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Activity Coefficient Estimation Methods. Bharat Chandramouli February 5, 2002. Activity Coefficient . The activity coefficient is a measure of the non-ideality of mixing Two components, Enthalpic and Entropic. Estimation/Measurement.

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## Activity Coefficient Estimation Methods

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**Activity Coefficient Estimation Methods**Bharat Chandramouli February 5, 2002**Activity Coefficient**• The activity coefficient is a measure of the non-ideality of mixing • Two components, Enthalpic and Entropic**Estimation/Measurement**• Activity coefficients in single component/simple mixtures easy to measure • Activity coefficients in water or octanol can be calculated from solubility given sufficiently sensitive methods**Need for estimation**• What about complex mixtures? • What about dynamic systems with changing compositions? • It becomes more practical to use estimation methods to approximate g in these cases**Estimation Methods**• Group contribution methods are most common because they have predictive ability • There are two group contribution methods commonly used for iom • calculation from solubility parameters • UNIFAC calculation**UNIFAC the UNIversal Functional group Activity Coefficient**model • The activity coefficient is calculated from two components Combinational (V, SA) Residual (interactions) (Experiment Fit)**UNIFAC**• The group contribution components consist of • volume contributor -Rk • surface area contribution -Qk • interaction parameter between functional groups Amk • To calculate interactions, similar sub-groups are assigned to groups and interactions are between these groups • Calculate activity coefficients by summing all contributions and interactions**UNIFAC-Simple example**• Ethanol CH3-CH2-OH**UNIFAC Methods**• Interaction parameters are fit from experimental data • This work is still ongoing and many parameters still not available**Hansen Solubility Parameter**• This method calculates activity coefficients from the solubility parameter • Theory of cohesive energy developed by Hildebrand for dispersive systems and extended by Hansen for polar and hydrogen bonding**Hansen Activity Coefficient**• The activity coefficient is given by Cohesive energy density Molar Volume Size effect term Enthalpy Entropy**The Size Effect Term**• i,omd is a measure of the effect of differing sizes of i and om on their entropy of mixing • This was derived by Flory and Huggins using statistical thermodynamics • For an infinitely dilute solution**Cohesive Energy (Ecoh)**• Closely linked to the heat of evaporation • It is a measure of a the ability of a liquid molecule to stay together • Theory of cohesive energy developed by Hildebrand for dispersive systems and extended by Hansen for polar and hydrogen bonding**Solubility parameter**• Solubility parameters are measures of cohesive energy cohesive energy solubility parameter coh. energy density**Calculating solubility parameters**• Hansen and others compiled molar attraction constants for functional groups, which are additive contributions to the solubility parameter**Attraction Constants (F)**• The product of V was found to vary linearly across homologous series • Additivity of structural sub-groups • F=V values compiled for dispersion and polar components of • Hansen later compiled additive contributions to Eh**Multi-component Mixtures**• How are om parameters calculated? • Parameters weighted using component mole fraction and molar volume to get “average om”**Cohesive Energy Density**• i,omA can be derived as • ib is a weighting factor based on dispersive forces, has been tabulated for a variety of compounds • ib corrects for the fact that polar and H bonding forces are localized**Activity Coefficient**• Putting the two components together lniom = +**Calculation**• First, calculate group contributions for each component in the mixture • Calculate “om” parameters by weighting with mole fraction and molar volume • Calculate parameters for compound of interest • Calculate activity coefficient**Hansen or UNIFAC?**• UNIFAC more powerful interaction • UNIFAC not universal–missing parameters • Hansen has certain inconsistencies as certain parameters have to be culled from different sources. Very sensitive to parameter choice • ib not widely available for many compounds, so estimation may be difficult**Where do you use this?**• Water solubility estimation • Solvent-Water partitioning (Kow)**gas**Compound Thermodynamic Equilibrium? Particle type Temperature Humidity particle Gas/Particle Partitioning • What happens when a semivolatile organic (SOC) encounters a particle??**Partitioning Modes**• Mode of SOC-particle interaction depends on the particle • Adsorption Solid particle, no organic liquid layer (dust, inorganic salts) • Absorption Particle either liquid, or has substantial liquid layer (combustion particles, secondary organic aerosol) • SOCs such as PAHs, and alkanes primarily partition to organic or carbonaceous aerosols rather than to mineral-based aerosols**Predictive Partitioning models**• Pankow (1994) for absorptive partitioning fom- fraction extractable organic matter igom- activity coefficient of SOC in om MWom-molecular weight of om

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