Alcohol Nomenclature and Classification

A chemist hands you a bottle labeled "3-methyl-2-butanol." They expect you to draw the exact molecule without ever seeing it. That contract is honored across every lab and journal on Earth. It is what systematic nomenclature buys you. Alcohols are the single most important oxygen-containing functional group in organic chemistry. They are the products of countless reductions and additions. They are the substrates for oxidations and substitutions. They also form the scaffold underlying sugars, steroids, and half of pharmaceutical chemistry. Before any of that mechanistic richness can be discussed, you need a naming system. It must be precise enough to specify not just which atoms are present. It must also show where the hydroxyl sits and how substituted its carbon is. That carbon's substitution pattern is the single best predictor of how the molecule will react. This article builds alcohol nomenclature from the ground up. It covers how IUPAC assigns the parent chain and locant. It covers how common names persist alongside the systematic system. Most importantly for everything that follows, it covers how alcohols are classified. They are primary (1°), secondary (2°), and tertiary (3°). This classification is based on the carbon skeleton attached to the C–OH carbon. This classification is not bureaucratic decoration; it is a mechanistic lever. A tertiary alcohol reacts with HBr in seconds at room temperature. A primary alcohol under the same conditions barely reacts at all. The reason is steric and electronic, rooted in carbocation stability. You cannot predict reactivity without first being able to name. That is to say, you must recognize the substitution class correctly. The big picture is a branching tree. First, identify the longest carbon chain containing the OH-bearing carbon. Number it to give OH the lowest locant. Name it as an "-ol." Second, classify each stereocenter-adjacent or reactive carbon. Do this by counting how many carbons are directly bonded to it. Third, extend the same logic to molecules with two, three, or more hydroxyl groups. These are diols, triols, and polyols. They require their own locant sets. They retain the "-diol/-triol" suffix pattern rather than stacking multiple "-ol" endings. Along the way we treat common names (isopropanol, tert-butyl alcohol, glycerol). They remain in everyday and even regulatory use. A competent chemist must translate fluently between both vocabularies. By the end you will be able to name any acyclic or cyclic alcohol from its structure. You will be able to draw the structure unambiguously from either an IUPAC or common name. You will be able to assign 1°/2°/3° classification instantly by inspection. You will also be able to correctly name and locant polyols. This includes the special conventions for glycols. This scaffolding is the necessary foundation for understanding Structure and Hydrogen Bonding in Alcohols. It also prepares you for contrasting the alcohol functional group. You will compare it against its close relative in Ether Nomenclature and Structure.

Key takeaways
  • IUPAC alcohol names replace the alkane's terminal "-e" with "-ol"; the OH-bearing carbon gets the lowest possible locant consistent with the parent chain choice.
  • The parent chain must contain the carbon bearing OH — chain selection is not just "longest chain," it is "longest chain through the OH carbon."
  • Classification (1°, 2°, 3°) counts carbon substituents directly bonded to the carbinol carbon (the C–OH carbon), not hydrogens.
  • Common names (isopropanol, tert-butanol, allyl alcohol) survive in industrial and everyday use and must be recognized alongside systematic names.
  • Diols and triols use locants for each OH and the suffix "-diol"/"-triol"; the parent "-e" is retained before adding these suffixes (e.g., "ethanediol," not "ethandiol").
  • Cyclic alcohols are named as "cycloalkanols," with C1 fixed at the OH-bearing ring carbon.
  • Key idea: naming an alcohol correctly is inseparable from correctly identifying its carbinol carbon's substitution class, because that class governs nearly every downstream reaction.

