Which reaction has > 0?
11% of national qualifiers got this right
Explanation
draftKey idea: For entropy changes, count moles of dissolved species and consider how ions order the surrounding water. Creating free ions from a neutral solid usually lowers ΔS° because each ion binds nearby water molecules into a more ordered hydration shell, overriding the increase from breaking up the solid lattice. Conversely, when ions combine to form a neutral species, those ordered water molecules are released, raising the entropy of the system.
(A) : liquid → solid is a freezing process, which reduces molecular disorder, so .
(B) : converts one highly ordered molecular solid into 60 separate graphite units. Although the mole count rises, both are rigid, low-entropy solids, and breaking strong covalent cage bonds into another solid network gives only a small, often near-zero or even negative, entropy change (experimentally for this transformation because graphite's ordered layered lattice offsets the gain from separation).
(C) : dissolving a salt into ions seems to increase disorder, but the two ions are small and highly charged, so they strongly organize surrounding water molecules into rigid hydration shells. This ordering effect dominates, making for this dissolution (a classic case where intuition about "more particles = more entropy" fails).
(D) : here two separately hydrated ions combine into two neutral species. The tightly held hydration water around and is released as those ions disappear, freeing water molecules into the bulk solvent. This net release of ordered water increases the overall entropy, so .
Answer: D
Assumes any phase change increases entropy without noting that liquid→solid is a freezing/ordering process, which actually decreases entropy.
Assumes that increasing the number of moles of solid particles always increases entropy, ignoring that both C60 and graphite are ordered solids where the lattice arrangement dominates the entropy change.
Treats dissolution of a solid into ions as automatically entropy-increasing, missing that small highly charged ions rigidly order nearby water molecules, making the overall entropy change negative.
Correctly recognizes that combining two hydrated ions into neutral molecules releases the ordered hydration shell water into the bulk solvent, increasing the system's entropy.
USNCO 2025 National Part I exam, question 23. © American Chemical Society; reproduced for non-commercial practice.