Predict entropy changes from gaseous particle counts
Use the change in the number of gaseous molecules as one guide to the sign of a reaction's entropy change.
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
What should be compared for the gas-mole entropy prediction?
What you will learn
- Compare gaseous stoichiometric amounts on each side
- Predict the entropy sign from a change in gas particle number
- Qualify the prediction when phases also change
More gas particles usually means more arrangements
For a reaction with gases, compare the balanced number of gaseous molecules on both sides. An increase in gaseous particles generally increases the number of possible arrangements and gives a positive contribution to ΔS; a decrease generally gives a negative contribution.
Use the balanced equation, not just the written species count. Coefficients matter: 2H₂(g) + O₂(g) → 2H₂O(g) changes three moles of gas to two.
Other phase changes still matter
The gaseous-mole rule is a useful qualitative prediction, but a reaction may also form or consume liquids and solids. Consider those phase changes and any supplied entropy data before making a final claim.
Do not compare the number of chemical formulae without including coefficients or state symbols. One mole of a gas occupies a different entropy role from one mole of a solid lattice.
Pause and explain
For 2H₂(g) + O₂(g) → 2H₂O(g), what is the gaseous-mole change?
Worked example
Predict the qualitative entropy sign for N₂(g) + 3H₂(g) → 2NH₃(g), using gaseous particle counts.
Show the worked solution
- Count four moles of gas on the reactant side.
- Count two moles of gas on the product side.
- Fewer gaseous particles generally means fewer arrangements.
Answer The gaseous-mole count falls from four to two, so ΔS is expected to be negative from this contribution.
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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 gas-count contribution to ΔS for 2SO₂(g) + O₂(g) → 2SO₃(g).
Give me a hint
Compare the coefficient totals for gaseous species.
Compare my reasoning
- Reactants have 2 + 1 = 3 moles gas.
- Products have 2 moles gas.
- A decrease in gas particles tends to lower entropy.
The gas count decreases from three to two moles, so the gas-count contribution to ΔS is negative.
Look for these in your work
- Coefficients counted
- Gas phases identified
- Sign inferred
For CaCO₃(s) → CaO(s) + CO₂(g), state the expected entropy direction and identify the strongest phase clue.
Give me a hint
Compare the phases and note that a gas is produced from solids.
Compare my reasoning
- The reactant is a solid.
- The products include a gas.
- Producing gas greatly increases accessible particle arrangements.
Entropy is expected to increase, so ΔS is positive; formation of CO₂(g) from solid reactant gives a strong increase in accessible arrangements.
Look for these in your work
- Phases read
- Gas formation identified
- Positive direction explained
A student predicts ΔS solely by counting two gas molecules on each side, while one side also includes a solid and the other a liquid. What else must be considered?
Give me a hint
Gas counts are one contribution; phase and particle arrangements also matter.
Compare my reasoning
- Include all state changes.
- Consider the more or less constrained arrangements in solids and liquids.
- Use supplied standard entropies if available for a quantitative or definitive comparison.
The gas count alone is incomplete. The solid-to-liquid change and the supplied entropy values, if available, must also be considered before assigning the net ΔS sign.
Look for these in your work
- Gas-count limitation stated
- Other phase change included
- Data use recommended
Common mistakes
- Ignoring equation coefficients
- Counting liquid or solid formula units as gas particles
- Treating the gas-count rule as exact when other phase changes dominate
- Forgetting to balance the equation first
What can you explain now?
What should be compared for the gas-mole entropy prediction?
Compare with the explanation
Balanced moles of gas on each side
Coefficients and state symbols determine the gas amounts.
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Make it stick
Why must a gas-mole count use balanced coefficients and remain a qualitative clue when phases also change?
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.