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Adamantane is the saturated cage hydrocarbon ${\mathrm{C}}_{10}{\mathrm{H}}_{16}$. Its carbon framework is a compact three-dimensional network of fused chair-like six-membered rings, with the connectivity recorded by its tricyclic structural name.^[ref]

The rigid cage restricts conformational motion. Symmetry can make several carbon or hydrogen positions equivalent in a spectrum, while substitution breaks those equivalences. The molecule therefore provides a useful example of how three-dimensional connectivity and molecular symmetry influence chemical reactivity and spectroscopic counting.

Dimethyl ether, also called methoxymethane, is an ether with an oxygen atom bonded to two methyl groups. Its structural formula is $\mathrm{C}{\mathrm{H}}_3-\mathrm{O}-\mathrm{C}{\mathrm{H}}_3$ and its molecular formula is ${\mathrm{C}}_2{\mathrm{H}}_6\mathrm{O}$. It is a constitutional isomer of ethanol: the atoms have the same inventory but different connectivity.^[ref]

The oxygen connectivity gives a useful molecular comparison. Ethanol contains an oxygen–hydrogen bond; dimethyl ether does not. Thus the two chemical structures present different possibilities for hydrogen bonding, even though weighing equal numbers of their molecules would not distinguish their common elemental formula.

Their physical identity can be tested by measurements beyond composition. NIST tabulates a normal boiling point near $248.3\mathrm{K}$, approximately $-24.9{}^{\circ }\mathrm{C}$, for dimethyl ether. This illustrates why a small carbon-containing molecule can be a gas under ordinary room conditions: phase behavior follows its interactions and external conditions, rather than molecular formula alone.^[ref]

Ketene is the compound $\mathrm{C}{\mathrm{H}}_2=\mathrm{C}=\mathrm{O}$, also called ethenone. More generally, ketenes contain the cumulative $\mathrm{C}=\mathrm{C}=\mathrm{O}$ unit.^[ref] Adjacent double bonds make this a different functional group from an ordinary isolated alkene or ketone.

Attack by a suitable nucleophile at the electrophilic carbon can convert a ketene into a carboxylic-acid derivative; addition of water, for example, gives an acid. Substitution around the terminal carbon affects both reaction selectivity and competing pathways. The displayed parent formula should not be confused with every substituted member of the ketene class.

Species entry in NIST Chemistry WebBook, SRD 69, published and hosted by the National Institute of Standards and Technology. No personal entry author is credited. The displayed 2026 copyright year is distinct from an entry publication or revision date.

Online text: webbook.nist.gov/cgi/cbook.cgi?ID=C877247

Cited passages: Formula C8H5KO4; Molecular weight 204.2212; CAS Registry Number 877-24-7; footer copyright.

The clearest comparison is between the two amines, which have the same molecular formula and molar mass. isopropylamine can donate N–H hydrogen bonds to neighbouring nitrogen lone pairs; trimethylamine has no N–H donor. The resulting intermolecular association raises the primary amine's boiling point, allowing it to remain liquid at room temperature, whereas trimethylamine is gaseous. Independent phase-change data place their normal boiling points on opposite sides of room temperature.^[ref]

acetone has a substantial carbonyl dipole and London dispersion forces sufficient for a room-temperature liquid, even though it cannot build a strong donor–acceptor hydrogen bond network by itself. isobutane has mainly London dispersion forces and a compact shape and remains gaseous. acetamide combines carbonyl acceptors with two N–H donors, allowing an extended, directionally bonded crystal lattice; favourable packing as well as intermolecular association stabilizes its solid state.

These compounds have similar molar masses, so mass alone cannot explain the differences. The hydrogen-bond acceptor parameter also cannot predict the phase on its own: a pure substance needs complementary donors to exploit strong acceptor sites, and freezing additionally depends on crystal packing and entropy. A stronger acceptor does not automatically imply a higher melting point for arbitrary molecules.

Take the bond axis as $z$. The heavy-atom $2s$ and $2p_z$ atomic orbitals can mix with hydrogen $1s$ to make three sigma-symmetry molecular orbitals. In the qualitative valence ordering, these are a low predominantly heavy-atom $2s$ level, a bonding $\sigma$ level and a higher ${\sigma }^{\ast }$ level. The perpendicular $2p_x,2p_y$ orbitals form a degenerate approximately nonbonding $\pi$ pair because hydrogen has no valence orbitals of the matching sideways symmetry. The filled heavy-atom $1s$ core is omitted from the diagram.

Counting valence electrons givesThus both exhibit paramagnetism: CH has one unpaired electron and NH has two in its ground state. For NH, Hund's rules favour separate parallel-spin occupation of the two degenerate $\pi$ orbitals. The corresponding observed ground terms are $X{}^2\Pi$ and $X{}^3{\Sigma }^{-}$; the total bond order is approximately one in this simple sigma-bond/nonbonding-pi description.^[ref]

The nitrogen-derived orbital energies lie lower than the corresponding carbon-derived ones on an approximate common energy scale, while the isolated hydrogen $1s$ reference is unchanged. The bonding orbitals consequently have different polarizations and mixing coefficients; drawing identical energies for C and N would miss the screening trend. The figure specifies ordering and occupancy, not measured gaps or a numerical prediction from (a).

