Enthalpy of dimerization of benzene in water

McMillan-Mayer theory of solutions revisited: simplifications and extensions

McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the solvent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentration, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {N(A), μ(B), V, T}, to those relevant to the experiment, i.e., fixed {N(A), N(B), p, T}, where μ denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature.

Uptake of benzene and alkylbenzenes by cation- and anion-exchange resins from aqueous solutions

Uptakes of benzene and 12 alkylbenzenes (from toluene to n-pentylbenzene including xylene and trimethylbenzene isomers) by both strong acid cation (Dowex 50W-X4 and X8) and strong base anion (Dowex 1-X4 and X8) exchange resins have been studied in aqueous solutions at 25 degrees C; their distribution constants (K) have been determined. The relationship between the octanol-water partition coefficient (K(ow)) and the resin affinity for solutes has been analyzed. The K values of benzene and alkylbenzenes were larger than the K values of aliphatic hydrocarbons expected from the K(ow) values. While the K value was increased with the alkyl chain length, no further increase in the K value was observed for n-butylbenzene and n-pentylbenzene.

Origin of peak asymmetry and isotherm nonlinearity in micellar electrokinetic chromatography: Variation of peak shape with buffer concentration

The diffuse fronts and sharp rears of peaks of nitrobenzene (nbz) solubilized at high concentrations in 50 mM SDS and 2.5, 25, and 50 mM sodium tetraborate buffers were modeled in MEKC by measurements of, and fits to, concave upward isotherms, and by numerical solution of the continuity equation. The isotherms varied with buffer concentration, with the smallest limiting slope and largest curvature found for the 50 mM tetraborate buffer. The Brunauer, Emmett, and Teller isotherm described the peak profiles in all buffers, with symmetrical peaks observed at sub- and low-mM levels of nbz, anti-Langmuirian peaks observed at 10-20 mM levels, and aquiline peaks resembling curved noses observed at 20-30 mM levels. The variation of the partition coefficient with nbz and buffer concentrations was shown to result from nonideal thermodynamics. High-buffer concentrations salt out nbz from the mobile phase, as quantified by a mobile-phase activity coefficient related to the Setchenov constant of nbz in sodium tetraborate. The activity coefficient of nbz in SDS micelles was shown to resemble that measured by other researchers for benzene in micelles of sodium octyl sulfate, i.e. it decreases with increasing solute concentration and increases with electrolyte concentration. Many examples from the literature are discussed, in which the variation of the intramicellar activity coefficient with solute mole fraction is consistent with peaks having diffuse fronts and sharp rears.

Potential of mean force between two hydrophobic solutes in water

We study the potential of mean force between two nonpolar solutes in the Mercedes Benz model of water. Using NPT Monte Carlo simulations, we find that the solute size determines the relative preference of two solute molecules to come into contact ('contact minimum') or to be separated by a single layer of water ('solvent-separated minimum'). Larger solutes more strongly prefer the contacting state, while smaller solutes have more tendency to become solvent-separated, particularly in cold water. The thermal driving forces oscillate with solute separation. Contacts are stabilized by entropy, whereas solvent-separated solute pairing is stabilized by enthalpy. The free energy of interaction for small solutes is well-approximated by scaled-particle theory.