Solubility calculation using Henry constant

While Table 4.3 shows solubility both above and below the hydrate point, at the three-phase hydrate condition Handa s predictions show a sharp maximum in solubility with pressure at constant temperature. In Holder s laboratory, Toplak (1989) measured the solubility of gas in liquid water around the hydrate point, both in water that had formed hydrates and in water with no residual structure his results show no dramatic change in pure component solubility at the three-phase (Lw-H-V) condition. Kobayashi and coworkers (Besnard et al., 1997) measured a significant solubility increase at the hydrate point beyond that calculated using Henry s law. However, comprehensive solubility measurements around the hydrate point await further experiments. 

FIGURE 9.5 Pressure versus liquid mole fraction of hydrogen (1) in the IL [hmim][NTf2] calculated using Henry s constant of Equation 9.26 fitted to data of Kumelan et al. (From J. Kumelan, A. P. S. Kamps, D. Tuma, and G. Maurer, 2006, Solubility of Hj in the Ionic Liquid [bmim][PFJ, Journal of Chemical and Engineering Data. 51, 11.) — 7 = 293.2 K. 

A good resource for Hf and He, is Lange [3]. Although this nearly exhaustive reference source does not list Henry s law constants as such, the book does provide huge resources on gas solubility in various solvents, from which Henry s law constants can be calculated using the following equation (see App. C) ... 

The calculation methods for the gas solubility are largely based on the Henry constant, which gives a relationship between the liquid-phase concentration of a physically dissolved gas and its partial pressure. The determination of such coefficients in presence of chemical reactions becomes complicated and, therefore, different estimations based on chemically inert systems are often applied. One of these methods uses the Henry coefficients of similar, but chemically inert, species in order to estimate the solubility of a reactive component An example is represented by the N2O analogy for the determination of CO2 solubility in amine solutions [47]. 

Many computational studies of the permeation of small gas molecules through polymers have appeared, which were designed to analyze, on an atomic scale, diffusion mechanisms or to calculate the diffusion coefficient and the solubility parameters. Most of these studies have dealt with flexible polymer chains of relatively simple structure such as polyethylene, polypropylene, and poly-(isobutylene) [49,50,51,52,53], There are, however, a few reports on polymers consisting of stiff chains. For example, Mooney and MacElroy [54] studied the diffusion of small molecules in semicrystalline aromatic polymers and Cuthbert et al. [55] have calculated the Henry s law constant for a number of small molecules in polystyrene and studied the effect of box size on the calculated Henry s law constants. Most of these reports are limited to the calculation of solubility coefficients at a single temperature and in the zero-pressure limit. However, there are few reports on the calculation of solubilities at higher pressures, for example the reports by de Pablo et al. [56] on the calculation of solubilities of alkanes in polyethylene, by Abu-Shargh [53] on the calculation of solubility of propene in polypropylene, and by Lim et al. [47] on the sorption of methane and carbon dioxide in amorphous polyetherimide. In the former two cases, the authors have used Gibbs ensemble Monte Carlo method [41,57] to do the calculations, and in the latter case, the authors have used an equation-of-state method to describe the gas phase. 

If the solubility, vapor pressure, and molecular weight of a compound are known, Henry s law constant can be calculated using the Eq. (1). Table 5 presents the vapor pressures and solubilities and Henry s law constants for priority pollutants ... 

The p/S ratio of compounds is the method of choice to calculate the Henry s law constant. Assuming constant activity coefficients in the liquid phase over the entire range of solubility, this relationship is applicable if the total pressure is near 1 atm and if there is no association of molecules in the vapour phase (Lyman, 1985). The input parameters p and have to refer to the same state of the chemicals that is for solid compounds they both have to be obtained either for the solid or for the subcooled state. This indirect approach can obviously not be applied for chemicals completely miscible with water (with infinite water solubility) nor is it suitable for compounds of high water solubility, because significant method errors occur. If limited to substances with relatively low water solubility (5 < 1 mol/1), the pJS ratio provides fairly accurate estimates of the Henry s law constant (OECD, 1993a). However, the resulting data for Henry s law constant are subjected to the variability in the p and values used as input and the respective uncertainties caused by propagated errors have to be taken into account. 

