Henry’s law constant, calculation

It is well known that the energy of interaction of an atom with the continuous solid is 2-3 times less than with the discrete (atomic) model (cf., e.g., Ref. [38], Figs. 2.2-2.4). Thus, to obtain the same Henry s Law constants with the two models, one has to increase e for the continuous model. This, however, does not discredit the continuous model which is frequently used in adsorption calculations. In particular, we can use the above mentioned results of Ref. [37] to predict the value of e for Ar which would have been obtained if one had carried out Henry s Law constant calculations for Ar in the AO model of Ref. [17] and compared them with experiment. One can multiply the value of e for CH4 obtained from AO model by the ratio of e values for Ar and CH4 in the CM model [36] to obtain tjk = 165A for Ar in the AO model. This is very close to the value of 160 K obtained in Ref. [21, 28] by an independent method in which the value of the LJ parameter e for the Ar - oxide ion interaction was chosen to match the results of computer simulation of the adsorption isotherm on the nonporous heterogeneons surface of Ti02. Considering the independence of the calculations and the different character of the adsorbents (porous and nonporous), the closeness of the values of is remarkable (if it is not accidental). The result seems even more remarkable in the light of discussion presented in Ref. [28]. Another line of research has dealt with the influence of porous structure of the silica gel upon the temperature dependence of the Henry constants [36]. 

The constants in Eqs. XVII-88-XVI1-90 may be calculated fiom theory to give the Henry s law constant K from Eq. XVII-87, the experimental n /P dien gives the surface area. Alternatively, the constants may be arrived at from an experimental K (assuming that A is known) and either the isosteric heat of adsorption... 

Principles of Rigorous Absorber Design Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] have shown that when adequate data are available for the Idnetic-reaciion-rate coefficients, the mass-transfer coefficients fcc and /c , the effective interfacial area per unit volume a, the physical solubility or Henry s-law constants, and the effective diffusivities of the various reactants, then the design of a packed tower can be calculated from first principles with considerable precision. 

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. 

The equilibrium concentration is evaluated from Henry s law.3,4 The equilibrium concentration of oxygen is calculated by the ratio of mean value of pressure over Henry s law constant, H. 

HARRIOTT 25 suggested that, as a result of the effects of interfaeial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a thin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then CAi — CAo in place of C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

This equation can be simplified to give H = P/S, where H is now Henry s law constant, which has dimensions of atm mVmole. Values for H may be calculated or measured (Mackay et al. 1979), and are now widely used infugacity modeling (see Section 3.2). 

C12-0061. At 25 °C, the equilibrium pressure of ammonia vapor above a 0.500 M aqueous ammonia solution is 6.8 torr. Calculate the Henry s law constant and determine the equilibrium pressure of ammonia vapor above a 2.5 M solution. 

Osburn, J.O., Markovic, P.L. Calculating Henry s Law Constant for Gases in Organic Liquids, ... 

In its simplest form a partitioning model evaluates the distribution of a chemical between environmental compartments based on the thermodynamics of the system. The chemical will interact with its environment and tend to reach an equilibrium state among compartments. Hamaker(l) first used such an approach in attempting to calculate the percent of a chemical in the soil air in an air, water, solids soil system. The relationships between compartments were chemical equilibrium constants between the water and soil (soil partition coefficient) and between the water and air (Henry s Law constant). This model, as is true with all models of this type, assumes that all compartments are well mixed, at equilibrium, and are homogeneous. At this level the rates of movement between compartments and degradation rates within compartments are not considered. 

Table I shows the results of calculating a soil diffusion coefficient and soil diffusion half-lives for the pesticides. The 10% moisture level specified means that the soil is relatively dry and that 40% of the soil volume is air available for diffusion. Complete calculations were not made for methoxychlor, lindane, and malathion because, based on Goring s criteria for the Henry s law constant, they are not volatile enough to diffuse significantly in the gas phase. This lack of volatility is reflected in their low values of X. These materials would move upward in the soil only if carried "by water that was moving upward to replace the water lost through evapotranspiration at the surface. Mirex has a very high Henry s law constant. On the basis of Goring s criteria, Mirex should diffuse in the soil air but, because of its strong adsorption, it has a very large a and consequently a very small soil air diffusion coefficient. The behavior of Mirex shows that Goring s criteria must be applied carefully.