Where this lives today

Alcohol classification is not an academic exercise; it is the first diagnostic question asked in synthetic planning, in pharmacology, and in industrial process chemistry. In drug design, distinguishing a primary from a secondary or tertiary hydroxyl on a molecule immediately tells a medicinal chemist which one will survive metabolic oxidation longest (tertiary alcohols resist oxidation to carbonyls because there is no C–H bond left on the carbinol carbon for a dehydrogenase to remove) and which one is a synthetic handle for further derivatization. Steroid hormones — testosterone, estradiol, cortisol — are literally defined by the position and class of their hydroxyl groups; a 17β-hydroxyl (secondary) versus a 3-hydroxyl elsewhere on the ring system produces entirely different receptor binding, and the systematic naming machinery built here is exactly what lets biochemists specify these positions unambiguously in the literature. In materials science and industrial chemistry, ethylene glycol (ethane-1,2-diol) and propylene glycol (propane-1,2-diol) are manufactured on a colossal scale — tens of millions of tonnes annually — as antifreeze components and polymer (polyester, PET) precursors, precisely because their diol structure (two primary or one primary/one secondary OH) allows them to serve as difunctional monomers in condensation polymerization. Glycerol (propane-1,2,3-triol), a triol with two primary and one secondary hydroxyl, is a byproduct of biodiesel manufacture and a feedstock for nitroglycerin, cosmetics, and food humectants — its triple functionality and hydrogen-bonding capacity (foreshadowed properly in the study of Structure and Hydrogen Bonding in Alcohols) both trace back to correctly counting and naming three distinct OH-bearing carbons. In carbohydrate chemistry, every sugar is fundamentally a polyol (a polyhydroxy aldehyde or ketone), and the entire vocabulary of anomeric carbons, epimers, and glycosidic linkages rests on being able to specify, unambiguously, which ring or chain carbon bears which hydroxyl and of what class. Analytical and synthetic chemists routinely exploit classification differences directly: selective oxidation reagents (like Dess–Martin periodinane) are chosen because they oxidize primary alcohols to aldehydes and secondary alcohols to ketones but cannot touch a tertiary alcohol at all — a direct, industrially exploited consequence of the classification scheme developed in this article. Finally, when chemists later study substitution and elimination mechanisms (SN1/SN2/E1/E2 as applied to alcohol derivatives, and the broader chemistry connecting alcohols to Ether Nomenclature and Structure via Williamson synthesis), the very first question asked is always "primary, secondary, or tertiary?" — because that single classification, established here purely by naming logic, is the single strongest predictor of mechanism available in the entire toolkit.

Ask the tutor: How does the 1°/2°/3° classification of an alcohol determine whether it reacts with HBr by an SN1 or SN2 mechanism?

The physical picture — chain, locant, and substitution class

The alcohol functional group is a carbon singly bonded to an –OH, where that oxygen carries two lone pairs and an O–H bond polarized by oxygen's higher electronegativity (χO=3.44\chi_O = 3.44 vs χC=2.55\chi_C = 2.55, Pauling scale). Naming has two independent jobs. The first job is purely combinatorial: find the parent chain, number it, name substituents, done — exactly as in alkane nomenclature but with the added constraint that the chain must run through the carbinol carbon and the OH locant must be minimized. The second job is chemical: classify the carbinol carbon by how many other carbons are bonded to it, because this number sets the local steric environment and — via hyperconjugation and inductive donation from alkyl groups — the electron density and stabilization available to any positive charge that might develop there in a reaction. These two jobs are logically separate but visually simultaneous: once you have drawn the structure and located C1 (or wherever OH sits), you can read off both the name and the classification from the same picture. A carbinol carbon bonded to one other carbon is primary; to two others, secondary; to three others, tertiary; and — a case worth knowing exists — a carbinol carbon bonded to zero other carbons (i.e., just CH3OH, methanol) is sometimes called "unclassified" or trivially primary-like, since there is no C–C bond to speak of at all. The chain-selection rule deserves emphasis because it is the most common source of naming errors. Unlike simple alkanes, where you simply pick the longest chain, an alcohol's parent chain is the longest chain that passes through the carbon bearing the OH group — even if a longer chain exists elsewhere in the molecule that does not include that carbon. Numbering then proceeds to give the OH substituent (expressed as the "-ol" suffix locant) the lowest possible number, and this takes priority over lowest locants for alkyl substituents when the two rules conflict.

Figure
Anatomy of an IUPAC alcohol name: chain selection, locant, and substitution class
4-methyl-2-pentanol: chain must run through C–OH C1 C2 (OH) C3 C4 C5 CH₃ OH Longest chain THROUGH C2 (the OH carbon) = 5 carbons (pentanol) Numbering from left gives OH the locant "2" — lower than numbering from right ("4") Classify C2 (carbinol C) Bonds from C2 go to: • C1 (one carbon) • C3 (one carbon) • H • OH Two C substituents on carbinol C ⇒ SECONDARY (2°) alcohol

Cyclic alcohols follow the same two rules with one adjustment: the ring carbon bearing OH is automatically assigned locant 1, since a ring has no natural "end" to number from. Substituents are then numbered around the ring in whichever direction gives the lowest locant set, exactly as with substituted cycloalkanes.

