Ice melts spontaneously at room temperature even though melting is endothermic (absorbs heat from surroundings). The second law of thermodynamics predicts this because:
AThe energy released to the surroundings as heat increases the universe's entropy enough to offset the system's entropy decrease
BLiquid water has vastly more accessible microstates than crystalline ice, so the system's entropy increases, and the universe's total entropy increases
CAll endothermic processes are spontaneous because they increase the randomness of the surroundings
DThe bond energy of ice is lower than liquid water, making the enthalpy change favorable
Melting increases the entropy of the system — liquid water has far more accessible arrangements than a crystal lattice. Even though the system absorbs heat (endothermic), the increase in the system's entropy is sufficient to make ΔS_universe > 0. Option A describes an exothermic process, which is the opposite scenario. Option C is wrong — endothermic processes reduce the surroundings' entropy; whether they are spontaneous depends on whether the system's entropy gain compensates. Option D is incorrect: melting is endothermic, meaning ΔH > 0 for the system.
Question 2 Multiple Choice
A chemist runs a reaction that decreases the entropy of the reaction mixture (ΔS_system < 0). Can this reaction still be spontaneous?
ANo — the second law prohibits any process that decreases the entropy of the system
BYes — if the reaction is sufficiently exothermic, the heat released increases the surroundings' entropy enough to make ΔS_universe > 0
CYes, but only at temperatures near absolute zero, where enthalpy dominates
DNo — spontaneous reactions require both ΔH < 0 and ΔS_system > 0
The second law applies to the *universe*, not just the system. A system can decrease in entropy as long as the surroundings gain at least as much. In an exothermic reaction, heat flows to the surroundings, increasing their entropy. At low enough temperatures, this surroundings entropy gain can outweigh the system entropy decrease, making ΔS_universe > 0 and the process spontaneous. A freezer making ice is the everyday example: the system (water) decreases in entropy, but the heat pumped to the room increases surroundings entropy more than enough to compensate.
Question 3 True / False
Entropy increases when a reaction produces more moles of gas than it consumes, because gas molecules have far more accessible microstates than solids or liquids.
TTrue
FFalse
Answer: True
Gases have translational, rotational, and vibrational freedom across a large volume — each molecule has an enormous number of positions and energy states available. Solids and liquids are far more constrained. When a reaction converts solids or liquids into gas molecules, the number of accessible microstates explodes. This is a reliable heuristic: reactions like CaCO₃(s) → CaO(s) + CO₂(g) have positive ΔS because one mole of gas is produced from solid reactants.
Question 4 True / False
The second law of thermodynamics states that the entropy of any system increases during a spontaneous process.
TTrue
FFalse
Answer: False
This is the most common misstatement of the second law. The correct claim is that the entropy of the *universe* (system + surroundings) increases during any spontaneous process: ΔS_universe > 0. A system's entropy can decrease spontaneously — ice forms in a freezer, proteins fold, and crystals precipitate, all with ΔS_system < 0. What cannot happen spontaneously is a decrease in the universe's total entropy. Confusing 'system' with 'universe' leads to apparent paradoxes (like 'how can a highly ordered crystal form spontaneously?') that dissolve once the surroundings are included.
Question 5 Short Answer
Why can't enthalpy change alone predict whether a process is spontaneous, and what role does entropy play in completing the explanation?
Think about your answer, then reveal below.
Model answer: Enthalpy change measures heat flow, but some spontaneous processes are endothermic (ice melting, gas expansion) and some non-spontaneous processes are exothermic. Spontaneity depends on ΔS_universe = ΔS_system + ΔS_surroundings. Entropy captures the tendency of matter and energy to disperse into the maximum number of microstates. A process is spontaneous when the total increase in accessible arrangements (for the universe) outweighs any decrease — this is what enthalpy alone misses.
This is why Gibbs free energy (ΔG = ΔH − TΔS) is needed: it combines both factors at a given temperature. At low temperatures, the enthalpy term dominates (exothermic reactions are favored); at high temperatures, the TΔS term dominates (high-entropy processes are favored). The temperature dependence reveals why some processes switch from non-spontaneous to spontaneous as temperature changes — for example, why water evaporates spontaneously above its boiling point but condenses spontaneously below it.