Henry’s isotherm

Hemoproteins, reactions of iron in, 4 367 Henry s isotherms, 30 242 Heptacyclotetradecane, deuterium exchange, 25 135, 136 Heptane... 

Upon rearrangement, the electrochemical equivalent of the Langmuir isotherm is obtained. If 0 1, Eq. (20) reduces to Henry s isotherm... 

Equation (2.207), like Henry s isotherm, is applicable for relatively low concentrations. At such kinetics there may be no difference between the adsorption and desorption rates. With increase in concentration the effect of a limited munber of active sites begins to appear. A consequence is that the adsorption rate law becomes nonlinear and equation (2.206) assiunes the following format... 

It is more convenient, however, to compare reaction rates at a constant concentration in the solution. The activation energy determined under such conditions is known as the apparent value and represents the energy of activation of the elementary act itself as well as heat change of the preceding equilibrium. At low surface concentration C of a reagent (in the Henry s isotherm region), C varies with volume concentration C and exponentially depends on the heat of adsorption... 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

The ideal gas law equation of state thus leads to a linear or Henry s law isotherm. A natural modification adds a co-area term ... 

Make a plot of Eq. XVII-69 as 6 versus P, and, for comparison, one of a Langmuir adsorption isotherm of same limiting or Henry s law slope. Comment on the comparison. 

In the present study we try to obtain the isotherm equation in the form of a sum of the three terms Langmuir s, Henry s and multilayer adsorption, because it is the most convenient and is easily physically interpreted but, using more a realistic assumption. Namely, we take the partition functions as in the case of the isotherm of d Arcy and Watt [20], but assume that the value of V for the multilayer adsorption appearing in the (5) is equal to the sum of the number of adsorbed water molecules on the Langmuir s and Henry s sites ... 

The results of a comparison between values of n estimated by the DRK and BET methods present a con. used picture. In a number of investigations linear DRK plots have been obtained over restricted ranges of the isotherm, and in some cases reasonable agreement has been reported between the DRK and BET values. Kiselev and his co-workers have pointed out, however, that since the DR and the DRK equations do not reduce to Henry s Law n = const x p) as n - 0, they are not readily susceptible of statistical-thermodynamic treatment. Moreover, it is not easy to see how exactly the same form of equation can apply to two quite diverse processes involving entirely diiferent mechanisms. We are obliged to conclude that the significance of the DRK plot is obscure, and its validity for surface area estimation very doubtful. 

Henry s law corresponds physically to the situation in which the adsorbed phase is so dilute that there is neither competition for surface sites nor any significant interaction between adsorbed molecules. At higher concentrations both of these effects become important and the form of the isotherm becomes more complex. The isotherms have been classified into five different types (9) (Eig. 4). Isotherms for a microporous adsorbent are generally of type I the more complex forms are associated with multilayer adsorption and capillary condensation. 

Equation 6 shows that the adsorption of component 1 at a partial pressureis reduced in the presence of component 2 as a result of competition for the available surface sites. There ate only a few systems for which this expression (with 5 1 = q 2 = 5 ) provides an accurate quantitative representation, but it provides useful quaUtative or semiquantitative guidance for many systems. In particular, it has the correct asymptotic behavior and provides expHcit recognition of the effect of competitive adsorption. For example, if component 2 is either strongly adsorbed or present at much higher concentration than component 1, the isotherm for component 1 is reduced to a simple linear form in which the apparent Henry s law constant depends onp. ... 

Thermodynamics requires that a linear limit be approached in the Henry s law region for all isotherm equations. 

This three-parameter equation behaves linearly in the Henry s law region and reduces to the Langmuir isotherm for m = 1. Other well-known isotherms include the Radke-Prausnitz isotherm [Radke and Prausnitz, Ind. Eng. Chem. Fundam., 11, 445 (1972) AIChE J., 18, 761 (1972)]... 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

The stripping operation takes place isothermally at 298 K and follows Henry s law. 

It should be stressed that in the case of linear isotherm, the peak broadening effect results from eddy diffusion and from resistance of the mass transfer only, and it does not depend on Henry s constant. In practice, such concentration profiles are observed for these analyte concentrations, which are low enough for the equilibrium isotherm to be regarded as linear. 

With the adsorbate concentration low enough, the Langmuir isotherm transforms into the linear equation and becomes the simplest isotherm of adsorption, as described by Henry s law. 

The adsorption free energy and other parameters may be determined, provided that a proper adsorption isotherm is identified and is fitted to experimental data. However, it is usually difficult to unequivocally choose an appropriate isotherm an experimental isotherm may well be fitted to a multitude of theoretical isotherms having several adjustable parameters. If the adsorption isotherm at a very small surface coverage is accessible experimentally, the adsorption free energy can be determined from the limiting slope of the isotherm, as all isotherms reduce to Henry s law when 6 0 ... 

The simplest adsorption isotherm is that of Henry s law (linear adsorption isotherm),... 

In other words, the model predicts a limiting form of a linear (Henry s Law) type of isotherm as the polymer concentration tends to zero. 

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]. ... 

This expression is analogous to Henry s Law for gas-liquid systems even to the extent that the proportionality constant obeys the van t Hoff equation and Ka = K0e AH/RT where AH is the enthalpy change per mole of adsorbate as it transfers from gaseous to adsorbed phase. At constant temperature, equation 17.1 becomes the simplest form of adsorption isotherm. Unfortunately, few systems are so simple. 

The simplest adsorption equation is Henry s Law, that is, the loading is directly proportional to the sorbate partial pressure. X= KP This linear isotherm equation adequately describes some adsorbents and, in the limit of low coverage, it actually describes most sorbents. For adsorption that is truly described by Henry s Hnear relationship, the loadings are low, the adsorption is bound to be essenhaUy isothermal and there are several published analytical solutions to describe both batch kinetics and column dynamic behavior for such systems. 

Adsorption constant, Henry s Law coefficient, slope of the chord of the isotherm, dimensionless... 

---