Figure
Primary, secondary, and tertiary alcohols — counting carbons on the carbinol carbon
Classification by carbon count on C–OH OH R H, H 1° (primary) 1 carbon on C–OH OH R R′ H 2° (secondary) 2 carbons on C–OH OH R R′ R″ 3° (tertiary)

The core ideas

For an acyclic saturated monoalcohol with nn carbons in the parent chain, the systematic name follows directly from the alkane name:

name=locant-[substituents]-alkane⏟dropped-[locant]-ol\text{name} = \text{locant-}[\text{substituents}]\text{-alkan}\underbrace{e}_{\text{dropped}}\text{-}[\text{locant}]\text{-ol}

where: the parent alkane name (e.g., "pentane") loses its terminal "-e" and gains "-ol"; the OH locant is inserted immediately before "-ol"; substituent locants and names are alphabetized and prefixed as usual. The locant-minimization rule that governs numbering is a strict priority ordering:

locant(OH)  <  locant(substituents)  <  alphabetical order of citation\text{locant}(\text{OH}) \;<\; \text{locant}(\text{substituents}) \;<\; \text{alphabetical order of citation}

where: the OH suffix locant is chosen to be as low as possible first; only when OH placement is fixed (or tied) do substituent locants get minimized; alphabetical order affects only how names are written, never which locants are chosen. For classification, define nCn_C as the number of carbon atoms directly σ\sigma-bonded to the carbinol carbon (excluding the OH oxygen and any H):

class={primary (1°)nC=1secondary (2°)nC=2tertiary (3°)nC=3\text{class} = \begin{cases} \text{primary (1°)} & n_C = 1 \\ \text{secondary (2°)} & n_C = 2 \\ \text{tertiary (3°)} & n_C = 3 \end{cases}

where: nCn_C counts carbon substituents only, never hydrogens or the OH itself; methanol (nC=0n_C=0) is a degenerate case sometimes classified separately since it has no C–C bond at the carbinol carbon at all. For polyols, the naming rule generalizes by retaining the full alkane stem (unlike monools, the terminal "-e" is kept) and appending a multiplying prefix plus "-ol":

name (polyol)=locants1,2,…,k-alkane⏟retained-(di/tri/tetra)ol\text{name (polyol)} = \text{locants}_{1,2,\ldots,k}\text{-alkan}\underbrace{e}_{\text{retained}}\text{-}\text{(di/tri/tetra)ol}

where: kk is the number of OH groups; the locant set is written as a comma-separated list before "-diol"/"-triol"; the "-e" is retained because "-diol" begins with a consonant-adjacent vowel cluster that would otherwise create an unpronounceable elision (contrast "ethanol" from "ethane" + "-ol," where the vowel is dropped, versus "ethane-1,2-diol," where it is not).

Derivation AMechanism 1: choosing the parent chain and assigning the lowest OH locant

Goal. Given a skeletal structure with a hydroxyl group and one or more branch points, derive the unique correct IUPAC name step by step, showing why chain choice and numbering direction are not arbitrary.

Step 1 — Locate every OH group and identify candidate parent chains. Draw out the full carbon skeleton. Identify the carbon(s) bearing OH. Any chain considered as the "parent" must pass through every OH-bearing carbon carbon you intend to name with a suffix — you are not permitted to name OH as a substituent prefix ("hydroxy-") if a chain exists that includes it, because the OH functional group has suffix priority over simple alkyl branches under IUPAC seniority-of-suffix rules.

Step 2 — Among chains through the OH carbon(s), pick the longest. Consider the molecule (CH₃)₂CH–CH(OH)–CH₂–CH₃. The carbon bearing OH is bonded to an isopropyl-like branch on one side and an ethyl chain on the other. Tracing through the OH carbon, the longest continuous chain is: (CH₃)–CH(CH₃)–CH(OH)–CH₂–CH₃, a five-carbon (pentanol) backbone, with a methyl substituent hanging off. A shorter alternative chain that avoids the OH carbon (there is none longer here, but in general such a chain would be irrelevant) is never chosen, because the OH carbon's inclusion is mandatory.

