Absolute Entropy and Entropy Change
Use absolute molar entropy values and phase-specific coefficient sums rather than formation-enthalpy zero rules.
AP Chemistry Topic 9.2 · CED printed p. 167 / PDF p. 174. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Balanced thermochemical equations
- Molar properties and units
Standard molar entropy S° is an absolute molar property, not an entropy of formation. The reference behind absolute entropy is the ideal perfect crystal at 0 K. Elements at ordinary temperatures can have substantial S°; do not erase their values because their standard formation enthalpies are zero. To calculate the reaction change, use . Multiply each tabulated molar value by the balanced coefficient, add each side, then subtract reactants from products. State labels and temperature matter: liquid water and water vapor do not have the same molar entropy. The calculated result belongs to the equation’s amount of reaction. Reverse the equation and its ΔS° changes sign; scale the equation and ΔS° scales by that factor. Check the sign against phase or gas-count reasoning when those comparisons are meaningful, but trust complete measured values over a crude slogan when effects compete.
Let's work through it
- For H2O(l) → H2O(g), suppose the stated-temperature S° values are 69.9 and 188.8 J mol−1 K−1.
- Both coefficients are one. Subtract final minus initial: ΔS° = 188.8 − 69.9 = 118.9 J mol−1 K−1 for one mole vaporized.
- The positive sign agrees with increased matter dispersal into the gas phase.
- For 2H2O(g) → 2H2O(l), reverse and double: ΔS° = −237.8 J K−1 per mole of that written reaction. Do not assign zero to either phase.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
Why do coefficients appear in an entropy sum?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
Why do coefficients appear in an entropy sum?
Worked answer and reason
Each tabulated value is per mole, and the equation specifies how many moles change.
Entropy change is extensive with respect to the reaction amount.
Retrieval 2
Are elemental gas S° values zero at 298 K?
Worked answer and reason
No. Standard molar entropy is an absolute property with a 0 K perfect-crystal reference.
The zero formation-energy convention is different.
Catch the tempting mistake
- State labels can be dropped when subtracting entropies.
- Different phases have different accessible arrangements and different tabulated S° values.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 9 problem 2 · ap application · data
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For the teacher
- Inspect coefficient multiplication and units before calculator arithmetic; have students explain the distinction between S° and ΔHf°.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 9.2.A
- Calculate the standard entropy change for a chemical or physical process based on the absolute entropies (standard molar entropies) of the species involved in the process.
- 9.2.A.1
- The entropy change for a process can be calculated from the absolute entropies of the species involved before and after the process occurs. EQN: ΔS° reaction = ΣSo products − ΣSo reactants
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 — Required topic-numbered learning objectives and essential knowledge, all continuations and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- OpenStax Chemistry 2e §16.3, The Second and Third Laws of Thermodynamics — Absolute entropy reference and the distinction between system and total entropy.
Glossary and deeper reading · 3 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Entropy
Entropy is a state function related to the number of microscopic arrangements compatible with a macroscopic state. Changes depend on both matter and energy distribution, so visual messiness alone is not a reliable measure. For example, an ideal gas expanding at fixed temperature has more accessible positional arrangements and increased entropy.
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Standard molar entropy
Standard molar entropy is the molar entropy of a substance in its specified standard state at a stated temperature. It is an absolute-property value rather than an entropy of formation. For example, an element can have a positive standard molar entropy even though its standard formation enthalpy is zero.
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Standard enthalpy of formation
Standard enthalpy of formation is the enthalpy change for forming one mole of a substance from its elements in their standard reference forms. The substance's phase and specified temperature matter. For example, an element in its standard reference form has zero standard formation enthalpy by convention.