PCCP View Article Online PAPER View Journal | View Issue Calculation of the Gibbs free energy of solvation and Cite this: Phys. Chem. Chem. Phys., 2013, dissociation of HCl in water via Monte Carlo 15, 13578 simulations and continuum solvation models Matthew J. McGrath,*ab I-F. Will Kuo,c Brice F. Ngouana W.,de Julius N. Ghogomu,d Christopher J. Mundy,f Aleksandr V. Marenich,b Christopher J. Cramer,b Donald G. Truhlarb and J. Ilja Siepmannbg The Gibbs free energy of solvation and dissociation of hydrogen chloride in water is calculated through a combined molecular simulation/quantum chemical approach at four temperatures between T = 300 and 450 K. The Gibbs free energy is first decomposed into the sum of two components: the Gibbs free energy of transfer of molecular HCl from the vapor to the aqueous liquid phase and the standard-state Gibbs free energy of acid dissociation of HCl in aqueous solution. The former quantity is calculated Received 24th April 2013, using Gibbs ensemble Monte Carlo simulations using either Kohn–Sham density functional theory or a Accepted 21st June 2013 molecular mechanics force field to determine the system’s potential energy. The latter Gibbs free energy DOI: 10.1039/c3cp51762d contribution is computed using a continuum solvation model utilizing either experimental reference data or micro-solvated clusters. The predicted combined solvation and dissociation Gibbs free energies www.rsc.org/pccp agree very well with available experimental data. 1 Introduction Studies of the thermophysical properties of HCl dissolution in water were performed early in the last century using electro- The interaction between hydrogen chloride and water has been chemical cells,7,8 and the structures of both dilute and concen- studied for many years due to the importance of HCl as a strong trated HCl solutions have been probed in neutron and X-ray acid (including acid dissociation in very cold nanoclusters1) 9,10 Published on 21 June 2013. Downloaded by University of Minnesota - Twin Cities 14/08/2013 03:48:12. diffraction experiments, including studies on the chloride ion and of HCl–ice systems and chloride ions at the air/water solvation structure.11 Experimental measurements of the vapor interface in atmospheric chemistry.2–5 Interest has also been pressures of HCl over water have been reported for various shown in the supercritical water–HCl system, as supercritical concentrations and temperatures,12–19 including vapor- and water is becoming increasingly popular for applications such as liquid-phase mole fractions of HCl as functions of tempera- waste disposal; the nature of supercritical water, however, ture.20 Equations to predict the HCl vapor pressure,21–25 as well drastically alters the behavior of strong acids.6 as its Henry’s law constants,26 have also been developed based on previous experimental data. There is some disagreement in the literature concerning the a Laboratoire des Sciences du Climat et de l’Environnement, value of the acid dissociation constant of HCl in aqueous 27 CEA-Orme des Merisiers, F-91191 Gif-sur-Yvette CEDEX, France. solution (Ka,aq). Ruaya and Seward report values for a wide E-mail: [email protected] range of temperatures, including a value of 0.71 at T = 298 K, b Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, showing good agreement with some previous studies. However, University of Minnesota, Minneapolis, Minnesota 55455, USA c Physical and Life Sciences Directorate, Lawrence Livermore National Livermore, a value of Ka,aq less than unity would imply a significant California 94550, USA amount of undissociated HCl at room temperature, which is d Department of Chemistry, University of Dschang, B.P. 67, Dschang, Cameroon unexpected at low temperatures for a strong acid, and Ruaya e Laboratoire Subatech, 4 rue Alfred Kastler, La Chantrerie BP 20722, and Seward27 mention other values that are about an order of 44307 Nantes CEDEX 3, France f magnitude larger. Much larger values make more intuitive sense Physical Sciences Division, Pacific Northwest National Livermore, P.O. Box 999, 23,24,28,29 Richland, Washington 99352, USA and have been reported by various research groups. It 24 g Department of Chemical Engineering and Materials Science, is also of interest to note that Clegg and Brimblecombe University of Minnesota, Minneapolis, Minnesota 55455, USA recommended using a form of Henry’s law constant that avoids 13578 Phys. Chem. Chem. Phys., 2013, 15, 13578--13585 This journal is c the Owner Societies 2013 View Article Online Paper PCCP the need to know ‘‘inaccessible parameters’’ including the acid various other techniques. Among these are QM/MM methods50,51 dissociation