Step 3 — Number the chosen chain to minimize the OH locant. Number from the end that gives OH the lower locant. Numbering left-to-right from the isopropyl end: C1 = terminal CH₃ of the branch's chain, C2 = CH bearing the methyl branch, C3 = CH(OH), C4 = CH₂, C5 = CH₃. This assigns OH locant 3. Numbering from the other end would assign OH locant 3 as well only if the chain is symmetric — here it is not, so you must explicitly compare: numbering from the right end (starting at the terminal ethyl CH₃) gives C1 = CH₃, C2 = CH₂, C3 = CH(OH), C4 = CH(CH₃), C5 = CH₃ — also locant 3 for OH, a tie. When OH locants tie, the next tiebreaker is the substituent (methyl) locant: the first numbering gives methyl at C2, the second at C4. Lower wins, so numbering must run from the isopropyl end, giving methyl at C2.

Step 4 — Assemble the name. Parent: pentan-3-ol (or "3-pentanol" in the older locant style). Substituent: 2-methyl. Alphabetize (only one substituent here) and combine:

name=2-methylpentan-3-ol\text{name} = \text{2-methylpentan-3-ol}

Step 5 — Sanity check by re-deriving the structure from the name. "Pentan-3-ol": five-carbon chain, OH at C3. "2-methyl": a methyl at C2. Redrawing: CH₃–CH(CH₃)–CH(OH)–CH₂–CH₃ — identical to the starting structure. The name is unambiguous and round-trips correctly.

Go deeper · Derivation B · 1 minMechanism 2: naming and classifying a diol, and assigning 1°/2°/3° character to each carbinol carbon
Derivation BMechanism 2: naming and classifying a diol, and assigning 1°/2°/3° character to each carbinol carbon

Goal. Extend chain/locant logic to a molecule with two hydroxyl groups, and independently classify each OH-bearing carbon — showing that a single molecule can contain carbinol carbons of different classes.

Step 1 — Draw the target structure. Consider 4-methylpentane-1,2-diol: a five-carbon chain with a methyl branch at C4, and OH groups at C1 and C2. Structure: HOCH₂–CH(OH)–CH₂–CH(CH₃)–CH₃.

Step 2 — Verify the parent chain includes both OH carbons. The longest chain touching both C1 and C2 (the OH-bearing carbons) is the five-carbon pentane backbone drawn above; no rearrangement of chain choice can shorten the locant set below {1,2}, so this is confirmed optimal.

Step 3 — Assign the lowest locant set (not just the lowest single locant) for the two OH groups. For polyols the rule generalizes from "lowest single locant" to "lowest locant set," compared term-by-term. Numbering from the left gives OH locants {1,2}; numbering from the right would give OH locants {4,5}. Comparing first points of difference, 1<41 < 4, so left-to-right numbering wins decisively.

Step 4 — Retain the parent "-e" and append the diol suffix. Because "-diol" is being added (not simple "-ol"), the alkane stem keeps its terminal "-e": "pentane" + "-1,2-diol" → pentane-1,2-diol. Add the methyl substituent locant (C4) and alphabetize:

name=4-methylpentane-1,2-diol\text{name} = \text{4-methylpentane-1,2-diol}

Step 5 — Classify each carbinol carbon independently. C1 (bearing one OH) is bonded to: two H's, the OH oxygen, and C2. Only one carbon substituent ⇒ C1 is a primary alcohol carbon. C2 (bearing the other OH) is bonded to: C1, C3, one H, and its OH oxygen. Two carbon substituents ⇒ C2 is a secondary alcohol carbon.

Step 6 — State the composite classification. The molecule is correctly described as containing one primary and one secondary hydroxyl group — it is not meaningfully described by a single global "class" label, because classification is a local, per-carbon property. This is the general lesson: whenever a molecule carries more than one OH group, each must be classified separately, and reactivity predictions (e.g., which OH oxidizes faster, which undergoes SN1 substitution more readily) must be made carbon-by-carbon.

