What is Entropy?
In unit 5 you were introduced to the world of thermochemistry. That is, applying the rules of thermodynamics to our study of chemistry! During this unit, you learned about one key measure of energy: heat or enthalpy. In unit 9, our view of thermodynamics will be expanded past simply heat to measure reactions in terms of two other measures: entropy and Gibbs’ Free Energy. In doing so, we’ll explore a reaction’s spontaneity. In simple terms, a spontaneous process will occur without an outside intervention like adding energy to the system. For example, a ball rolling down a hill is a spontaneous process because it occurs without needing anything to happen. However, the reverse process, rolling the ball back up, is non-spontaneous. It takes work to roll a ball up a hill. In this section, we’ll dive into the idea of entropy.
Entropy can be thought of as a measure of “chaos” in a system. Essentially, entropy answers the question of “how ordered is this system?” Entropy is also described as the number of possible arrangements in a system. Essentially, the more spread out and chaotic the system is, the higher the entropy.
Entropy is important to chemists because it helps them understand energy flows in terms of creating order or disorder, especially when discussing reversible processes. To understand this, you can think about a practical example: your bedroom can get messy pretty easily. You can ruin the sheets, punch holes in the wall, throw clothes everywhere, get crazy (Fiveable does not endorse dirty rooms. In fact, go clean your room). This process is a process in which entropy increases. The room went from ordered to disordered meaning entropy increased. You can also use your energy to clean your room. This would mean your room would go from disordered to ordered and the entropy of your room would decrease. This situation explains how systems tend towards chaos—it didn’t take energy to ruin your room but it did take energy to clean it. This is part of the Second Law of Thermodynamics which we’ll discuss in more detail later in this guide.
Entropy and States of Matter
There are meaningful connections between entropy and states of matter as well. In general, solids have the least amount of disorder, followed by liquids, and finally, gases have the most entropy. This makes sense when you think about the properties of solids, liquids, and gasses. Solids are tightly packed in and have little movement between the pieces of the solid (either atoms or molecules). Therefore there is the least amount of entropy. Moving to liquids, we see more movement in the molecules and more disorder. Finally, gases are extremely chaotic. Remember that in a gas the molecules theoretically are wildly flying around. Compare this to a solid where there is not much movement at all.
We can represent state changes in the following way:
X (s) ⇌ X (l) ⇌ X (g)
Moving forward along this chain increases entropy and moving backward decreases entropy.
The Three Laws of Thermodynamics
For unit 9, there are three fundamental laws of thermodynamics that you will want to know. You will not have to memorize them verbatim for the AP exam but can be applied to explanations for problems and will give a greater conceptual understanding of the material that will be invaluable.
Law #1: The Law of Conservation of Energy
You’re probably already familiar with the First Law of Thermodynamics. This law is also known by a more common name: the Law of Conservation of Energy. This tells us that energy can never be created or destroyed but rather can only change form. For example, energy can change from potential energy to kinetic energy, but the energy between the system and the surroundings is constant. Anything lost to the system is gained by the surroundings and vice versa. From this we also know that the total energy of an isolated system remains constant.
Law #2: Energy Quality and Entropy Increases In Isolated Systems
As far as our discussion of entropy goes, the second law of thermodynamics is perhaps the most important. There are two main parts of this law.
The first part of the second law of thermodynamics refers to energy quality. It tells us that as energy is converted from form to form and/or transfers from body to body, some of it is lost to the surroundings as heat. For example, suppose a power plant runs a turbine to create electricity. In that case, some of the mechanical energy of the turbine is converted to electrical energy while some of it is lost as heat energy via friction. This same idea is applicable to any energy usage.
The second part of the second law of thermodynamics refers to entropy changes in an isolated system. The second law of thermodynamics tells us that in an isolated system, entropy will tend to either increase or stay constant. The second law of thermodynamics states that for any spontaneous process, the overall ΔS must be greater than or equal to zero.
Law #3: Absolute Zero
The third law of thermodynamics is the least important for unit 9 but is still incredibly important. This law tells us that at absolute zero (0K = -273.15°C), entropy is a constant zero. This is because at absolute zero, all molecular motion stops and there is no disorder. The formal definition of this law is that “the entropy of a system approaches a constant value as its temperature approaches absolute zero.”
