Relative polarity - definition and meaning

I am struggling with understanding the parameter called "Relative Polarity" (RP). I know it is supposed to be an arbitrary scale, but I fail to grasp what the values represent. I understand that higher values mean "more polar", but nowhere have I found a proper definition.


As far as I know, the values are fixed between 0 and 1, 1 being the RP of water and 0 (I assume?) of some hydrocarbon (correct me please? I haven't found any compound for which RP = 0). In terms of physics I can think of several ways to describe polarity of a solvent:


* Static dipole moment of the molecule
* Spectral shift of the electronic spectral peaks of specified standards
* (Arbitratily) normalized dielectric constant, i.e. how well does the solvent block electric field
* Amount of specified standards that can be dissolved
* etc.


Are any of the above the quantity by which RP is described?


Also, is the scale linear? Meaning, if I mix equal volumes of a solvent with RP 1 and a solvent with RP 0.5, will I get a mixture with RP 0.75? Or maybe it's not equal volumes, but weights/moles?


If there is a book where this is explained, feel free to direct me to it.




Polarity itself is an ill-defined term, rather it is an umbrella term which includes several intermolecular interactions with a probe molecule. It is perhaps a futile exercise to assign a particular meaning to polarity or relative polarity without a full context. It is just like the common term popular among students which is "stability of a given compound", and my question is "stable with respect to what parameter?".


The table you referred to comes from Dr. Reichardt's work almost for all his life. The basic idea is based on solvatochromism, which means, that certain dyes change their color (hence the energy levels) depending on the solvent's *polarity*. From wavelength shift measures, one can calculate the energy of electronic transition using wavelength energy relationship. Now you assign a number to a chosen solvent, say water, and then use that to scale the rest of the energy of transitions of other solvents. Water then has a "relative polarity" of 1.00. With that one cannot have a relative polarity of zero, because the energy of electronic transition cannot be zero for a chosen dye.


Do not assign *physics* to these numbers. These are just convenient scales for measuring how polar a given solvent is.


See IUPAC's definition [Definition](https://goldbook.iupac.org/terms/view/P04710)



> 
> When applied to solvents, this rather ill-defined term covers their
> overall solvation capability (solvation power) for solutes (i.e. in
> chemical equilibria: reactants and products; in reaction rates:
> reactants and activated complex; in light absorptions: ions or
> molecules in the ground and excited state), which in turn depends on
> the action of all possible, nonspecific and specific, intermolecular
> interactions between solute ions or molecules and solvent molecules,
> excluding such interactions leading to definite chemical alterations
> of the ions or molecules of the solute. Occasionally, the term solvent
> polarity is restricted to nonspecific solute/solvent interactions only
> (i.e. to van der Waals forces).
> 
> 
> 


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You should read the article [**Solvatochromic Dyes as Solvent Polarity Indicators**, *Chem. Rev.* 1994, 94, 8, 2319–2358](https://pubs.acs.org/doi/10.1021/cr00032a005), which will give you a much better understanding of the general topic of defining polarity. There's an obvious focus on Reichardt's own scales, but with a mention of numerous other ways it is done.


For the widely used Reichardt's normalized polarity scale $E\mathrm{^N\_T}$ , the absolute transition energies $E\mathrm{\_T}$ of a [particular dye](https://en.wikipedia.org/wiki/Reichardt%27s_dye) (and other closely-related analogues) in a chosen solvent are rescaled such that the value of tetramethylsilane (TMS) is *defined* as 0 and water is *defined* as 1. Taken directly from the article mentioned above:


[![2](https://i.stack.imgur.com/ewvli.png)](https://i.stack.imgur.com/ewvli.png)


So obviously this formula returns exactly 0 if you choose TMS as a solvent, and exactly 1 if you choose water as a solvent. But this zero is only as physically meaningful as zero degrees Celsius (which is to say, not at all) - you can go to negative values. In particular, you can measure the electronic transition of Reichardt's dye in a vacuum, and by the same normalization, one obtains a polarity of -0.111 for the vacuum. This makes sense, because no matter how poorly polarizable a solvent is, it will still be able to shield charges better than nothing at all. You can also go above 1, by the way. This can happen in ionic melts, and interestingly in the extremely strong hydrogen bond donor [hexafluoroisopropanol](https://en.wikipedia.org/wiki/Hexafluoro-2-propanol) (1.068). The 0 and 1 anchors of the normalized scale are *arbitrary*, but *usefully chosen*. If you want to extract physics out of these polarity values, then you have to go back to the absolute polarity scale $E\mathrm{\_T}$, whose values actually have units of $\mathrm{kcal\ mol^{-1}}$ (for historical reasons) as opposed to the dimensionless values of the normalized scale.


As a last comment, the polarity of solvent mixtures (however you decide to define it) typically behaves in an *extremely* non-linear fashion if taken across the entire range of 100% solvent A to 100% solvent B, but for similar solvents and small intervals of composition change, you can interpolate approximate linear behaviour.


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