090733 Avoid Common Pitfalls

090733 Avoid Common Pitfalls - Environmental Management...

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Unformatted text preview: Environmental Management Avoid Common Pitfalls When Using Henry’s Law Francis L. Smith Wilcrest Consulting Associates, LLC Allan H. Harvey National Institute of Standards and Technology Here is practical guidance on the use of Henry’s law in engineering calculations and how to account for the temperature dependence of the Henry’s constant — which is often ignored but which can be crucial for accurate process design. H enry’s law and the Henry’s constant are widely used in chemical and environmental engineering. Unfortunately, many people do not appreciate that the Henry’s “constant” is not a true constant, but instead has a significant non-linear temperature dependence. Ignoring this temperature dependence can lead to serious inaccuracies. This article discusses the temperature dependence of the Henry’s constant and suggests ways of estimating this dependence when data are limited or not available. It also briefly discusses other common pitfalls to be avoided when using Henry’s law. The focus is on dilute aqueous systems, such as those found in environmental applications, but much of the information is also appropriate for other applications. Thermodynamic basics CEP published a series of articles by Carroll (1–3) covering many aspects of Henry’s law and its uses in chemical engineering. This article will not repeat the material presented there, but will summarize a few key concepts that are relevant to this discussion. In a given solvent, the Henry’s constant for solute i, Hi, is defined as an infinite-dilution limit: H i = lim xi → 0 fi xi (1) where fi and xi are the fugacity and the mole fraction of the solute, respectively. (Variables other than mole fraction are sometimes used to describe the amount of solute; this will be discussed later.) Equation 1 may be applied at any temperature or pres- sure, and the solvent may be a liquid, a vapor, a supercritical fluid, or even a solid. Most applications, however, involve a liquid solvent. Furthermore, it is usually convenient to define Hi at a pressure equal to the solvent’s vapor pressure. (Reference 1 explains how to use these values at higher pressures.) When restricted to the solvent’s vaporpressure curve, Hi becomes a function of temperature only. For environmental work at pressures near ambient, this “restricted” Henry’s constant is adequate. (The pressure dependence is ignored in the remainder of this article.) More-complex methods covering wide ranges of temperatures and pressures, such as those encountered in geochemistry, may be found elsewhere (4–6). Since real systems never reach the limit of infinite dilution, most applications of Henry’s law involve the use of Eq. 1 without the infinite-dilution limit. The assumption that fi /xi remains constant for non-zero values of xi is reasonable for many environmental applications, where the goal is to describe the solubility or volatility of small amounts of contaminants in water. With the proportionality between fi and xi established by Henry’s law for one phase (e.g., an aqueous phase being purified), one needs only a model for fi in the other phase in order to design a separation process based on phase equilibrium. For steam or air stripping, where the coexisting phase is a vapor, an ideal-gas assumption is often sufficient, or corrections for nonideality may be added. If the coexisting phase is a liquid (for example, in liquid-liquid extraction), Raoult’s law is the simplest assumption; this may be corrected by a liquid-phase activity model as appropriate. CEP September 2007 www.aiche.org/cep 33 Environmental Management Nomenclature Ci ∆Cp,sol fi Hi Hi* ∆Hsol ∆Hvap pisat R T Tc T0, T1 xi xiaq xworg = any of various measures of composition in the liquid phase (various units may be used) = heat capacity of solution, J/mol-K = fugacity of solute i, MPa = Henry’s constant for solute i, MPa = the “solubility form” of the Henry’s constant for solute i, MPa–1 = enthalpy of solution, J/mol = enthalpy of vaporization, J/mol = vapor pressure of pure component i at the temperature of the solution, MPa = molar gas constant = 8.314472 J/mol-K = temperature, K = critical temperature of the solute, K = initial and final temperatures for an extrapolation of Hi, K = mole fraction of solute i = mole fraction of the organic solute in the aqueous phase = mole fraction of