Worked examples

Example 1 (foundational): naming and classifying 3-methyl-2-butanol. Structure: CH₃–CH(OH)–CH(CH�3)–CH₃, i.e., the carbinol carbon (C2) is flanked by a methyl (C1) on one side and an isopropyl-type branch (C3, itself bearing a methyl) on the other. Chain selection: the longest chain through the OH carbon is four carbons: C1(CH₃)–C2(CHOH)–C3(CH)–C4(CH₃), with a methyl substituent on C3. Numbering: from the left, OH is at C2; from the right, OH would be at C3. Since 2<32 < 3, number from the left. OH locant = 2, methyl substituent locant = 3. Name:

3-methylbutan-2-ol(equivalently, "3-methyl-2-butanol")\text{3-methylbutan-2-ol} \quad (\text{equivalently, "3-methyl-2-butanol"})

Classification: C2 (carbinol carbon) is bonded to C1 (a methyl) and C3 (an isopropyl-like carbon) — two carbons total, plus one H and the OH. So nC=2n_C = 2, making this a secondary (2°) alcohol. As a limiting-case check: if the C3-methyl branch were absent (i.e., the molecule were simply butan-2-ol, CH₃–CH(OH)–CH₂–CH₃), the carbinol carbon would still be bonded to two carbons (C1 and C3) and would still be classified 2° — confirming that the classification rule counts connectivity, not molecular size, and is stable under simplification of the rest of the skeleton.

Example 2 (applied): common-name/IUPAC translation for isopropyl alcohol and its industrial relevance. "Isopropyl alcohol" (rubbing alcohol) is the common name built from the substituent name "isopropyl" (the two-carbon-branch group (CH₃)₂CH–) plus "alcohol." To find the IUPAC name, first draw the structure: (CH₃)₂CH–OH. The parent chain must contain the carbinol carbon; the longest such chain is three carbons: C1(CH₃)–C2(CHOH)–C3(CH₃). Numbering from either end gives OH locant 2 (a symmetric molecule, so both directions tie exactly — the classic worth-noting limiting case where locant choice becomes irrelevant by symmetry). The IUPAC name is:

propan-2-ol\text{propan-2-ol}

Classification: C2 is bonded to C1 and C3, two carbons, both methyls — nC=2n_C = 2, a secondary alcohol, consistent with the "iso-" prefix's usual (though not universal) correlation with branching at a secondary center. Industrially, propan-2-ol's secondary OH oxidizes readily to acetone (propan-2-one) and is manufactured on a scale of billions of kilograms per year for use as a solvent and disinfectant — precisely because its intermediate polarity (moderately hydrogen-bonding, moderately lipophilic due to the two methyls) makes it miscible with both water and many organic residues, a property traceable directly to its secondary, doubly-alkyl-substituted carbinol carbon.

Example 3 (exam/competition level): naming a polysubstituted cyclic triol and classifying all three carbinol carbons. Consider a cyclohexane ring bearing three OH groups and one methyl substituent, with the following connectivity: ring carbons C1 (OH, also bonded to a methyl substituent — i.e., C1 bears both OH and CH₃), C2 (OH), C4 (OH), and no other substituents (C3, C5, C6 bear only H's). This is a triol. Step 1 — Ring numbering starts at an OH-bearing carbon by convention, but with three OH groups and one methyl, we must find the numbering direction and starting OH carbon that gives the lowest locant set for all suffix and prefix substituents combined, with OH locants taking priority. Candidate locant sets for the three OH groups, trying different starting points and directions, include {1,2,4}, {1,3,5}, and others depending on where we place "C1." Enumerating around the ring (OH, OH, H, OH, H, H going one way) shows that starting the numbering at one of the OH carbons adjacent to another OH carbon, and proceeding toward the third OH the short way, gives OH locants {1,2,4} — verified as the lowest achievable set by comparing against all six possible starting points and both directions (no other placement beats first-point-of-difference 1 versus a competing 1, then 2 versus a competing higher second locant). Step 2 — With OH locants fixed at {1,2,4}, the methyl substituent (on the same carbon as one OH, C1) receives locant 1 automatically since it shares that ring carbon. Step 3 — Assemble the name, retaining the parent "-e" for the triol suffix:

name=1-methylcyclohexane-1,2,4-triol\text{name} = 1\text{-methylcyclohexane-1,2,4-triol}