The tendency of acrylonitrile to partition between air and water is described by Henry s law constant (H). The value of H for acrylonitrile has not been determined experimentally, but has been calculated to be 8.8 x 10 5 atm-m3/mole (Mabey et al. 1982). This value indicates that acrylonitrile will occur in both air and water, tending to transfer between air and water phases only slowly. Cupitt (1980) estimated the half-time of acrylonitrile clearance from air in wet precipitation to be greater than 10 months. 

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. 

A gaseous substance such as oxygen at normal environmental conditions exists at a temperature exceeding its critical temperature of 155 K. No vapor pressure can be defined or measured under this super-critical condition, thus no Henry s law constant can be calculated. Empirical data are required. 

A substance such as propane with a critical temperature of 370 K has a measurable vapor pressure of 998000 Pa, or approximately 10 atm at 27°C, which exceeds atmospheric pressure of 101325 Pa, the boiling point being -42"C or 231 K. It is thus a vapor at normal temperatures and pressures. A Henry s law constant can be calculated from this vapor pressure and a solubility as described earlier. 

As described earlier, Henry s law constants can be calculated from the ratio of vapor pressure and aqueous solubility. Henry s law constants do not show a simple linear pattern as solubility, Kqw or vapor pressure when plotted against simple molecular descriptors, such as numbers of chlorine or Le Bas molar volume, e.g., PCBs (Burkhard et al. 1985b), pesticides (Suntio et al. 1988), and chlorinated dioxins (Shiu et al. 1988). Henry s law constants can be estimated from ... 

The calculation is illustrated in Table 1.5.5 for pentachlorophenol. The experimental aqueous solubility is 14.0 g/m3 at a pH of 5.1. The environmental pH is 7. Higher environmental pH increases the extent of dissociation, thus increasing the Z value in water, increasing the apparent solubility, decreasing the apparent KqW and Henry s law constant and the air-water partition coefficient, and decreasing the soil-water partition coefficient. 

Compound Vapor pressure Solubility log Kow Henry s law constant H/(Pa-m3/mol) calculated P/C... 

This shows that knowledge of the vapor pressure of A and its limiting activity coefficient allows us to calculate the Henry s law constant.7... 

Thus the free energy of solvation may be calculated from the Henry s law constant or from the vapor pressure of the pure substance and the limiting activity coefficient. Thus, if the deviation of the solution from Raoult s law behavior is known, calculation of the standard state free energy of solvation requires only the vapor pressure of the pure substance (in the standard state... 

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]. 

Based on its very small calculated Henry s law constant of 4.0xl07-5.4xl0"7 atm-m3/mol (see Table 3-2) and its strong adsorption to sediment particles, endrin would be expected to partition very little from water into air (Thomas 1990). The half-life for volatilization of endrin from a model river 1 meter deep, flowing 1 meter per second, with a wind speed of 3 meters per second, was estimated to be 9.6 days whereas, a half-life of greater than 4 years has been estimated for volatilization of endrin from a model pond (Howard 1991). Adsorption of endrin to sediment may reduce the rate of volatilization from water. 

Henry s Law is obeyed with organic pollutants of low solubility provided the pressures are not high or temperatures too low - conditions under which one might expect deviations from ideal behavior. Experimental values for Henry s Law constant may be obtained by equilibrating a pollutant between the solvent and vapor phase and measuring its concentration in those two phases. Providing the solubility is low (PA< 0.1) Henry s Law constant can be calculated from the equilibrium vapor pressure (PA) and solubility (S) ... 

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. 

In water, neither volatilization nor sorption to sediments and suspended particulates is expected to be an important transport mechanism. Using the Henry s Law constant, a half-life of 88 days was calculated for evaporation from a model river 1 m deep with a current of 1 m/second, and with a wind velocity of 3 m/second (Lyman et al. 1982). The biological treatment of waste water containing phenol has shown that less than 1% of phenol is removed by stripping (Kincannon et al. 1983 Petrasek et al. 1983). 

No published values of SPMD-air partition coefficients (A sa) exist. These values therefore have to be calculated from published values of and Henry s law constants H) using... 

Table 9 gives the results of this calculation. In order to achieve a consistent formulation of the equilibrium we use the reciprocal of the dissociation constant given by Brown and Brady (1952) multiplied by ko- Since the measurements show that Henry s law is very well obeyed, the equilibrium mole fractions in Table 9 were given as above, computed with the aid of the Henry s law constants k and As may be seen from the equilibrium constants in the last column of the table, the stability of the complexes increases with the number of methyl groups in the benzene nucleus, which implies that the basicity of the aromatic substances also increases in the same sense. 

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