Vocabulary
The following words are mentioned explicitly in the College Board Course and Exam Description for this topic.
| Term | Definition |
|---|---|
| dispersal of matter | The spreading out of particles over a larger volume, allowing them greater freedom of movement. |
| entropy change | The difference in entropy between the final and initial states of a system during a chemical or physical process. |
| kinetic energy distribution | The range and spread of energy values among particles in a system, which broadens as temperature increases. |
| kinetic molecular theory | A model explaining the behavior of gases based on the motion of particles and the distribution of kinetic energy among them. |
| moles of gas-phase products | The quantity of gaseous substances produced in a reaction, used to compare entropy changes in gas-phase reactions. |
| moles of gas-phase reactants | The quantity of gaseous substances that react in a chemical reaction, used to compare entropy changes in gas-phase reactions. |
| phase change | A transition between states of matter, such as from solid to liquid or liquid to gas. |
Frequently Asked Questions
What is entropy and why is it important in chemistry?
Entropy (S) measures how dispersed energy and matter are in a system—think of it as the number of ways particles and energy can be arranged (microstates). Boltzmann’s equation S = k ln W links entropy to microstates. Practically for AP Chem: entropy increases when matter becomes more spread out (solid → liquid → gas, or gas expansion) and when energy is more spread out (higher T broadens the Maxwell–Boltzmann distribution). For reactions with gases, compare total moles of gas: more product moles → ΔS° usually positive; fewer → ΔS° negative. Entropy matters because it’s a key part of Gibbs free energy, ΔG = ΔH − TΔS, which decides spontaneity on the exam (Topic 9.3 connections). On AP free-response and multiple-choice you’ll be asked to identify sign and relative magnitude of ΔS for phase changes, mixing, and gas changes (CED 9.1.A). For a focused review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and more unit resources (https://library.fiveable.me/ap-chemistry/unit-9). Practice with plenty of problems (https://library.fiveable.me/practice/ap-chemistry).
How do I know if entropy increases or decreases in a reaction?
Quick checklist to tell if entropy (ΔS) increases or decreases: - Matter dispersal: ΔS increases when particles become freer or occupy more volume—solid → liquid → gas raises S; mixing of gases raises S (CED 9.1.A.1). - Gas count: for gas-phase reactions, if total moles of gaseous products > reactants, ΔS is usually positive; if fewer gas moles, ΔS is usually negative. - Energy dispersal: raising temperature broadens kinetic-energy distribution and increases S (CED 9.1.A.2). - Compare tabulated standard molar entropies (S°) or use microstate idea (Boltzmann) when you need magnitude or sign. Examples: 2 H2(g) + O2(g) → 2 H2O(l): big decrease in gas moles → ΔS < 0. H2O(l) → H2O(g): ΔS > 0. On the AP exam they’ll ask for sign/relative magnitude (Learning Objective 9.1.A)—practice identifying these with the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and more problems at (https://library.fiveable.me/practice/ap-chemistry).
Why does entropy increase when a solid melts into a liquid?
When a solid melts to a liquid the particles become less confined: they can move past each other and occupy more positions. That “freedom” means the matter is more dispersed and there are many more possible microstates (ways to arrange energy and positions). By the Boltzmann equation S = k ln W, increasing the number of microstates W raises entropy S, so ΔSfusion is positive. On the AP exam you should phrase this in CED terms: entropy increases when matter becomes more dispersed (9.1.A.1). You can also mention energy dispersal: in melting some energy goes into increasing molecular motion (KMT), broadening the distribution of kinetic energies and further increasing S. For a quick review of definitions, examples, and exam-style practice, see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and the Unit 9 overview (https://library.fiveable.me/ap-chemistry/unit-9). For extra practice problems, try the AP practice bank (https://library.fiveable.me/practice/ap-chemistry).
I'm confused about entropy - is it just about disorder or something more?
Short answer: entropy isn’t just “disorder”—it’s a measure of how widely matter and energy are dispersed and how many microstates (ways to arrange particles/energy) are available. In AP terms (CED 9.1.A), S increases when matter spreads out (solid → liquid → gas, or gas expansion; more moles of gas products → higher S) and when energy is more spread (higher T broadens the Maxwell–Boltzmann distribution). Boltzmann’s idea connects S to the number of microstates: more microstates = higher entropy. On the exam you’ll most often be asked to identify the sign or relative size of ΔS for processes (phase changes, gas changes, mixing, heating)—think “more dispersal = +ΔS.” For a quick review, check the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and do practice problems at (https://library.fiveable.me/practice/ap-chemistry) to get comfortable predicting signs and magnitudes.
What's the difference between entropy increasing due to temperature vs volume changes?