water dissolved in the organic phase Greek Letters = infinite-dilution value for the activity coefficient γiinf of solute i in the solvent, dimensionless Where do Henry’s constants come from? A review of the many data sources for Henry’s constants is beyond the scope of this article. However, it is helpful to understand how these data are obtained. Henry’s constants cannot be measured simply by placing a meter into a solution. Rather, they are derived indirectly from experiment via Eq. 1. For a sparingly soluble gaseous solute, the determination of Hi is straightforward from Eq. 1 (although the experiments may be difficult). Measurements of the solubility xi at low gas partial pressures yield Hi directly (perhaps after small corrections for gas nonideality to improve the value of fi). For a liquid solute that is nearly immiscible with the solvent, such as toluene with water, use of Eq. 1 is again straightforward. For the case where component i forms an organic-rich phase that is nearly immiscible with an aqueous phase, the solute fugacity in the solute-rich phase (which must be equal to that in the solvent-rich phase) can be approximated by Raoult’s law: Hi = (1 − x ) p org w xiaq sat i (2) where xworg is the mole fraction of water in the organic phase, xiaq is the mole fraction of the organic solute in the 34 www.aiche.org/cep September 2007 CEP aqueous phase, and pisat is the vapor pressure of pure component i at the temperature of the solution. A comprehensive collection of mutual solubility data for hydrocarbons with water and seawater is available in Ref. 7. For solutes with large or complete miscibility with the solvent (such as lower alcohols with water), the determination of Henry’s constant must again come from Eq. 1, but full analysis of the phase equilibrium is typically required. This usually involves fitting a liquid-activity model to experimental data and extrapolating the solute fugacity back to infinite dilution with the model. Equation 1 ultimately reduces to: H i = γ iinf pisat ( 3) where γiinf is the infinite-dilution value for the activity coefficient of solute i in the solvent. An engineer who cannot find a tabulated Henry’s constant is not necessarily stymied. If good phase-equilibrium data exist for the solute-solvent pair at the temperature of interest, a reliable value of Henry’s constant can be derived. Temperature dependence As stated earlier, the Henry’s “constant” is not constant with respect to temperature. Figure 1 illustrates some typical behavior of Hi(T) for several solutes in water. (Other aspects of Figure 1 will be discussed later.) The values for CO2 are taken from the correlation of Fernández-Prini, et al. (8), while those for other solutes come from the correlating equations used by de Hemptinne, et al. (9). These are not necessarily the best values in the range plotted, but only the qualitative behavior is important for this discussion. The Henry’s constant typically increases with temperature at low temperatures, reaches a maximum, and then decreases at higher temperatures. The temperature at which the maximum occurs depends on the specific solute-solvent pair. As a rule of thumb, the maximum tends to increase with increasing solute critical temperature for a given solvent and with increasing solvent critical temperature for a given solute. Clearly, the use of a Henry’s constant that was derived at 25°C at a different temperature could lead to serious design errors. Even a variation as small as 10 K can cause the Henry’s constant to change by a factor of two, which could have a serious impact on many designs. In some cases, reliable values for Henry’s constants are available over the entire temperature range of interest. For example, for common gases in water, the correlation of Fernández-Prini, et al. (8) extends from 0°C to the critical point of water. In other cases, solubility data are available so that Henry’s constants can be derived by the methods described in the previous section. But in many cases, only a 100,000 n-Octane Henryʼs Constant, MPa 10,000 Methyl-cyclohexane 1,000 Tc = 30.9°C CO2 Toluene 100 10 1 20 40 80 100 120 140 160 180 60 Temperature, °C I Figure 1. Temperature dependence of Henry’s constant for several solutes in water, showing the performance of the vapor-pressure extrapolation method starting at 25°C. The horizontal axis is linear in reciprocal absolute temperature. few data, or perhaps only a single measurement, will be available, often at or near 25°C. Sometimes