Using Eqs. (8=Ha) and (8-llbE we can calculate the Henry s law constants from the known solubilities (which give the mole fracs) and the vapor pressures. 

In Approach A, the fugacity coefficients of the liquid (pf and vapor phase are needed. They describe the deviation from ideal gas behavior and can be calculated with the help of equations of state, for example, cubic equations of state and reliable mixing rules. In Approach B, besides the activity coefficients s value for the standard fugacity is required. In the case ofVLE usually the fugacity of the pure liquid at system temperature and system pressure is used as standard fugacity. For the calculation of the solubilities of supercritical compounds Henry constants are often applied as standard fugacity (see Section 5.7). 

An alternative is the usage of the Henry constant H,j as standard fugacity Using the Henry constant as standard fugacity, the following expression is obtained for the calculation of gas solubilities in a binary system ... 

In comparison to the standard fugacity "pure liquid at system temperature and system pressure" used for VLE calculations, there is the great disadvantage of the Henry constant that it is not a pure component property, but has to be derived from experimental gas solubility data. 

For supercritical gases no liquid phase and thus no values for vi and Ahvi exist. In Table 5.15 hypothetical values for the molar liquid volume and the solubility parameter for some well-known light gases at = 25" C are listed. As nothing better is available, these values are also applied at other temperatures as well. The Henry constant can finally be calculated using Eq. (5.56), where instead of the vapor pressure the fugacity of the hypothetical liquid is used. 

Hydrolysis Half-Life (H-tm) The hydrolysis half-life of a chemical is the time that it takes to reach one-half or 50% of its original concerrtration. The rate of chemical hydrolysis is highly dependent upon the compound s solubility, tempera-ture and pH. Since other envirorunental factors such as photolysis, volatility (i.e., Henry s law constants) and adsorption can affect the rate of hydrolysis, these factors are virtually eliminated by performing hydrolysis experiments under carefuUy controlled laboratory conditions. The hydrolysis half-lives reported in the Uterature were calculated using experimentally determined hydrolysis rate constarrts. 

The impact of these liquid phase reactions on the phase equilibrium properties is thus an increased solubility of NH3, CO2, H2S and HCN compared with the one calculated using the ideal Henry s constants. The reason for the change in solubility is that only the compounds present as molecules have a vapour pressure, whereas the ionic species have not. The change thus depends on the pH of the mixture. The mathematical solution of the physical model is conveniently formulated as an equilibrium problem using coupled chemical reactions. For all practical applications the system is diluted and the liquid electrolyte solution is weak, so activity coefficients can be neglected. 

Then, the solubility ratio Hcham Hchaw can be calculated from the experimantally measured permeation rates of CH4 arid the viscosities of the aqueous membrane solutions using Equation 29. It should be noted that Hch4,m is not the Henry constant of CH4 for the aqueous amine solution but that for the aqueous membrane solution which is in contact with CO2 and contains unreacted amine and reaction products, i.e., carbamate ion and protonated amine. 

The Henry s law constant for the solubility of radon in water at 30°C is 9.57 X 10-6 Mlmm Hg. Radon is present with other gases in a sample taken from an aquifer at 30°C. Radon has a mole fraction of 2.7 X 10-6 in the gaseous mixture. The gaseous mixture is shaken with water at a total pressure of 28 atm. Calculate the concentration of radon in the water. Express your answers using the following concentration units. 

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

Pollutants with high VP tend to concentrate more in the vapor phase as compared to soil or water. Therefore, VP is a key physicochemical property essential for the assessment of chemical distribution in the environment. This property is also used in the design of various chemical engineering processes [49]. Additionally, VP can be used for the estimation of other important physicochemical properties. For example, one can calculate Henry s law constant, soil sorption coefficient, and partition coefficient from VP and aqueous solubility. We were therefore interested to model this important physicochemical property using quantitative structure-property relationships (QSPRs) based on calculated molecular descriptors [27]. 