Step 4 — Classify each carbinol carbon individually. C1 bears OH and is bonded to: the ring carbons C2 and C6 (two ring carbons), plus the exocyclic methyl carbon — three carbons total. So C1 is a tertiary (3°) alcohol carbon (and also, incidentally, a stereocenter candidate since it bears four different groups: OH, CH₃, and two different ring paths). C2 bears OH and is bonded only to ring neighbors C1 and C3 — two carbons — making C2 a secondary (2°) alcohol carbon. C4 bears OH and is bonded only to ring neighbors C3 and C5 — two carbons — making C4 also secondary (2°). This example demonstrates the fully general result: a single small molecule can simultaneously contain one tertiary and two secondary alcohol centers, and correct classification requires examining each carbinol carbon's local substitution independently of the others, exactly as the diol mechanism established.

Limiting cases, scope & common traps

CaseCorrect handlingCommon error
OH on a carbon with only H's and no other carbon (methanol)nC=0n_C = 0; often just called "methanol," not assigned 1°/2°/3°Forcing it into "primary" by miscounting an H as a carbon
Symmetric molecule (e.g., propan-2-ol)Both numbering directions tie; either gives the same locantAssuming a "tie" means the rule failed — it just means direction is irrelevant here
Two OH groups on the same carbon (geminal diol / hydrate)Named as an "-diol" with a repeated locant, e.g., propane-1,1-diol; usually unstable, dehydrates to a carbonylAssuming geminal diols are common isolable species — most are not (equilibrium favors the carbonyl + water)
Longer chain exists but skips the OH carbonNever choose it as parent — parent chain must contain the OH carbonDefaulting to "longest chain overall" as in alkane naming
Substituent locants vs. OH locant conflictOH (as principal characteristic group / suffix) always wins lowest-locant priorityMinimizing substituent locants first and OH second
Common names (isopropanol, tert-butanol, glycerol, ethylene glycol)Recognize and translate freely; still widely used in industry and biologyTreating common names as "wrong" or obsolete — they are simply non-systematic, not incorrect
Cyclic alcoholsOH carbon is always C1; number the ring to minimize the full substituent locant setNumbering the ring as if it were a chain, ignoring the OH-fixes-C1 rule

The chemist behind it

Modern IUPAC nomenclature is a collective institutional achievement rather than the work of one individual, but its most direct intellectual ancestor is the Geneva Nomenclature Congress of 1892, whose guiding architect among organic chemists was Charles Adolphe Wurtz — though Wurtz died in 1884, the systematic committee-based approach to naming that he championed throughout his career (rational nomenclature tied to structural theory rather than to derivation or trivial history) shaped the Geneva rules directly. Wurtz was a central figure in mid-19th-century French organic chemistry, best known for the Wurtz reaction (coupling of alkyl halides with sodium) and for his vigorous defense of structural theory — the idea that a compound's properties follow from a definite arrangement of atoms and bonds, not merely from its empirical formula. That conviction is precisely what nomenclature must encode: a name is only useful if it maps onto one, and only one, structural arrangement.

Origins · 1 minCharles Adolphe Wurtz and how this was discovered
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Charles Adolphe Wurtz
1817–1884 · French organic chemistry, structural theory, precursor to systematic nomenclature

Wurtz trained under Justus von Liebig and became one of the foremost advocates of Kekulé and Couper's structural theory in France, at a time when many chemists still resisted the idea that molecules had definite three-dimensional connectivity. He discovered the Wurtz coupling reaction (1855), contributed to early glycol and diol chemistry (he is credited with the first synthesis and naming discussions of ethylene glycol derivatives), and chaired preparatory work that fed directly into the 1892 Geneva Congress, which established the first international systematic organic nomenclature — the direct ancestor of modern IUPAC rules. His insistence that names should encode structure unambiguously is the philosophical seed of every locant rule used above.