no data at all will have been measured. If measuring it (or contracting for its measurement) are not options, one must rely on predictive schemes that estimate a Henry’s constant from molecular structure (and perhaps other properties such as solute chromatographic parameters). These methods (10–14), which are beyond the scope of this article, typically provide a value at a single temperature, such as 25°C. The following sections discuss how to extrapolate Henry’s constants from a single data point at a given temperature (e.g., 25°C) when temperature10,000 dependent data are lacking. Estimating temperature dependence using vapor pressure The starting point for intelligent extrapolation of Henry’s constants is Eq. 3. When extrapolating from a known value of Hi at temperature T0 to temperature T1, Eq. 3 becomes: H i (T1 ) γ iinf (T1 ) pisat (T1 ) ≈ × H i (T0 ) γ iinf (T0 ) pisat (T0 ) (4) zontal axis has units of degrees Celsius, it is actually linear in inverse absolute temperature (but reversed, so that temperature increases along the axis from left to right). As expected from the Clausius-Clapeyron equation, log10pisat is nearly linear in inverse temperature. The temperature dependence of γiinf is modest near ambient temperature, so that the temperature variation of Hi is primarily a consequence of the variation in pisat. At higher temperatures, γiinf varies much more rapidly, so that the temperature variation of Hi becomes more strongly dependent on the combined variations of both pisat and γiinf. The behavior noted in Figure 2 suggests an extrapolation procedure. Especially for small temperature intervals near ambient conditions, the relatively minor contribution of γiinf(T) in Eq. 4 can be ignored and a reasonable extrapolation obtained from: H i (T1 ) pisat (T1 ) ≈ H i (T0 ) pisat (T0 ) (5) Equation 5 is particularly convenient because the vapor-pressure function pisat(T) is known for many solutes of interest, while temperature-dependent values of γiinf are seldom available. Figure 3 shows the performance of this vapor-pressureratio extrapolation method, Eq. 5, for toluene in water with a single value at 25°C as the starting point. Equation 5 provides an excellent extrapolation for this temperature range — much better than if Hi had been assumed to be constant. γ — Toluene – Water 1,000 Toluene – Water Henry’s Constant, MPa 100 10 Toluene Vapor Pressure, kPa The interrelated temperature dependencies of Henry’s constant Hi, infinite-dilution activity coef1 80 100 120 140 160 180 60 20 40 ficient γiinf, and solute vapor pressure pisat can be Temperature, °C demonstrated by plotting them together. Figure 2 shows these variables for a typical solute (toluene) I Figure 2. Interdependence of Henry’s constant, solute vapor pressure and infinite-dilution activity coefficient (Eq. 3) for toluene in water. Note the different on a logarithmic scale; note that while the horipressure units on the Henry’s constant and the vapor pressure. CEP September 2007 www.aiche.org/cep 35 Environmental Management γiinf(T1)/γiinf(T0) for use in Eq. 4. It is important to use a model that is designed to include temperature dependence; some predictive models are 100 designed only for 25°C and therefore are inappropriate for this purpose. The modified UNIFAC 80 model (16) yields the temperature variation of γiinf; the COSMO-RS method (17) might also be use60 ful, although its use in this context has not been documented in the literature. Hwang, et al. (18) studied the infinite-dilution 40 Vapor Pressure Ratio vapor-liquid partition constant (which is closely Single Point Single Data Point @ 25°C Extrapolation related to the Henry’s constant) in the context of 20 Toluene – Water steam stripping for organic pollutants in water. Henryʼs Constant They established a databank for 404 common 0 organic pollutants, including many EPA-desig50 30 20 0 10 40 60 nated priority pollutants, at 100°C and 25°C. In Temperature, °C cases where high-temperature data were lacking, I Figure 3. Illustration of vapor-pressure extrapolation technique (Eq. 4) for they used the vapor-pressure extrapolation the Henry’s constant of toluene in water. method, supplementing it with activity coefficients estimated with UNIFAC. They tabulated In Figure 1, the vapor-pressure-ratio extrapolation is suggested values for log10[γiinf(100°C)/γiinf(25°C)] for sevplotted for four compounds over a wider temperature range. eral different classes of organic compounds. Because the horizontal