Predict entropy changes from state and temperature
Use the number of accessible particle-and-energy arrangements to explain entropy changes during state and temperature changes.
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 23. Use the syllabus sign convention for lattice enthalpy (gaseous ions forming the ionic solid); state phases, signs, units and temperature. Written practice is self-checked
Before you begin
- Use AS enthalpy changes and Hess's law, formulae for ions, balanced equations, and temperature in kelvins.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which phase generally has the greatest entropy for the same substance?
What you will learn
- Define entropy in terms of arrangements of particles and energy
- Predict entropy signs for state changes and their reverses
- Predict how entropy changes when temperature changes
Entropy counts accessible arrangements
Entropy, S, is described in this syllabus as the number of possible arrangements of particles and their energy in a system. More accessible arrangements correspond to greater entropy.
For a pure substance, gas particles have more spatial freedom than liquid particles, which have more freedom than a solid lattice. Melting and vaporisation therefore increase entropy; freezing and condensation decrease it.
Temperature and mixing change the accessible arrangements
At a fixed physical state, increasing temperature makes more energy arrangements accessible and increases entropy; lowering temperature decreases entropy. For dissolving, consider both the dispersal of solute particles and their interactions with the solvent rather than assuming every dissolution has the same sign.
Use phase, temperature and composition information in a question. A sign prediction should identify the change in accessible arrangements, not rely only on words such as ‘disorder’.
Pause and explain
What is the sign of ΔS for a substance that melts at constant temperature?
Worked example
Predict the sign of ΔS for liquid water freezing and explain the change.
Show the worked solution
- Freezing changes a mobile liquid to an ordered solid lattice.
- The particles have fewer spatial arrangements in the solid.
- Entropy decreases.
Answer ΔS is negative: freezing forms a more ordered solid with fewer accessible particle arrangements than the liquid.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Predict the entropy sign when steam condenses to liquid water at constant temperature.
Give me a hint
Compare the freedom of gas and liquid particles.
Compare my reasoning
- Condensation changes gas to liquid.
- Particles have less spatial freedom in the liquid.
- Entropy decreases.
ΔS is negative because condensation reduces the number of accessible particle arrangements.
Look for these in your work
- State change correct
- Freedom compared
- Negative sign justified
A solid warms from 250 K to 290 K without changing state. Predict the sign of its entropy change.
Give me a hint
Keep the phase fixed and compare accessible energy arrangements.
Compare my reasoning
- The final temperature is higher.
- More energy arrangements become accessible.
- Entropy increases.
ΔS is positive as the solid warms, because higher temperature increases the number of accessible energy arrangements.
Look for these in your work
- Temperature direction correct
- Energy arrangements invoked
- Positive sign stated
A student says every salt dissolving in water must have positive entropy change because the crystals disappear. Give a more careful explanation.
Give me a hint
Consider both dispersal of ions and ordering of water around them.
Compare my reasoning
- Dissolution disperses ions from a crystal.
- Hydration creates interactions and can order nearby water molecules.
- The net entropy sign depends on the balance in the stated process.
Dissolution can increase particle dispersal, but hydration also changes water arrangements. The net entropy sign depends on the particular solute and solution; it cannot be assigned solely because the crystal disappears.
Look for these in your work
- Dispersal recognised
- Hydration effect recognised
- Conclusion qualified
Common mistakes
- Claiming entropy is simply messiness without particle-and-energy arrangements
- Reversing the signs for melting and freezing
- Ignoring temperature
- Assuming every dissolution has the same entropy sign
What can you explain now?
Which phase generally has the greatest entropy for the same substance?
Compare with the explanation
Gas
Gas particles have the greatest spatial freedom.
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Make it stick
How do particle freedom, energy arrangements and temperature help you predict entropy signs?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.