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For a molecule to have a smell it's necessary that the molecule be volatile enough to be in the air. So I think that excludes molecules which are solid at room temperature and atmospheric pressure. Maybe the question then is equivalent to: what is the highest molecular weight organic compound which is liquid at room temperature and atmospheric pressure?

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    $\begingroup$ It can't be a simple as solid vs liquid. Some solids, for example, have distinct odours. Some of these are not, strictly, the odour or the material but of reaction products of the material (osmium has a sharp and dangerous smell because of the formation of osmium tetroxide). And menthol is a solid with a high vapour pressure and a very distinct odour. $\endgroup$ – matt_black Sep 10 at 12:18
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    $\begingroup$ A smell is not a property of a chemical, but of a nose ability to detect it Without knowledge of threshold partial pressure sensitivity for all compounds, the question cannot be answered. $\endgroup$ – Poutnik Sep 11 at 5:48
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    $\begingroup$ Wax, as in a candle, has a pretty distinctive smell, and it's pretty big. $\endgroup$ – Roger Sep 11 at 13:55
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I'll quote from$\ce{^{[1]}}$:

The general requirements for an odorant are that it should be volatile, hydrophobic and have a molecular weight less than approximately 300 daltons. Ohloff (1994) has stated that the largest known odorant is a labdane with a molecular weight of 296. The first two requirements make physical sense, for the molecule has to reach the nose and may need to cross membranes. The size requirement appears to be a biological constraint. To be sure, vapor pressure (volatility) falls rapidly with molecular size, but that cannot be the reason why larger molecules have no smell, since some of the strongest odorants (e.g. some steroids) are large molecules. In addition, the cut-off is very sharp indeed: for example, substitution of the slightly larger silicon atom for a carbon in a benzenoid musk causes it to become odorless (Wrobel and Wannagat, 1982d).

A further indication that the size limit has something to do with the chemoreception mechanism comes from the fact that specific anosmias become more frequent as molecular size increases. At the “ragged edge” of the size limit, subjects become anosmic to large numbers of molecules. An informal poll among perfumers, for example has elicited the fact that most of them are completely anosmic to one or more musks (e.g. Galaxolide® mw 244.38) or, less commonly, ambergris odorants such as Ambrox®, or the larger esters of salicylic acid.

One can probably infer from this that the receptors cannot accommodate molecules larger than a certain size, and that this size is genetically determined (Whissel-Buechy and Amoore, 1973) and varies from individual to individual.

References

$\ce{[1]}$: "Structure-odor relationships: a modern perspective", by Luca Turin (Dept of Physiology, University College London, UK) and Fumiko Yoshii (Graduate School of Science and Technology, Niigata University, Japan), which appears as chapter 13 of: Handbook of Olfaction and Gustation. Richard L. Doty (ed.). 2nd ed., Marcel Dekker, 2003.

$\ce{[2]}$: Ohloff, G. (1994) Scent and fragrances: the fascination of odors and their chemical perspectives [Berlin, Springer].

$\ce{[3]}$: Whissell-Buechy D. and Amoore J.E.(1973) Odour-blindness to musk: simple recessive inheritance Nature Sep 21;245 (5421):157-8.

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    $\begingroup$ Highly enlightening. As per Google, steroids cause body odor but do they have their own distinct smell? $\endgroup$ – M. Farooq Sep 10 at 3:42
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    $\begingroup$ The chapter from which I quoted indicates they do ["some of the strongest odorants (e.g. some steroids) are large molecules"], though don't know what they smell like. And I found this: ncbi.nlm.nih.gov/pmc/articles/PMC2822864 $\endgroup$ – theorist Sep 10 at 3:56
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    $\begingroup$ @pentane Sorry, the source from which I'd obtained the chapter incorrectly cited it as coming from the 3rd edition. It's actually from the 2nd edition (see: trove.nla.gov.au/work/29206984?q&versionId=46501355 ). I've corrected this in my answer. A draft of the entire chapter (titled "Structure-odor relations...", rather than "Structure-odor relationships...."; the latter is how it appears in the book's TOC), uploaded by Fumiko Yoshii (the 2nd author), can be found at: researchgate.net/publication/… $\endgroup$ – theorist Sep 11 at 7:50
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    $\begingroup$ Why does it need to be hydrophobic? Don't odorants solve in water when they are in the nose, so a receptor can detect them? $\endgroup$ – cheeesus Sep 11 at 11:29
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    $\begingroup$ @cheeesus It's not the water solubility that's important, it's that hydrophobicity implies weak electrostatic interaction and therefore greater volatility. Hydrophilic molecules are polar (and often include hydrogen bond donors or acceptors) and therefore have strong electrostatic interactions among themselves in addition to strong interactions with water. For instance, ethanol, which is polar and acts a both a H-bond acceptor and donor, has a vapor pressure of 5.95 kPa, while propane, a nonpolar molecule with a similar molecular mass and geometry has a vapor pressure of 853.16 kPa. $\endgroup$ – WaterMolecule Sep 11 at 21:44

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