History
- 1855 — Wurtz reports the coupling reaction bearing his name, reinforcing structural (not just compositional) thinking about organic molecules.
- 1858 — Kekulé and Couper independently propose tetravalent carbon and chain-forming bonds, the structural basis nomenclature must encode.
- 1874 — van 't Hoff and Le Bel propose the tetrahedral carbon, adding the stereochemical dimension later needed for R/S-aware alcohol naming.
- 1892 — the Geneva Nomenclature Congress establishes the first internationally agreed systematic rules for naming organic compounds, including alcohols.
- 1947 onward — IUPAC (founded 1919) issues periodically revised recommendations refining locant, suffix, and retained-name rules into the modern system used today.
Why do we drop the "-e" in "ethanol" but keep it in "ethane-1,2-diol"?

The dropped/retained "-e" follows a simple euphonic and precedent-based IUPAC convention: when the suffix being added starts with a vowel that would otherwise create an awkward double-vowel or ambiguous elision, the terminal "-e" of the alkane stem is dropped only in specific single-suffix cases like "-ol," "-al," "-one," "-oic acid." However, when a multiplying prefix (di, tri, tetra) intervenes between the stem and the vowel-initial suffix, as in "-diol," the "-e" is retained because "ethandiol" would be a harder-to-parse and non-standard string, whereas "ethanediol" is unambiguous and matches the general pattern used across all multiplied suffixes in IUPAC nomenclature.

Can a carbon be both a stereocenter and classified as primary?

No — a primary carbinol carbon is bonded to only one other carbon plus two hydrogens and the OH, so it necessarily has two identical substituents (the two H's) and cannot be a stereocenter, since a stereocenter requires four different groups. Secondary and tertiary carbinol carbons, in contrast, can be stereocenters if their remaining substituents happen to differ — for example, the C2 of 3-methylbutan-2-ol is a genuine stereocenter because it bears OH, H, methyl, and the isopropyl-derived branch, all four different.

Is "isopropanol" an acceptable name, or must I always say "propan-2-ol"?

Both are acceptable in different registers. IUPAC's 2013 recommendations formally retain "propan-2-ol" as the preferred name for regulatory and publication purposes, but "isopropanol" (and its older form "isopropyl alcohol") remains an accepted common name in general use, in industry, and in many national pharmacopoeias. A working chemist should be fluent in both directions of translation, since real-world labels, safety data sheets, and older literature use common names extensively.

How do you name an alcohol where the OH group is on a ring carbon that also bears a double bond nearby, like 2-cyclohexen-1-ol?

The ring is numbered starting at the OH-bearing carbon (fixed as C1 by convention for the principal characteristic group), and then the numbering direction around the ring is chosen to give the lowest locant to the next point of unsaturation — here, the double bond between C2 and C3 requires the lower of those two numbers to appear, so numbering proceeds toward the closer alkene carbon. The resulting name, "cyclohex-2-en-1-ol," specifies unambiguously that OH sits at C1 and the double bond spans C2–C3, distinguishing it cleanly from the alternative connectivity where the alkene would be further from the OH.

Does classification (1°/2°/3°) change if the alcohol is dissolved in water or otherwise not in the gas phase?

No — classification is a purely structural, connectivity-based property (how many carbons are bonded to the carbinol carbon), and it does not depend on solvent, phase, temperature, or concentration. What does change with environment is reactivity and hydrogen-bonding behavior built on top of that fixed classification; the classification itself is an invariant label read directly off the Lewis structure, the same way you would read off molecular formula or connectivity.

Why does the diol/triol case need a "locant set" comparison instead of just picking the single lowest number?

With more than one identical suffix group, there is no single "the" locant to minimize — you must compare the entire ordered list of locants between competing numbering schemes, term by term, at the first point of difference. For example, comparing candidate sets {1,2,4} and {1,3,4}, both start with 1, so you move to the second number: 2 beats 3, so {1,2,4} wins outright, even though the final numbers (4 versus 4) are tied and irrelevant to the decision.

What happens to classification when the "other" substituent on a secondary carbon is itself part of a ring, rather than an open chain?

Classification only counts how many carbon atoms are directly bonded to the carbinol carbon, not what kind of carbon (ring, chain, aromatic, or otherwise) those substituents are. A ring carbon bearing OH and bonded to two other ring carbons (plus one H) is secondary, exactly as if those two carbons were open-chain alkyl groups; the classification rule is purely a bond-counting rule and is indifferent to whether the attached carbons happen to be constrained into a ring.

Where this leads