Henry coefficients

Henry coefficients are generally determined independently from other isotherm parameters analyzing the response to pulse injections performed with very low amounts of solutes to ensure linear isotherm behavior (Section 6.5.3.1). The linearity can be tested by comparing two or three pulse responses belonging to different concentrations. If the results for the determined Henry coefficients are identical, the system is linear. H is calculated by moment analysis using the measured Pt c+inj+piant and Equations 6.134 and 6.137  

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Based on equations (3.25) and (3.26) for the linear area of adsorption of dissolved oxygen on a thin semiconductor film (F being the Henry coefficient), we can derive the following equation ... 

In the special case of an ideal single catalyst pore, we have to take into account that diffusion is quicker than in a porous particle, where the tortuous nature of the pores has to be considered. Hence, the tortuosity r has to be regarded. Furthermore, the mass-related surface area AmBEX is used to calculate the surface-related rate constant based on the experimentally determined mass-related rate constant. Finally, the gas phase concentrations of the kinetic approach (Equation 12.14) were replaced by the liquid phase concentrations via the Henry coefficient. This yields the following differential equation ... 

Dupont et al. [60] studied the same reaction, but used [BMIM][PF6] and [BMIM][BF4] as ionic liquids. A special focus of their investigations was on the influence of H2-pressure on conversion. The Henry coefficient solubility constant was determined by pressure drop experiment in a reactor, which is a known procedure to measure gas solubilities [93]. The values reported by these authors were FC=3.0xl0-3 mol IT1 atm1 for [BMIM][BF4]/H2 and 8.8x10 4 mol L 1 atm-1 for [BMIM][PF6]/H2 at room temperature, which differ significantly from those determined by the 1H-NMR technique (see Table 41.2) [59]. However, their values indicated that molecular hydrogen is almost four times more soluble in [BMIM][BF4] than in [BMIM][PF6] under the same pressure. According to the authors, this is reflected by the values of conversion (ee), which were 73% (93% ee) for [BMIM][BF4] and 26% (81% ee) for [BMIM][PF6] at 50 bar H2 pressure (Table 41.9, entries 2 and 4). 

In this formula, [H2] is the concentration of hydrogen in the liquid in equilibrium with the gas phase, related by the Henry coefficient. 

This simplified description of molecular transfer of hydrogen from the gas phase into the bulk of the liquid phase will be used extensively to describe the coupling of mass transfer with the catalytic reaction. Beside the Henry coefficient (which will be described in Section 45.2.2.2 and is a thermodynamic constant independent of the reactor used), the key parameters governing the mass transfer process are the mass transfer coefficient kL and the specific contact area a. Correlations used for the estimation of these parameters or their product (i.e., the volumetric mass transfer coefficient kLo) will be presented in Section 45.3 on industrial reactors and scale-up issues. Note that the reciprocal of the latter coefficient has a dimension of time and is the characteristic time for the diffusion mass transfer process tdifl-GL=l/kLa (s). 

Good approximate values could be obtained using Eq. (16). For a 1 1 mixture of methanol and methyl formate, calculated (H calc = 520 MPa) and measured (H jexp = 495 MPa) Henry coefficients only differ by less than 5% [24]. 

In general, the intrinsic kinetics, the diffusion, mass transfer and Henry coefficients are either known or can be estimated, while the Hatta number can be determined. This is the first step in assessing the working regime of the reactor. 

In the limit of low pressure the front end of the adsorption isotherm is approximated by the Henry regime which states that the number of adsorbed molecules per unit volume is proportional to the pressure and to the Henry coefficient, Kh. ... 

Here kgr is the surface reaction rate constant, Rr is the adsorption equilibrium constant for product R, Pr is the partial pressure of R and Kp is the reaction equilibrium constant. At low loading the reaction rate simply becomes proportional to the product of the intrinsic rate constant and the Henry coefficient. 

For propane, n-pentane and n-hexane the differential heats of adsorption over FER dropped more rapidly, right after 1 molecule was adsorbed per Bronsted acid site. Similar results were obtained with TON. In contrast, with MOR and FAU the drop in the differential heats of adsorption for n-alkanes occurred at lower coverages, indicating that only a certain fraction of the Bronsted acid sites were accessible to the adsorbing alkane probe molecules. With MFI the drop did not occur until 2 molecules of n-alkane were adsorbed per Bronsted acid site, suggesting perhaps a higher stoichiometry of about two n-alkanes per Bronsted acid site. In the cases of i-butane and i-pentane the drop occurred around one alkane per Bronsted acid site. Finally, n-butane adsorption isotherms measured over TON framework type catalysts having three different A1 contents (Si/Al2 = 90, 104, 128) showed Henry coefficients to increase with increase in the A1 content [5], Based... 

Often the ratio of Henry coefficients, related to adsorption at zero loading, is used for predicting the selectivity of adsorption for mixtures. The ratio of Henry coefficients for linear and mono-branched alkanes with carbon number n = 5-8 are summarized for various zeolites in Figure 13.10 [15]. The Henry coefficient ratios were 1 for FAU, 2 for BEA, MOR and MFI, 6-9 for TON and 10-14 for MTT. Interestingly, CBMC simulations suggest that the ratio of Henry coefficients, actu-... 

Figure 13.10 Ratio of Henry coefficients for linear and branched alkanes over various framework types [15].

A good example for reactant shape selectivity includes the use of catalysts with ERI framework type for selective cracking of linear alkanes, while excluding branched alkanes with relatively large kinetic diameters from the active sites within the narrow 8-MR zeolite channels [61, 62]. Here molecular sieving occurs both because of the low Henry coefficient for branched alkanes and because of the intracrystalline diffusion limitations that develop from slow diffusivities for branched alkane feed molecules. 

K is the overall mass-transfer coefficient based on the liquid phase. A is the total interfacial area in the gas-liquid dispersion. C is the concentration in the liquid phase. C thus corresponds to equilibrium with the gas phase of composition y. H is the Henry coefficient for the gas. In the case of oxygen or a sparingly soluble compound, H is large and resistance to mass transfer is located in the liquid phase. 

The unsaturated zone can be modeled as a bottleneck boundary of thickness 8 = 4 m. The TCE concentration at the lower end of the boundary layer is given by the equilibrium with the aquifer and at the upper end by the atmospheric concentration of TCE, which is approximately zero. Thus, you need to calculate the nondimensional Henry coefficient of TCE at 10°C, KTCB a/w(10°C). 

We now define the Henry s law constant (some authors call it the Henry coefficient or the Henry constant), k, by... 

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]. 

The thermodynamic equilibrium is calculated with the Henry coefficients corrected for the electrolyte influence. As nitric acid is a strong electrolyte, the solubilities of nitrogen oxides in water [81] must be recalculated according to [20] to account for the non-ideal electrolyte behavior. 

The Henry coefficient is obtained from the solubility and vapor pressure data from this table as follows = (w lRT)IC. Other values are provided in Table 6. 

Each term on right side of Equation 2.2 represents an individual resistance as depicted in Figure 2.4. Hollow fiber diameters are rfoux and The term H is the Henry coefficient (liquid-gas equilibrium constant) for the species in question. In the case of liquid-liquid contact, the term H in Equation 2.2 should be replaced by mo, the equilibrium distribution coefficient between tube side liquid and shell side liquid. 

Wienke, G. Gmehling, J. Prediction of octanol - water - partition coefficients. Henry-coefficients and water solubilities using UNIFAC. Toxicol. Environ. Chem. 1998, 65, 57-86. 

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