d-Menthol vs dl-menthol: Does an enantiomer and its racemic mixture have different melting points?

I am checking out [Wikipedia](https://en.wikipedia.org/wiki/Menthol) and it shows a different melting point (m.p.) for *l*-menthol $(\pu{42 ^\circ C}$ to $\pu{45 ^\circ C})$ vs *dl*-menthol $(\pu{36 ^\circ C}$ to $\pu{38 ^\circ C}).$ 


How is this possible? *d*-menthol and *l*-menthol being [enantiomers](https://en.wikipedia.org/wiki/Enantioselective_synthesis), shouldn't they have identical physical properties including the m.p.? 



> 
> The two enantiomers of a molecule possess the same physical properties (*e.g.*, melting point, boiling point, polarity etc.) and so behave identically to each other.
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If so, why would the racemic mixture have any different m.p.? *I.e.* you can't just physically mix two pure materials with the same m.p. and end up with a material with a different m.p., right?


I checked out *Common Fragrance and Flavor Materials* by Surburg and Panten [1, p. 55] just to be sure and the data agrees. The m.p. of the *d*-menthol and *dl*-menthol again seem to be different:



> 
> Other physical constants of commercially available levorotatory and racemic
>  menthols are: (−)-menthol [2216-51-5], *mp* $\pu{43 °C},$ $n\_\mathrm{D}^{20}~1.4600,$ $[α]\_\mathrm{D}^{20}~–50^\circ;$ (±)-
>  menthol [15356-70-4], *mp* $\pu{38 °C},$ $n\_\mathrm{D}^{20}~1.4615.$
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### References


1. Surburg, H.; Panten, J. *Common Fragrance and Flavor Materials: Preparation, Properties and Uses*, 5th, Completely Revised and Enlarged edition; Wiley-VCH: Weinheim, **2006**. ISBN 978-3-527-31315-0.




In stereochemical vocabulary, a racemic mixture (racemate) is one that has equal amounts (50:50) of left- and right-handed ($d$- and $l$-) enantiomers of a chiral molecule. According to [Wikipedia: Racemic Mixture](https://en.wikipedia.org/wiki/Racemic_mixture#cite_note-4), a racemic mixture can be crystallized in four ways:



> 
> **Conglomerate (sometimes racemic conglomerate):** If the molecules of the substance have a much greater affinity for the same enantiomer than for the opposite one, a mechanical mixture of enantiomerically pure crystals will result. The melting point of the racemic conglomerate is always lower than that of the pure enantiomer. Addition of a small amount of one enantiomer to the conglomerate increases the melting point. Roughly 10% of racemic chiral compounds crystallize as conglomerates.
> 
> 
> **Racemic compound (sometimes true racemate):** If molecules have a greater affinity for the opposite enantiomer than for the same enantiomer, the substance forms a single crystalline phase in which the two enantiomers are present in an ordered 1:1 ratio in the elementary cell. Adding a small amount of one enantiomer to the racemic compound decreases the melting point. But the pure enantiomer can have a higher or lower melting point than the compound. A special case of racemic compounds are kryptoracemates, in which the crystal itself has handedness (is enantiomorphic), despite containing both enantiomorphs in a 1:1 ratio.
> 
> 
> **Pseudoracemate (sometimes racemic solid solution):** When there is no big difference in affinity between the same and opposite enantiomers, then in contrast to the racemic compound and the conglomerate, the two enantiomers will coexist in an unordered manner in the crystal lattice. Addition of a small amount of one enantiomer changes the melting point just little bit or not at all.
> 
> 
> **Quasiracemate:** A quasiracemate is a co-crystal of two similar but distinct compounds, one of which is left-handed and the other right-handed. Although chemically different, they are sterically similar (isosteric) and are still able to form a racemic crystalline phase. One of the first such racemates studied, by Pasteur in 1853, forms from a 1:2 mixture of the bis ammonium salt of (+)-tartaric acid and the bis ammonium salt of (−)-malic acid in water. Re-investigated in 2008,[6] the crystals formed are dumbbell-shape with the central part consisting of ammonium (+)-bitartrate, whereas the outer parts are a quasiracemic mixture of ammonium (+)-bitartrate and ammonium (−)-bimalate.
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The most common type of racemate is the racemic compound (2nd type). The crystal of a racemic compound is composed of enantiomer pairs, distributed in an organized array, and representing a true molecular compound. Thus, these racemic compounds have unique physical properties, including melting points, solubility, density, and solid state spectra, different from that of either crystalline enantiomer ([Crystallization: MSU.edu](https://www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/suppmnt4.htm)). Specifically, melting points of this kind of recemates can be either higher, identical, or lower than that of their corresponding pure enantiomers. The reference 1 states that the thermodynamic and crystallographic approaches have unambiguously demonstrated that *racemic*-menthol is a racemate. Hence, showing unique physical properties different from that of either crystalline enantiomer such as melting point being lower than that of either pure enanthiomer can be expected.