Take dry air as unity, and compare each gas at the same temperature and pressure. In the ideal gas approximation, $\rho =pM/(RT)$, so the relative density isHere $M$ is molar mass. The following values use modern approximate molar masses; rounding and historical atomic weight conventions can shift the last figures.

“Olefiant gas” is confirmed as a historical synonym of Ethylene in the NIST Chemistry WebBook, SRD 69. In this gas list, “carbonic acid” means carbon dioxide, not an isolated vapour of aqueous ${\mathrm{H}}_2{\mathrm{CO}}_3$. “Alcohol” and “ether” refer to ethanol and diethyl ether, rather than their entire modern chemical classes.^[ref]

The order is therefore Ammonia, then carbon monoxide and Ethylene nearly tied, then air, then carbon dioxide and nitrous oxide nearly tied, then ethanol vapour, then diethyl ether vapour. Nearly equal molar masses do not imply equal chemical behaviour.

If instead molecular hydrogen is chosen as unity, divide each molar mass by about $2.016\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ and state that convention. In the older nominal ${\mathrm{H}}_2=2$ approximation, the corresponding values are about $22,14,22,14.5,8.5,14,23,37$ in the source order. These are a different reference scale, not different substances.

The vapour comparisons are not comparisons of the liquid densities. Pure ethanol and diethyl ether must be considered at conditions where they remain gaseous, or by a low-pressure gas approximation. Their liquids can be lighter than water while their vapours are heavier than air.

At coexistence, the two phases have equal chemical potential. For a single component, $d\mu =-sdT+vdp$, with entropy and volume measured on the same molar or mass basis. Equating the phase derivatives along coexistence gives $\Delta vdp=\Delta sdT$. Reversible latent heat satisfies $L=T\Delta s$, henceHere $p$ and $T$ are coexistence pressure and absolute temperature, $L$ is latent heat for transforming phase 1 to phase 2, and $\Delta v=v_2-v_1$ uses the same amount of material as $L$.

For vaporization, neglect liquid molar volume compared with ideal-vapour volume $RT/p$. The ideal-vapour Clausius-Clapeyron approximation becomesUsing the normal boiling reference $T_b=373.15\mathrm{K}$, $p_b=1.01325\times 10^5\mathrm{Pa}$ and the supplied constant $L_e$ givesThis deliberately constant-latent-heat extrapolation does not reproduce the supplied triple-point pressure exactly. It predicts the liquid-vapour branch, metastable against ice below the triple-point temperature; it is not a precision sublimation-pressure prediction.

The phase diagram has solid, liquid and vapour regions meeting at the triple point. The sublimation and vaporization boundaries have positive slopes, whereas the ordinary ice–water boundary slopes negatively because ice has larger specific volume. The liquid–vapour line terminates at a critical point; the original schematic below emphasizes topology and marks the supplied triple point.

For the melting-pressure estimate, Archimedes' principle gives ${\rho }_i=0.90{\rho }_w=900\mathrm{kg}{\mathrm{m}}^{-3}$, soConvert the molar evaporation heat using water molar mass $M\simeq 0.0180\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$, rounded from the tabulated value $18.0153\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$.^[ref] An enthalpy cycle through vapour then givesThis uses the question's temperature-independent evaporation heat all the way to the triple point; no replacement experimental fusion heat is inserted. The melting pressure inferred from flotation and latent heats, on holding $L_f$ and $\Delta v$ constant, isusing $T_t=273.16\mathrm{K}$ and $T=270.15\mathrm{K}$. Linearizing the logarithm about the triple point gives $53.4\mathrm{MPa}$ instead of $53.7\mathrm{MPa}$. Both are estimates within the stated constant-property approximation; the negative melting slope makes a positive pressure necessary to lower the melting temperature.

Salicylic acid is 2-hydroxybenzoic acid, ${\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{O}}_3$: a benzene ring bears adjacent hydroxyl and carboxylic acid groups.^[ref]

The two groups supply distinct chemical sites. Acid–base reactions can change their protonation, while derivatization at the phenolic oxygen changes the molecular identity. Their adjacent arrangement also permits intramolecular hydrogen bonding, so moving one group to a different ring position can alter properties despite preserving elemental composition. This makes the compound a useful example of the difference between a formula and a positional isomer.

Squalene is a thirty-carbon unsaturated hydrocarbon, ${\mathrm{C}}_{30}{\mathrm{H}}_{50}$, with six carbon–carbon double bonds.^[ref] Its long chain can be folded and cyclized during the biosynthesis of sterols, making it a useful connection between an acyclic precursor and complex fused-ring structures.

The sequence and geometry of the double bonds matter: they determine which groups can approach during a cyclization. Biological pathways use enzymes to control that geometry and the reaction cascade. Hydrogenation of the double bonds changes the compound's identity, rather than merely purifying the original squalene.