constant, and commented on the difficulty in deter- and calculation from experimental data,52 such as gas-phase 30 53 mining its true value. Balbuena et al. report the Gibbs free energy proton affinities and aqueous pKa,aq values. The structure of of HCl dissociation in water along the water saturation curve below concentrated HCl solutions has also been determined by empiri- the critical temperature, ranging from about À11 kcal molÀ1 at cally fitting X-ray scattering data.54 T = 300 K to around À5 kcal molÀ1 near T =500K(basedon In the above molecular simulation studies, no effort was experimentally measured acid dissociation constants31). Ho et al.32 made to compute the Gibbs free energy of aqueous solvation for give a formula to estimate Ka,aq at elevated temperatures as a HCl or its Henry’s law constant. The goal of the current study is function of the solvent density and temperature. At T =473K to compute these thermodynamic properties across a tempera- (the lowest temperature at which their formula is valid), this ture range of 150 K (T = 300–450 K), through the use of first formula predicts log(Ka,aq) = 0.55, which gives a Gibbs free energy principles Monte Carlo simulations and quantum mechanical À1 28 of acid dissociation, DGa,aq, of 1.2 kcal mol .Robinson, continuum solvation approaches. The chemical equilibria for 23 33 Marsh and McElroy, and Pokrovskii all give values of DGa,aq = the solvation and dissociation of gaseous HCl are given by: À8.4 kcal molÀ1 at T = 298 K. Pokrovskii33 points out a discrepancy HCl 2 H + +Cl À (1) between their values and those of Ruaya and Seward,27 and argues (g) (aq) (aq) that the data used by the latter group can be interpreted in 2 HCl(g) HCl(aq) (2) multiple ways. 2 + À In contrast, the Henry’s law constant of HCl in water appears to HCl(aq) H(aq) +Cl(aq) (3) be less ambiguous. Clegg and Brimblecombe34 report a value of 6 2 À2 À1 with the Henry’s law constant of KH =1.84Â 10 mol kg atm under ambient conditions. The 24 c þ c À following year, Clegg and Brimblecombe reported values around K ¼ H Cl g 2 (4) 6 2 À2 À1 H HCl 2.0 Â 10 mol kg atm for concentrations of HCl in solution pHCl between 0 and 200 mol kgÀ1 by using data from a variety of 26 where cX is the concentration of species X in the aqueous phase, sources, while Brimblecombe and Clegg recommend a value of + À 6 2 À2 À1 23 g is the geometric mean activity coefficient of H and Cl in 2.04 Â 10 mol kg atm at T = 298 K. Marsh and McElroy HCl solution, and p is the partial pressure of HCl over the calculated equilibrium constants for both the transfer of mole- HCl solution.26 It should be noted that other definitions of K can cular HCl from the vapor to aqueous phase (dimensionless) and H 3 be found in the literature. Eqn (4) can be rewritten in terms of the dissociation of HCl in water (in units of mole dmÀ ). Combin- the Gibbs free energy changes associated with eqn (2) and (3): ing these values (via eqn (11) in their paper) and converting units 6 2 À2 À1 results in KH =1.85Â 10 mol kg atm , which is very close to DG ðÞcÉ 2 24 K ¼ exp À comb (5) previous values, although Clegg and Brimblecombe note that H RT pÉ the disagreement grows at lower temperatures. The simulation literature surrounding the HCl–water system is o DGcomb = DGtrans + DGa,aq (6) just as extensive; in the interest of brevity, the following summary o will only be concerned with calculations involving the bulk aqueous where DGtrans, DGa,aq,andDGcomb are the Gibbs free energy of transfer of molecular HCl (obtained from the ratio of number Published on 21 June 2013. Downloaded by University of Minnesota - Twin Cities 14/08/2013 03:48:12. system and bulk solvation (i.e., studies dealing only with clusters or ice will be ignored). Molecular simulations of hydrogen chloride in densities), the standard-state Gibbs free energy of acid dissociation water have mostly been performed with the molecular dynamics in aqueous solution, and the Gibbs free energy of the combined ~ ~ technique, including simulations from first-principles35–41 and solvation–acid dissociation process, respectively. p and c are the using empirical force fields,30,42–45 including a study of HCl at standard pressure and the standard concentration, respectively. the air–water interface using QM/MM techniques.46 Some of these In this work, particle-based Monte Carlo simulations are 30,42,43 studies compute the pKa,aq of HCl in water, others compute carried out to compute DGtrans, and continuum solvation models 44 o the potential of mean force, while the rest examine the structure are used to compute DGa,aq.NoticethatDGtrans is not equivalent to of the solvating water molecules around the ions.