To address your statement "would it be fair to say that the boiling points would always be the same for the enantiomers as well as the racemic mixture, however the melting points may vary?": In most of the cases yes (see Table below). Also be aware that some other physical properties such as solubility can be different as well. For example, solubility of *racemic*-tataric acid (m.p.: $\pu{206 ^\circ C}$) is $\pu{25 g}$/$\pu{100 mL}$ while that of either enanthiomers of tataric acid (m.p.: $\pu{172 ^\circ C}$) is $\pu{135 g}$/$\pu{100 mL}$ ([Crystallization: MSU.edu](https://www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/suppmnt4.htm)).


The following table emphasizes this trend (Ref.2):


$$
\begin{array}{c|lcr}
\text{Stereoisomer} & \text{m.p., } \pu{^\circ C} & \text{b.p., } \pu{^\circ C} & [\alpha]^{20}\_D\text{ (in 20% EtOH)} \\
\hline
l\text{-Menthol} & 43.0 & 216.5 & -50.0 \\
dl\text{-Menthol} & 38.0 & 216.5 & 0.0 \\
d\text{-}neo\text{-Menthol} & -15.0 & 211.7 & +20.0 \\
dl\text{-}neo\text{-Menthol} & 52.0 & 211.7 & 0.0 \\
d\text{-}iso\text{-Menthol} & 82.5 & 218.6 & +26.0 \\
dl\text{-}iso\text{-Menthol} & 53.5 & 218.6 & 0.0 \\
d\text{-}neo\text{-}iso\text{-Menthol} & -8.0 & 214.6 & +2.0 \\
dl\text{-}neo\text{-}iso\text{-Menthol} & 13.5 & 214.6 & 0.0 \\
\end{array}
$$


**References:**


1. Yohann Corvis, Philippe Négrier, Stéphane Massip, Jean-Michel Leger, Philippe Espeau, "Insights into the crystal structure, polymorphism and thermal behavior of menthol optical isomers and racemates," *CrystEngComm* **2012**, *14(20)*, 7055-7064 (DOI: 10.1039/C2CE26025E).
2. Kenneth L. Waters, George D. Beal, "Some physical and chemical properties of commercial racemic menthol," *Journal of the American Pharmaceutical Association* **1945**, *34(2)*, 52-56 (<https://doi.org/10.1002/jps.3030340208>).


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If solid menthol were just amorphous, then you would expect the racemate and each enantiomer to exhibit identical melting points. However, if you read further on the Wikipedia page you reference, you'll see that racemic vs. enantiopure menthol crystallizes differently:



> 
> The two crystal forms for racemic menthol have melting points of 28 °C and 38 °C. Pure (−)-menthol has four crystal forms, of which the most stable is the α form, the familiar broad needles.
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(This information is trustworthy and corroborated in the primary literature; [here](https://pubs.rsc.org/en/content/articlelanding/2012/ce/c2ce26025e/unauth#!divAbstract) is one example)


The melting point of a crystalline solid has to do with how well the molecules can pack together. In other words, on a molecular level, there is an orientation dependence. The better the molecular packing, the stronger the intermolecular forces, and the higher the melting point - since it takes more energy to separate the molecules. This is why the enantiopure menthol has a higher melting point.


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