[Figure: see text]. Most chemical processes on earth are intimately linked to the unique properties of water, relying on the versatility with which water interacts with molecules of varying sizes and polarities. These interactions determine everything from the structure and activity of proteins and living cells to the geological partitioning of water, oil, and minerals in the Earth's crust. The role of hydrophobic hydration in the formation of biological membranes and in protein folding, as well as the importance of electrostatic interactions in the hydration of polar and ionic species, are all well known. However, the underlying molecular mechanisms of hydration are often not as well understood. This Account summarizes and extends emerging understandings of these mechanisms to reveal a newly unified view of hydration and explain previously mystifying observations. For example, rare gas atoms (e.g., Ar) and alkali-halide ions (e.g., K+ and Cl-) have nearly identical experimental hydration entropies, despite the significant charge-induced reorganization of water molecules. Here, we explain how such previously mysterious observations may be understood as arising from Gibbs inequalities, which impose rigorous energetic upper and lower bounds on both hydration free energies and entropies. These fundamental Gibbs bounds depend only on the average interaction energy of a solute with water, thus providing a deep link between solute-water interaction energies and entropies. One of the surprising consequences of the emerging picture is the understanding that the hydration of an ion produces two large but nearly perfectly cancelling, entropic contributions: a negative ion-water interaction entropy and a positive water reorganization entropy. Recent work has also clarified the relationship between the strong cohesive energy of water and the free energy required to form an empty hole (cavity) in water. Here, we explain how linear response theory (whose roots may also be traced to Gibbs inequalities) can provide remarkably accurate descriptions of the process of filling aqueous cavities with nonpolar, polar, or charged molecules. The hydration of nonpolar molecules is well-described by first-order perturbation theory, which implies that turning on solute-water van der Waals interactions does not induce a significant change in water structure. The larger changes in water structure that are induced by polar and ionic solutes are well-described by second-order perturbation theory, which is equivalent to linear response theory. Comparisons of the free energies of nonpolar and polar or ionic solutes may be used to experimentally determine electrostatic contributions to water reorganization energies and entropies. The success of this approach implies that water's ability to respond to solutes of various polarities is far from saturated, as illustrated by simulations of acetonitrile (CH 3CN) in water, which reveal that even such a strongly dipolar solute only produces subtle changes in the structure of water.

The Comité international des poids et mesures (CIPM) has projected a major revision of the International System of Units (SI) in which all of the base units will be defined by fixing the values of fundamental constants of nature. In preparation for this we have carried out a new, low-uncertainty determination of the Boltzmann constant, k B , in terms of which the SI unit of temperature, the kelvin, can be re-defined. We have evaluated k B from exceptionally accurate measurements of the speed of sound in argon gas which can be related directly to the mean molecular kinetic energy, 3 2 k B T . Our new estimate is k B = 1.380 651 56 (98) × 10 −23 J K −1 with a relative standard uncertainty u R = 0.71 × 10 −6 .

We report on two sets of isothermal acoustic measurements made with argon close to the triple point of water using a 50 mm radius, thin-walled, diamondturned quasisphere. Our two isotherms yielded values for the Boltzmann constant, k B , which differ by 0.9 parts in 10 6 , and have an average value of k B = (1.380 649 6 ± 0.000 004 3) × 10 −23 J · K −1 . The relative uncertainty is 3.1 parts in 10 6 , and the average value is 0.58 parts in 10 6 below the 2006 CODATA value (Mohr et al. Rev Mod Phys 80:633, 2008), and so the values are consistent within their combined (k = 1) uncertainties.

The perturbing effect of a waveguide on the boundary of a quasispherical cavity resonator is investigated both theoretically and experimentally. Expressions for the frequency perturbation to the triply degenerate TM1mn and TE1mn modes are derived using cavity perturbation theory. The fields in and around the waveguide are calculated in the static limit using finite-element software. Experiments performed using quasispherical and cylindrical cavity resonators confirm the accuracy and generality of the approach. The impact of this study on attempts to re-determine the Boltzmann constant (kB) by an acoustic resonance technique is briefly considered.

The principles and techniques of primary refractive-index gas thermometry (RIGT) are reviewed. Absolute primary RIGT using microwave measurements of helium-filled quasispherical resonators has been implemented at the temperatures of the triple points of neon, oxygen, argon and water, with relative standard uncertainties ranging from 9.1 × 10−6 to 3.5 × 10−5. Researchers are now also using argon-filled cylindrical microwave resonators for RIGT near ambient temperature, with relative standard uncertainties between 3.8 × 10−5 and 4.6 × 10−5, and conducting relative RIGT measurements on isobars at low temperatures. RIGT at optical frequencies is progressing, and has been used to perform a Boltzmann constant measurement at room temperature with a relative standard uncertainty of 1.2 × 10−5. Uncertainty budgets from implementations of absolute primary microwave RIGT, relative primary microwave RIGT and absolute primary optical RIGT are provided.