Temperature and volume both increase entropy, but they do it in different ways. - Temperature change: raises entropy by dispersing energy among particles. As T increases the Maxwell–Boltzmann distribution broadens, so more kinetic-energy microstates are accessible. Quantitatively, for a temperature change at constant pressure or volume, ΔS = ∫(Cp or Cv)/T dT (energy dispersal per degree of freedom)—this is the “dispersal of energy” idea in the CED (9.1.A.2). - Volume change (isothermal expansion): raises entropy by dispersing matter—gas molecules can occupy a larger region, so there are more positional (translational) microstates. For a reversible isothermal expansion of an ideal gas, ΔS = nR ln(V2/V1) (this is the gas-expansion/position-dispersal case in 9.1.A.1). So: T changes increase entropy by increasing accessible energy states; V changes increase entropy by increasing accessible positional states. For AP review see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and Unit 9 overview (https://library.fiveable.me/ap-chemistry/unit-9). For extra practice try the AP chemistry practice problems (https://library.fiveable.me/practice/ap-chemistry).
How do I predict the sign of entropy change for phase transitions?
Think about dispersal of matter and energy (CED 9.1.A.1–9.1.A.2). When a phase change makes particles freer and spread into a larger volume, entropy increases; when particles become more ordered or confined, entropy decreases. So: solid → liquid: ΔS > 0 (more freedom); liquid → gas: ΔS > 0 and usually larger than fusion; gas → liquid or solid: ΔS < 0. Magnitude ranking: vaporization (largest ΔS) > fusion (smaller ΔS) > sublimation depends but per mole going to gas is biggest change. Also remember temperature and volume: higher T or an isothermal expansion of a gas raises S. On the exam you’ll be asked to identify both sign and relative magnitude (LO 9.1.A), so justify answers by citing dispersal of matter/energy or change in moles of gas. For a quick review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL), the Unit 9 overview (https://library.fiveable.me/ap-chemistry/unit-9), and try practice problems at (https://library.fiveable.me/practice/ap-chemistry).
Why does heating up a gas increase its entropy according to kinetic molecular theory?
When you heat a gas you’re adding energy to its molecules, so by kinetic molecular theory the average kinetic energy and the range of molecular speeds increase. That broader Maxwell–Boltzmann distribution means molecules can occupy many more possible translational energy states (more accessible microstates). Entropy measures how spread out energy and matter are—S = k ln W—so as W (the number of microstates) grows when temperature rises, S increases. Put simply: heating disperses energy among more molecular motions and allowed arrangements, so entropy goes up (CED 9.1.A.2). For a quick review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL). For extra practice on these ideas, try AP-style problems at (https://library.fiveable.me/practice/ap-chemistry).
Can someone explain entropy in simple terms without all the complicated math?
Think of entropy as a measure of how spread out stuff and energy are. If particles can move into more places (solid → liquid → gas, or a gas expanding), entropy increases because matter is more dispersed. If energy is shared among particles more widely (temperature rises), entropy also increases because the kinetic energy distribution widens. You can also use the “more microstates = higher S” idea: more ways to arrange particles/energy means greater entropy. On the AP exam you’ll mainly use these ideas to predict the sign and relative size of ΔS (look for phase changes, change in moles of gas, or temperature changes). For a quick AP review, check the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL). If you want practice applying this without math, try the AP-style questions in the Unit 9 practice set (https://library.fiveable.me/practice/ap-chemistry).
How do I count gas molecules to determine if entropy increases in a chemical reaction?
Count the gas molecules (moles) on each side: add the stoichiometric coefficients only for species in the gas phase. If the total moles of gas-phase products > total moles of gas-phase reactants, entropy (S) generally increases because matter is more dispersed (CED 9.1.A.1). If gas moles decrease, S usually decreases. Example: N2(g)+3H2(g) → 2NH3(g): 1+3 = 4 mol gas reactants → 2 mol gas products → entropy decreases. Also remember temperature and phase matter: entropy increases going solid → liquid → gas, and S increases with temperature (CED 9.1.A.2). For AP questions they often only ask sign/relative magnitude, so this mole-count rule is usually enough for quick answers on multiple-choice or free-response. For a deeper review see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL), the unit page (https://library.fiveable.me/ap-chemistry/unit-9), and try practice problems (https://library.fiveable.me/practice/ap-chemistry).
What happens to entropy when you have more gas products than gas reactants?
If a reaction produces more moles of gas than it consumes, the entropy change ΔS° for the system is generally positive—entropy increases. That follows the CED idea that entropy rises when matter becomes more dispersed: more gas moles mean particles can occupy more microstates and a larger volume (at constant T), so energy and matter are more spread out (9.1.A.1, microstates/Boltzmann ideas). On the AP exam you’ll often just state ΔS > 0 and give the “more gas moles → greater dispersal → positive ΔS” justification. Quick caveat: this is a general rule for gas-phase stoichiometry; actual ΔS° also depends on molecular complexity, phase changes, and temperature, so calculate or use tabulated standard molar entropies when precision is required. For a short review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and unit resources (https://library.fiveable.me/ap-chemistry/unit-9). Practice problems: (https://library.fiveable.me/practice/ap-chemistry).
