The
hydrophobic effect is an umbrella term encompassing a number
of solvation phenomena associated with solutions of nonpolar species
in water, including the following: a meager solubility opposed by
entropy at room temperature; large positive hydration heat capacities;
positive shifts in the temperature of maximum density of aqueous mixtures;
increases in the speed of sound of dilute aqueous mixtures; and negative
volumes of association between interacting solutes. Here we present
a molecular simulation study of nonpolar gas hydration over the temperature
range 273.15–373.15 K and a pressure range −500 to 1000
bar to investigate the interrelationships between distinct hydrophobic
phenomena. We develop a new free energy correlation for the solute
chemical potentials founded on the Tait equation description of the
equation-of-state of liquid water. This analytical correlation is
shown to provide a quantitatively accurate description of nonpolar
gas hydration over the entire range of thermodynamic state points
simulated, with an error of ∼0.02 k
B
T or lower in the fitted chemical potentials. Our
simulations and the correlation accurately reproduce many of the available
experimental results for the hydration of the solutes examined here.
Moreover, the correlation reproduces the characteristic entropies
of hydration, temperature dependence of the hydration heat capacity,
perturbations in the temperature of maximum density, and changes in
the speed of sound. While negative volumes of association result from
pairwise interactions in solution, beyond the limits of our simulations
performed at infinite dilution, we discuss how our correlation could
be supplemented with second virial coefficient information to expand
to finite concentrations. In total, this work demonstrates that many
distinct phenomena associated with the hydrophobic effect can be captured
within a single thermodynamically consistent correlation for solute
hydration free energies.