Linear Henry region

In case of injection of a very small amount of analyte, its concentration is in the linear region of adsorption isotherm (Henry region of linear variation of adsorption with the equilibrium concentration of the analyte) and the derivative could be substituted with the slope of excess adsorption isotherm, also known as Henry constant, Kh, to get... 

For the simple Henry region everything is linear. The isotherm is N° / A = K x... 

A linear drop in the surface tension with increasing surfactant concentration (the Henry region) in agreement with eq. (11.12) corresponds to a linear increase in adsorption ... 

The Szyszkowski equation (II. 18) satisfies both limiting conditions it is consistent with the linear dependence of the surface tension on concentration within the Henry region, and agrees with eq. (11.17) at sufficiently high concentrations. At the same time, the criteria which define low and sufficiently high concentrations are set. Indeed, at low (as compared to a = IA) concentrations the logarithm can be expanded in series, yielding... 

This form is particularly useful as it provides the basis for a convenient way to extract the Henry constant from data at higher loadings (beyond the Henry region). A plot of ln(p/g) vs q should yield a linear asymptote with slope 2Ai and intercept - IniC (see Fig. 4) [14]. 

Assiuning the adsorbed phase to be a two-dimensional ideal gas and assuming the adsorption occurs in the Henry s law region (linear isotherm), the following equation of state can be substituted in Eq. (29) ... 

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)]... 

Another three-parameter equation that often fits data well and is linear in the Henry s law region is the UNILAN equation [Honig and... 

For the sorption of hydrocarbons in type-A zeolites at ordinary temperatures, the region of linearity of the isotherm is limited to very low pressures, and Henry constants are usually obtained by extrapolation from measurements outside the linear region. 

Figure 34 shows the results for alcohol (methanol, ethanol, 1-propanol and 1-butanol), ketone (acetone and diacetyl), terpene (pinene and linalool), aldehyde (n-nonyl aldehyde) and ester (acetic acid n-amyl ester and n-butyric acid ethyl ester) of various concentrations. Because of the linear characteristics of the CTL-based sensor, the plots are located in a similar region for a certain type of gas of various concentrations where the Henry-type adsorption isotherm holds. Thus, we can identify these gases with various concentrations by simple data-processing. 

The majority of physisorption isotherms may be grouped into the six types shown in Figure 2. In most cases, at sufficiently low surface coverage the isotherm reduces to a linear form (i.e. na oc p), with is often referred to as the Henry s Law region (On heterogeneous surfaces this linear region may fall below the lowest experimentally measurable pressure). 

A mathematical difficulty arises in the evaluation of the integral in the region below the first experimental point (p=px). First, the exact form of the adsorption isotherm is unknown in this range and secondly the ratio n/p is indeterminate as p tends to zero. A possible solution is to assume a linear variation of n versus p (i.e. Henry s law, as explained in Chapter 4) and then... 

The gas chromatographic method is based on the relation between the differential enthalpy of adsorption at zero coverage and the temperature dependence of the Henry s law constant, kn, as expressed in the form of Equation (4.3). In the low-pressure region, where Henry s law applies, the specific retention volume, Vj, is a linear function of kH (Purnell, 1962 Littlewood, 1970). This relationship makes it possible to make use of elution chromatography since... 

Inspection of the common normalized isotherm in Figure 9.3 reveals a number of distinctive features. At very low plp°, the isotherm is slightly convex with respect to the p/p° axis and it is evident that the linear, Henry s law region does not extend above p/p° 5x 10-4. Although the isotherm is not truly stepwise (i.e. not a true Type VI isotherm), it does exhibit a characteristic monolayer step. This is followed by a wavy second layer region and then a smooth multilayer curve. Thus, as the multilayer coverage is increased, the isotherm appears to conform to the normal Type II shape. 

One of the most significant points that we must consider in scientific studies, not limited to studies on photocatalysis, is distinction between evidence and consistency, as least as far as the author thinks. In other words, it is necessary to recognize every fact to be a necessary condition but not a sufficient condition in a strict scientific sense. For example, the fact that a reaction rate obeys the first-order rate law giving a linear relation in a plot of data as in Fig. 6 is only a necessary condition for a monomolecular reaction in homogeneous phase and also a necessary condition for heterogeneous photocatalytic reaction in diffusion-limited conditions or that in surface-reaction limited conditions with a Henry-type adsorption or a Langmuir-type adsorption in the lower-concentration region. 

The direction of propagation of a component within the TMBR depends on the dimensionless flow rates in each section of the process. Assuming a linear isotherm a component propagates with the fluid if the dimensionless flow rate is higher than the Henry coefficient. If the flow rate is smaller than the Henry coefficient a component is transported in the direction of the solid flow. Therefore, Lode et al. (2001) subdivided the separation region into the three regions shown in Fig. 8.10. 

To examine the effect of reaction kinetics on the reaction region the derived design criteria are applied for the reversible solid-phase reaction A B + C. A linear adsorption isotherm of the components is assumed, with Henry coefficients of 0.4 (reactant), 0.2 and 0.6 (products) respectively. A process with an equal number of columns in sections II and III is considered. The conversion that has to be reached is set to 99.99%. 

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