🎓 Prepared by students from Boğaziçi University

What is Entropy?

Entropy (S) is a measure of disorder or randomness in a system. The Second Law of Thermodynamics states that entropy of the universe always increases — it is the driver of spontaneous reactions.

Short answer

Entropy quantifies the number of microstates (molecular arrangements) available to a system. Higher entropy means more disorder. In spontaneous reactions, the total entropy change (system + surroundings) is positive: ΔS_universe > 0.

Low entropy (ordered) vs High entropy (disordered)

Low entropy

•Organized structure
•Few microstates
•Crystals, ice
•S is small

High entropy

•Random arrangement
•Many microstates
•Gas, liquid
•S is large

Step-by-step worked examples

Ice melts to water at 0°C. Does entropy increase?

Solid ice has ordered crystal structure (low S)
Liquid water has more random molecular motion (high S)
ΔS_system > 0 (entropy of system increases)
Reaction is spontaneous → ΔS_universe > 0

Gas dissolving in water at room temperature. Is it spontaneous?

Gas molecules expand into solution (many more microstates)
ΔS_system >> 0 (large positive entropy increase)
Spontaneous process (ΔS_universe > 0)

Why does spilled perfume spread through a room spontaneously?

Perfume molecules escape (high ΔS_system)
Molecules occupy larger volume → many more microstates
Process has ΔS_universe > 0 → spontaneous
Reverse (perfume gathering) has ΔS < 0 → never observed

Flashcards

Quick quiz

Q1.Which has higher entropy: ice or water?

Correct answer: B. Water is liquid → more molecular motion and disorder → higher entropy than solid ice.

Q2.In a spontaneous reaction, ΔS_universe is:

Correct answer: B. Second Law: spontaneous reactions always have ΔS_universe > 0.

Q3.Dissolving salt in water. System entropy ΔS_system is:

Correct answer: C. Solid salt dissociates → ions spread in solution → disorder increases → ΔS_system > 0.

Q4.Which process is entropy-driven?

Correct answer: B. Gas expanding to fill space has ΔS >> 0 — highly spontaneous and entropy-driven.

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Common mistakes

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Thinking entropy only applies to temperature. — Correct: Entropy is disorder — applies to molecules, arrangements, microstates.

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Confusing entropy with energy (enthalpy). — Correct: ΔH = heat; ΔS = disorder. Both drive spontaneity (Gibbs: ΔG = ΔH − TΔS).

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All exothermic reactions are spontaneous. — Correct: Spontaneity needs ΔG < 0 (both ΔH and ΔS matter).

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Entropy of a single system is always positive. — Correct: ΔS can be negative; it's ΔS_universe that must be > 0 for spontaneous.

FAQ

What is the definition of entropy?

A measure of disorder or the number of microstates (molecular arrangements) in a system.

Why does the universe tend toward higher entropy?

More disorder is statistically more probable — there are more ways to be disordered than ordered.

Can a system have negative ΔS?

Yes, but only if ΔS_surroundings is more positive. The total ΔS_universe must be > 0.

Is freezing water spontaneous at 0°C?

At exactly 0°C, ΔG = 0 (equilibrium). Below 0°C, freezing is spontaneous (ΔG < 0).