scale is linear in reciprocal absolute Van’t Hoff extrapolation temperature, the extrapolations are nearly linear on these coordinates. The accuracy of the extrapolation from 25°C An alternative method for extrapolation of single values with Eq. 5 deteriorates at higher temperatures, but it is quite for Henry’s constants uses the solute enthalpy of solution, good up to 50°C and not unreasonable up to perhaps 80°C. ∆Hsol, over a modest temperature range. A thermodynamic Note that the vapor pressure of CO2 does not exist above expression, usually associated with the name van’t Hoff, its critical temperature (Tc = 30.9°C), so Eq. 5 cannot be relates the Henry’s constant at the two absolute temperaused directly for the extrapolation of Hi above this temperatures T0 and T1: ture. However, the critical temperature of solute i does not ⎡ ⎛ ∆H sol ⎞ ⎛ 1 H i (T1 ) 1 ⎞⎤ introduce any irregularities into the behavior of Hi(T), so Hi ≈ exp ⎢ ⎜ − (6) ⎝ R ⎟ ⎜ T1 T0 ⎟ ⎥ ⎠⎝ H i (T0 ) ⎠⎦ can still be extrapolated to some extent above the solute ⎣ critical temperature by visual or graphical means based on the vapor pressure data below Tc. where R is the molar gas constant. Equation 6 derives from For some less-common solutes, the vapor-pressure data a differential expression, so its use over a finite temperature needed for Eq. 5 may not be known at the temperatures of range makes the implicit assumption that ∆Hsol remains interest. In such cases, estimation techniques for pisat(T) constant with temperature (so it cannot reproduce the curva(15) can be used to obtain the vapor-pressure ratio for Eq. 5. ture and maximum shown in Figure 1). This is usually a fair approximation for modest temperature differences of perEnhancing extrapolation haps 20 K, making the van’t Hoff approach reasonable for with infinite-dilution activity coefficients systems near ambient temperature, such as groundwater, Equation 5 can be improved upon if one can estimate the where the temperature variations are not large (19). If availtemperature dependence of the infinite-dilution activity able, data for the heat capacity of solution, ∆Cp,sol, can be coefficient γiinf; in such cases, Eq. 4 would be used. This is used to increase the range of reasonable extrapolation by only a small correction for short extrapolations near ambiproviding a temperature dependence for ∆Hsol. ent temperature, but becomes a major factor for larger Data for ∆Hsol (and ∆Cp,sol) for solutes in water are diffiextrapolations, especially to higher temperatures such as cult to measure experimentally. Published values are limited those used in steam stripping. and (as can be seen in tabulations such as that in Ref. 20) In the absence of experimental data, predictive models can vary substantially. Often, tabulated values of ∆Hsol are for activity coefficients can be used to estimate merely derived from values of Hi measured over a range of Henryʼs Constant, MPa 120 36 www.aiche.org/cep September 2007 CEP temperatures. If such data for Hi(T) already exist, it is a waste of effort and sacrifices accuracy to translate them into ∆Hsol and then use Eq. 6 — it is better to use the measured Hi(T) directly. (It is reasonable, though, to use Eq. 6 to interpolate measured data for Hi(T) over small temperature ranges, which was done by Washington (19)). However, if independent values of ∆Hsol exist at the desired temperature, either from calorimetric data or from a reliable estimation technique, Eq. 6 provides a reasonable method for extrapolating Henry’s constants over modest temperature intervals. Note that ∆Hsol can be either negative or positive, depending on whether the temperature of interest is below or above the maximum of Hi(T) (Figure 1). Occasionally (21), one sees an equation similar in form to Eq. 6, but with the negative of the pure-solute enthalpy of vaporization, –∆Hvap, in place of ∆Hsol. Such a substitution has little basis in thermodynamics, but it can provide an adequate estimate in some cases. This is because the Clapeyron equation relates ∆Hvap to the temperature dependence of the vapor pressure, so that the use of ∆Hvap in Eq. 6 becomes nearly equivalent to the vapor-pressure extrapolation method, Eq. 5. However, ∆Hvap is almost never measured independently, but is typically derived from data for pisat(T). Consequently, it is preferable to use Eq. 5 directly, in order to avoid loss of accuracy when pisat(T) is differentiated. Note also that the vapor-pressure extrapolation method, unlike