Why does entropy increase when particles have more space to move around?
Entropy rises when particles have more space because there are more possible microstates—more ways to arrange positions and speeds of the particles. With a larger volume each molecule can be in many more places, so the number of accessible microstates (W) increases. Boltzmann’s equation, S = k ln W, shows entropy S grows as W grows. Physically this matches the CED idea that entropy increases when matter becomes more dispersed: going from solid → liquid → gas or allowing a gas to expand at constant T gives particles more freedom and a larger volume to explore, so S increases. On the AP exam you should be able to identify the sign (positive for expansion/phase to gas) and relative magnitude (bigger volume or more moles of gas → larger ΔS). For a quick topic review check the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL), broader unit links (https://library.fiveable.me/ap-chemistry/unit-9), and lots of practice problems (https://library.fiveable.me/practice/ap-chemistry).
I don't understand how energy dispersal relates to entropy - can someone help?
Think of entropy as a measure of how spread out energy and matter are. When energy is dispersed among more ways (more microstates), entropy increases. Microscopically that means particles can occupy more states: at higher T the Maxwell–Boltzmann distribution broadens (kinetic energies are more spread out), so S rises. Phase changes show this: melting or vaporization lets particles move in more positions and share energy over more degrees of freedom → higher entropy. Gas expansion (at constant T) also increases entropy because the same energy is spread over a larger volume. Boltzmann’s equation (S = k ln W) links this idea: more possible microstates W → larger S. On the AP exam you’ll be asked to identify sign and relative magnitude of ΔS for processes (CED 9.1.A), so use these quick checks: more moles of gas or ↑T or phase: solid→liquid→gas → ΔS positive. For a compact review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and practice problems (https://library.fiveable.me/practice/ap-chemistry).
How do I remember which phase changes increase entropy and which decrease it?
Think “more freedom = more entropy.” If particles can move more and occupy more space, S increases; if they’re more ordered or confined, S decreases. So: solid → liquid → gas = entropy increases; gas → liquid → solid = entropy decreases. Also, at constant T, gas expansion (bigger volume) raises S. For reactions, compare moles of gas: if products have more gas moles than reactants, ΔS tends to be positive; fewer gas moles → ΔS negative. Remember energy dispersal too: raising temperature broadens the kinetic energy distribution and increases S. On the AP exam you may be asked to identify the sign and relative magnitude of ΔS (CED 9.1.A). A quick mnemonic: “Solid tight, gas takes flight.” For a deeper review and practice, check the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and thousands of practice problems (https://library.fiveable.me/practice/ap-chemistry).
What's the connection between temperature and the distribution of kinetic energy in gases?
Temperature controls how kinetic energy is spread among gas molecules. As T rises, the Maxwell–Boltzmann distribution broadens and shifts to higher energies: more molecules have higher speeds and there’s a wider range of kinetic energies (so more accessible microstates). That broader energy dispersal means energy is more spread out, so entropy (S) increases with temperature (Boltzmann’s idea: more microstates → larger S). In practice, at low T most molecules cluster near low kinetic energies; at high T the peak flattens and the tail toward high energy grows. This idea (distribution broadens with T → ΔS positive) is exactly what the CED calls out for Topic 9.1 and can show up in free-response or multiple-choice questions about entropy and thermal effects. For a quick review of these graphs and AP-style practice, see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and try problems at Fiveable’s practice page (https://library.fiveable.me/practice/ap-chemistry).
Why do we care about entropy changes in chemical reactions anyway?
You care about entropy because it tells you how matter and energy spread out—and that spreading affects whether reactions are likely to happen. Per the CED, entropy (S) increases when matter becomes more dispersed (solid → liquid → gas, more gas moles → higher S) and when energy is more spread out (higher T broadens the Maxwell–Boltzmann distribution). Knowing the sign and relative magnitude of ΔS (Learning Objective 9.1.A) helps you predict spontaneity through ΔG° = ΔH° − TΔS°: a positive ΔS makes ΔG more negative at higher T, favoring the reaction. On the AP exam you’ll often be asked to identify the sign/relative size of ΔS for phase changes, gas expansion, or mixing—so practice spotting dispersal of matter/energy (microstates, Boltzmann idea). For a concise refresher, see the Topic 9.1 study guide (https://library.fiveable.me/ap-chemistry/unit-9/intro-entropy/study-guide/rrwnj8YrrJ2xOtgibBsL) and try practice sets (https://library.fiveable.me/practice/ap-chemistry).