The estimation of the solubility at one atmosphere gas pressure was made by one of two procedures. If the solubility was measured at only one pressure at a given temperature, Henry s law was used, and the inverse of Henry s constant was calculated as X2(1 atm) = 1/H2 i = X2/P2. The procedure works well at moderate gas partial pressures, but at higher gas partial pressures of 25 atm or more the procedure often appears to give low solubility values. However, it is the only practical procedure when the solubility was measured at only one pressure. When solubility values were measured at several pressures at a given temperature, the data were fitted by a linear regression to an empirical function X2/P2 = a + bP2 to obtain the unit pressure solubility value. In some cases a quadratic rather than a linear function of pressure was used. 

The tentative equation summarized in Table V allows the calculation of the solubility at one atmosphere gas partial pressure which is numerically equal to the inverse of Henry s constant (equation 1). Although Henry s law may be adequate up to moderate pressures, it requires some corrections for the solubilities at higher pressures. Table VI summarizes some approaches that have been used to correlate solubility pressure isotherms. These have been discussed in many places including references [,21 and 22]. ... 

Henry s Law constant (i.e., H, see Sect. 2.1.3) expresses the equilibrium relationship between solution concentration of a PCB isomer and air concentration. This H constant is a major factor used in estimating the loss of PCBs from solid and water phases. Several workers measured H constants for various PCB isomers [411,412]. Burkhard et al. [52] estimated H by calculating the ratio of the vapor pressure of the pure compound to its aqueous solubility (Eq. 13, Sect. 2.1.3). Henry s Law constant is temperature dependent and must be corrected for environmental conditions. The data and estimates presented in Table 7 are for 25 °C. Nicholson et al. [413] outlined procedures for adjusting the constants for temperature effects. 

A simple environmental chamber is quite useful for obtaining volatilization data for model soil and water disposal systems. It was found that volatilization of low solubility pesticides occurred to a greater extent from water than from soil, and could be a major route of loss of some pesticides from evaporation ponds. Henry s law constants in the range studied gave good estimations of relative volatilization rates from water. Absolute volatilization rates from water could be predicted from measured water loss rates or from simple wind speed measurements. The EXAMS computer code was able to estimate volatilization from water, water-soil, and wet soil systems. Because of its ability to calculate volatilization from wind speed measurements, it has the potential of being applied to full-scale evaporation ponds and soil pits. 

A more comprehensive analysis of the influences on the ozone solubility was made by Sotelo et al., (1989). The Henry s Law constant H was measured in the presence of several salts, i. e. buffer solutions frequently used in ozonation experiments. Based on an ozone mass balance in a stirred tank reactor and employing the two film theory of gas absorption followed by an irreversible chemical reaction (Charpentier, 1981), equations for the Henry s Law constant as a function of temperature, pH and ionic strength, which agreed with the experimental values within 15 % were developed (Table 3-2). In this study, much care was taken to correctly analyse the ozone decomposition due to changes in the pH as well as to achieve the steady state experimental concentration at every temperature in the range considered (0°C [Pg.86]

The solvophobic model of liquid-phase nonideality takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. First, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbability, Henry s constant, and aqueous solubility (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

The exchange of chemical compounds from the gas phase to a surface, e.g. atmospheric particles, soil, water, vegetation or other surfaces, is controlled by the affinity of the compound to this surface. The ratio of vapour pressure to water solubility can be used as indicator between levels in the atmosphere and water surface (Henry s law H constant). In many model calculations, the ratio between POP levels in octanol and water, the octanol-water partitioning coefficient (Kow), is used as reference for the distribution of POP in organic material [14]. Consequently, the expression ///RT (Cair/Cwalcr) and Kow (Coctanoi/Cwater) provide the octanol-air partitioning coefficient (Koa) ... 

Carbonate equilibria in an open system. What is the pH of water in equilibrium with atmospheric C02 gas To answer such a question involves a knowledge of acid-base chemistry, the use of Henry s Law constant for the solubility of carbon dioxide and the use of the ENE to calculate the proton concentration of the equilibrium solution. The details of the equilibrium constants used are detailed below. 

---