the van’t Hoff type methods, implicitly corrects for the temperature dependence of ∆Hvap over the range of the extrapolation. Pitfalls with chemically reacting systems Some substances (NH3, Cl2, organic acids, etc.) partition within the aqueous phase, due to reversible equilibrium processes such as dissociation. Henry’s law describes only the equilibrium of a single neutral species of the substance between the two phases: [NH3]Gas Henryís Law [NH3]Aqueous However, within the aqueous phase, partitioning of the aqueous form of a substance may occur and would, therefore, need to be accounted for and described. This is done using one or more additional equilibrium expressions, such as: [NH3]Aqueous + [H2O] dissociation [NH4+] + [OH–] The consequence of such partitioning (2, 22, 23) is that, for a given gas-phase concentration, a larger quantity of the substance may actually exist within the aqueous phase at equilibrium than would be predicted by Henry’s law. This can be especially significant if a dissociated species participates in an additional reaction, such as an acid-base reaction that would consume OH-. Similarly, a much smaller amount may actually exist in the gas phase at equilibrium than would be predicted by Henry’s law if a quantitative analytical method that measures the sum of the associated and dissociated forms of the solute were used to determine the total quantity of the partitioned substance in the aqueous phase. Pitfalls with units A common problem with Henry’s constants is caused by the wide variety of possible units of measure. Because Henry’s law is used in many different disciplines, many different usages and conventions have developed. If proper care is not taken, it can be easy to use a reported Henry’s constant in a way that does not match the way in which the original value was defined — leading to serious errors. Because Henry’s constants vary over many orders of magnitude (Figure 1), errors due to units are more difficult to detect by inspection in this case than in many other engineering situations (for example, calculation of pure-component vapor pressures, where an engineer would have a good idea of the correct order of magnitude). The definition in Eq. 1 (fugacity divided by mole fraction) implies units of pressure for Hi. This is the most common usage for chemical engineers. However, in various contexts one sees gas-phase composition described by partial pressure, mass concentration, molar concentration, etc., while units for liquid-phase composition can include molality, molarity and weight fraction. When composition is used for the gas phase, it is important to note what the implied total pressure is. When mole or weight fraction is used for the liquid phase, it is not always obvious which is meant from the units of Henry’s constant, since fractions are dimensionless by convention. If the concentration units applied for both phases are the same, then the Henry’s constant itself becomes dimensionless. This is unfortunate — because depending on which units were used, different dimensionless Henry’s constants, with different values, exist for the same solute. Another source of confusion is that some practitioners (for example, Ref. 20) use Henry’s law in a “solubility” form, such as Ci = Hi*pi, where Ci is some measure of composition in the liquid phase and Hi* is effectively the reciprocal of the “volatility form” of the Henry’s constant (which has been used throughout this article). This means that the Henry’s constant for any solute has two different values, depending on whether Henry’s law took the solubility form or the volatility form. Therefore, two things are imperative. First, those who report Henry’s constants in the literature (both from original measurements or in compiling data from others) must be very clear about definitions. Second, those who use CEP September 2007 www.aiche.org/cep 37 Environmental Management Henry’s constants must pay close attention to be sure they understand how the numbers they are using were defined. Conversion among different units for Henry’s constant is possible, but can be complicated by the need to convert between mass and molar concentration units. Therefore, factors such as the molar mass of the solute and the density of water are employed. Some calculators for this purpose are available on the Internet (24, 25). When using such calculators, it is essential to be clear about the definition associated with each unit, especially dimensionless units. Finally, note