What is the order of the following compounds based on polarity?
The concept of solvent polarity is commonly used to describe solvent effects. For example, the Glossary of Terms Used in Physical Organic Chemistry (IUPAC Recommendations 1994) uses the following general definition (which was originally proposed by Christian Reichardt) of the term polarity:


  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).


However, the polarity of a solvent is not a physical quantity. Therefore, it is difficult to express quantitatively. Several scales exist that involve various physical properties in order to provide a measure of a solvent’s polarity.

In particular, the relative permittivity $\varepsilon_\mathrm{r}$ is often used as a quantitative measure of solvent polarity:

Hexane: $\varepsilon_\mathrm{r} = 1.8865$
Benzene: $\varepsilon_\mathrm{r} = 2.2825$
Methanol: $\varepsilon_\mathrm{r} = 33.0$
Water: $\varepsilon_\mathrm{r} = 80.100$

(values at 20 °C taken from “Laboratory Solvents and Other Liquid Reagents”, in CRC Handbook of Chemistry and Physics, 97th Edition (2016), William M. Haynes, ed., CRC Press/Taylor and Francis, Boca Raton, FL.)

By way of comparison, the empirical $E_\mathrm{T}(30)$ scale is based on the solvatochromism of Reichardt’s dye (Betaine 30):

Hexane: $E_\mathrm{T}(30) = 31.0\ \mathrm{kcal/mol}$
Benzene: $E_\mathrm{T}(30) = 34.3\ \mathrm{kcal/mol}$
Methanol: $E_\mathrm{T}(30) = 55.4\ \mathrm{kcal/mol}$
Water: $E_\mathrm{T}(30) = 63.1\ \mathrm{kcal/mol}$

(values taken from here)