows: S(solid) < S(liquid) << S(gas).

This diagram summarises the main changes of state. Use it with entropy signs: changes towards gas usually have positive ΔS, while changes towards solid usually have negative ΔS. Source

Entropy Changes During Dissolving

· Dissolving often gives ΔS > 0 because particles become more spread out in solution.
· Example: an ordered ionic lattice breaks up into mobile aqueous ions.
· However, entropy predictions for dissolving can depend on the substance and hydration effects, so use the data given if calculation is required.
· For CIE-style qualitative answers, focus on whether particles become more dispersed or more ordered.

Entropy Changes During Temperature Change

· Increasing temperature usually gives ΔS > 0.
· Reason: particles have more energy, so there are more possible ways to distribute energy among particles.
· Decreasing temperature usually gives ΔS < 0.
· A temperature change that also causes a change of state has an especially important entropy change.
· Exam phrase: higher temperature → more possible energy arrangements → higher entropy.

Entropy Changes in Reactions Involving Gases

· The number of gaseous molecules is the key quick-check in many exam questions.
· If the number of gas molecules increases, ΔS is usually positive.
· If the number of gas molecules decreases, ΔS is usually negative.
· If gas moles are unchanged, consider other factors such as state, complexity and data provided.
· Solids and liquids usually have much lower entropy than gases because their particles are less free to move.
· Exam phrase: more gas particles → more possible arrangements → higher entropy.

Calculating Standard Entropy Change, ΔS⦵

· Use: ΔS⦵ = ΣS⦵(products) − ΣS⦵(reactants).
· Σ means “sum of”.
· Always multiply each S⦵ value by the stoichiometric coefficient in the balanced equation.
· Units: J K⁻¹ mol⁻¹.
· Entropy is usually given in J, not kJ; do not mix units.
· Include state symbols carefully because S⦵ depends strongly on physical state.
· CIE does not require use of ΔS⦵ = ΔSsurr + ΔSsys for this topic.

Calculation Method

· Step 1: Write the balanced equation with state symbols.
· Step 2: Calculate total entropy of products using coefficients × S⦵.
· Step 3: Calculate total entropy of reactants using coefficients × S⦵.
· Step 4: Use ΔS⦵ = products − reactants.
· Step 5: Give the correct sign and units: J K⁻¹ mol⁻¹.
· Step 6: Briefly explain the sign, usually using change in gas molecules or change of state.

Common Exam Mistakes

· Forgetting to multiply S⦵ values by balancing numbers.
· Using reactants − products instead of products − reactants.
· Writing entropy units as kJ mol⁻¹ instead of J K⁻¹ mol⁻¹.
· Ignoring state symbols, especially H₂O(l) vs H₂O(g).
· Assuming all reactions with more products have positive entropy; focus especially on gaseous molecules.