that the expressions given above for estimating the temperature dependence of Henry’s constant are for the definition of Hi in Eq. 1. A subtle but signifi- cant point is that the ratio Hi(T1)/Hi(T0) is not the same in all sets of units. In particular, if units of volumetric concentration (such as moles per liter) are used, an additional temperature dependence is introduced by the variation of fluid-phase density with temperature. This can be on the order of 10% for a 30 K change near room temperature when such units are used for the vapor; the change of liquid density with temperature is usually small enough to neglect. If one is using Eq. 4 or Eq. 5 with such densitydependent composition units, the preferred procedure is to convert to the units of Eq. 1, perform the Hi(T) extrapolation in those units, and then convert back to the densitydependent units. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 38 Carroll, J. J., “What is Henry’s Law?,” Chem Eng. Progress, 87 (9), pp. 48–52 (Sept. 1991). Carroll, J. J., “Use Henry’s Law for Multicomponent Mixtures,” Chem Eng. Progress, 88 (8), pp. 53–58 (Aug. 1992). Carroll, J. J., “Henry’s Law Revisited,” Chem Eng. Progress, 95 (1), pp. 49–56 (Jan. 1999). Sedlbauer J., et al., “A New Equation for Correlation and Prediction of Standard Molal Thermodynamic Properties of Aqueous Species at High Temperatures and Pressures,” Chem. Geology, 163, pp. 43–63 (2000). Plyasunov, A. V., et al., “Semi-Empirical Equation of State for the Infinite Dilution Thermodynamic Functions of Hydration of Nonelectrolytes Over Wide Ranges of Temperature and Pressure,” Fluid Phase Equil., 183, pp. 133–142 (2001). Akinfiev, N. N., and L. W. Diamond, “Thermodynamic Description of Aqueous Nonelectrolytes at Infinite Dilution Over a Wide Range of State Parameters,” Geochim. Cosmochim. Acta, 67, pp. 613–629 (2003). Shaw, D. G., and A. Maczynski, eds., “IUPAC Solubility Data Series. 81. Hydrocarbons in Water and Seawater – Revised and Updated,” published in 12 parts in J. Phys. Chem. Ref. Data, (2005–2006). Fernández-Prini, R., et al., “Henry’s Constants and VaporLiquid Distribution Constants for Gaseous Solutes in H2O and D2O at High Temperatures,” J. Phys. Chem. Ref. Data, 32, pp. 903–916 (2003). de Hemptinne, J.-C., et al., “The Henry Constant for 20 Hydrocarbons, CO2 and H2S in Water as a Function of Pressure and Temperature,” presented at the 14th Symposium on Thermophysical Properties, Boulder, CO (June 2000). Cabani, S., et al., “Group Contributions to the Thermodynamic Properties of Non-Ionic Organic Solutes in Dilute Aqueous Solution,” J. Solution Chem., 10, pp. 563–595 (1981). Meylan, W. M., and P. H. Howard, “Bond Contribution Method for Estimating Henry’s Law Constants,” Environ. Toxicol. Chem., 10, pp. 1283–1293 (1991). The HENRYWIN software based on this method is available from the Environmental Protection Agency at www.epa.gov/oppt/ exposure/pubs/episuite.htm. Abraham, M. H., et al., “Hydrogen Bonding. Part 34. The Factors that Influence the Solubility of Gases and Vapours in Water at 298 K, and a New Method for Its Determination,” J. Chem. Soc. Perkin Trans. 2, pp. 1777–1791 (1994). Lin, S.-T, and S. I. Sandler, “Henry’s Law Constant of Organic Compounds in Water from a Group Contribution Model with Multipole Corrections,” Chem. Eng. Sci., 57, pp. 2727–2733 (2002). www.aiche.org/cep September 2007 CEP 14. Plyasunov, A. V., et al., “Group Contribution Values for the Thermodynamic Functions of Hydration at 298.15 K, 0.1 MPa. 4. Aliphatic Nitriles and Dinitriles,” J. Chem. Eng. Data, 51, pp. 1481–1490 (2006), and references therein. 15. Poling, B. E., et al., “The Properties of Gases and Liquids,” 5th ed., McGraw-Hill, New York, NY (2001). 16. Jakob, A., et al., “Further Development of Modified UNIFAC (Dortmund): Revision and Extension 5,” Ind. Eng. Chem. Res., 45, pp. 7924–7933 (2006). Additional parameters beyond those published in the open literature are available to members of the UNIFAC consortium. 17. Klamt, A., “COSMO-RS: From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design,” Elsevier, Amsterdam, the Netherlands (2005). 18. Hwang, Y.-L., et al., “Steam Stripping for Removal of Organic Pollutants from Water. 