The temperature variation of the hydrophobic effect
Henry's-law constants for solution of all the rare gases and the n-alkanes methane to n-octane in water have been fitted to functions of temperature chosen so that not only are the experimental values of ln KH reproduced, but also that on differentiation the correct parameters for solution at 298 K (ΔG°, ΔH°, ΔS°, and ΔC°p) are obtained. These fitting equations are then used to calculate parameters for solution in water from 273 to 523 K. At elevated temperatures the rare gases dissolve in water with much more positive ΔG° and ΔH°(but not ΔS°) values than in non-aqueous solvents, but as the temperature is lowered ΔH° and ΔS° values become increasingly more negative than in non-aqueous solvents. At elevated temperatures the alkanes dissolve in water with even more positive ΔH° and ΔS° values than expected by comparison with the rare gases (we regard these exceptionally positive values as hydrophobic effects of the second kind, ΔH°II and ΔS°II). Because of complete compensation between ΔH°II and ΔS°II at elevated temperatures, ΔG°II is nearly zero, and ΔG° for solution of alkanes is comparable to ΔG° for solution of the rare gases. As the temperature is lowered, structural effects of the alkane on the surrounding water molecules become important and lead to hydrophobic effects of the first kind, with ΔH°I and ΔS°I both being negative. There is incomplete compensation between ΔH°I and ΔS°I and so ΔG°I is positive, with alkanes giving rise to more positive ΔG° values than expected from rare-gas values. These more positive ΔG° values reach a maximum at ca. 370 K depending on the alkane. The methylene increment to ΔG° for solution of the alkanes reaches a maximum at 390 K, but whether or not this methylene increment is entropy- or enthalpy-controlled depends crucially on the temperature.