2. Vapor-Liquid Equilibrium Data,” Ind. Eng. Chem. Res., 31, pp. 1759–1768 (1992). The article’s supplementary material contains a databank of 404 compounds of environmental interest and other useful property data. 19. Washington, J. W., “Gas Partitioning of Dissolved Volatile Organic Compounds in the Vadose Zone: Principles, Temperature Effects and Literature Review,” Ground Water, 34, pp. 709–718 (1996). Calculations from the method developed in this article may be accessed at www.epa.gov/athens/ learn2model/part-two/onsite/esthenry.htm. 20. Sander, R., “Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry (Version 3),” available at www.henrys-law.org (1999). This website lists (without further evaluation) Henry’s constants collected from the literature for over 900 volatile substances in water. 21. U.S. Environmental Protection Agency, “FACT SHEET: Correcting the Henry’s Law Constant for Soil Temperature,” available at www.epa.gov/oswer/riskassessment/airmodel/ pdf/factsheet.pdf (2001). This contains a listing of Henry’s constants at 25°C for 93 compounds of interest in soil and groundwater pollution. 22. Snoeyink, V. L., and D. Jenkins, “Water Chemistry,” Wiley, Hoboken, NJ (1980). (See Chapter 4, “Acid-Base Chemistry,” especially Table 4.1.) 23. Prausnitz, J. M., et al., “Molecular Thermodynamics of FluidPhase Equilibria,” 3rd ed., Prentice Hall, Upper Saddle River, NJ (1999). (See Section 10.7.) 24. Weaver, J., and C. Owensby, “Henry’s Law Calculator,” www.epa.gov/athens/learn2model/part-two/onsite/henryslaw.htm. 25. Sander, R., “Converting Henry’s Law Constants,” www.mpchmainz.mpg.de/~sander/res/henry-conv.html. Conclusions It is important to recognize that the Henry’s “constant” is actually a strong, nonlinear function of temperature. For accurate design, it is preferable to have temperaturedependent data for Hi(T). Such data can be interpolated with a simple van’t Hoff equation (such as Eq. 6) over small temperature ranges or a more complex expression (such as those in Ref. 8 or Ref. 9) if a larger range is needed; these correlations can be extrapolated slightly over temperature if necessary. If temperature-dependent data are not available, Eq. 5 can be used to extrapolate for modest distances near ambient temperatures; this can be augmented by the use of infinite-dilution activity coefficients (Eq. 4), which become more important at higher temperatures. Additional pitfalls include failing to distinguish between the “solubility” and the “volatility” form of Henry’s law, failing to consider the implications of liquidphase solute partitioning, and failing to be careful about units of measure, especially dimensionless units. If one avoids these pitfalls, Henry’s law can be a useful tool in many engineering applications. CEP FRANCIS L. SMITH is the principal of Wilcrest Consulting Associates, LLC (2326 Bristol Band, Katy, TX 77450; Phone: (281) 579-1618; Fax: (413) 714-6660; E-mail: leesmith@attglobal.net). He works as an independent business and engineering consultant, specializing in chemical, environmental and utility engineering design and optimization, as well as the application of Value Improving Practices (VIPs) for the optimization of investment for capital projects. He previously has worked for 15 years with BASF Corp., Corporate Engineering, as a chemical and environmental process design engineer, and more recently for five years with Kellogg, Brown and Root as a chemical process design engineer, and as a VIPs facilitator. He has a BS and MEngr in chemical engineering from Cornell Univ., and a PhD in environmental engineering from the Univ. of Cincinnati. ALLAN H. HARVEY is a chemical engineer with the Physical and Chemical Properties Div., National Institute of Standards and Technology (325 Broadway, Boulder, CO 80305; Phone: (303 )497-3555; Fax: (303) 497-5224; E-mail: aharvey@boulder.nist.gov). He has been with NIST since 1994, working in the areas of phase-equilibrium thermodynamics, properties of humid gases, thermodynamics of dilute solutions, and properties of water and aqueous systems. Prior to coming to NIST, he worked for Simulation Sciences, Inc. He has a BS in chemical engineering from the Univ. of Missouri at Rolla and a PhD in chemical engineering from the Univ. of California at Berkeley. He is a member of AIChE and ASME. Acknowledgements The authors thank J. D. Olson, A. V. Plyasunov, R. Sander, and J. W. Washington for helpful discussions and suggestions. www.aiche.org/cep or Circle No.126 CEP September 2007 www.aiche.org/cep 39 ...
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This note was uploaded on 12/29/2011 for the course CHE 128 taught by Professor Scott,s during the Fall '08 term at UCSB.

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