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Static Isotherm Determination Methods

Batch method A known amount of adsorbent Vads with initially empty pores is added to a solution of the volume V) containing the solute with the concentration Co i. The mixture is then agitated in a closed vessel until equilibrium is reached. The final concentration in the solution (Ceq,j) is determined by standard analytical methods. From the following mass balance the appropriate equilibrium loading, q(Ceq), is calculated  [Pg.382]

Using different initial concentrations or adsorbent amounts, a relevant concentration range can be covered. The method can be easily expanded to multi-component mixtures, where the loadings are functions of all components present. Drawbacks are the time-consuming preparations of the different mixtures and the transferability of the results to packed columns (e.g., due to uncertainties in phase ratio/porosity). Because of the numerous steps of manual work [Pg.383]

Adsorption-desorption method An initially unloaded q = 0) column is equilibrated by a feed concentration, Cfeed. which may be a single-component or multi-component mixture. Equilibrium is achieved by pumping a sufficient quantity of feed through this column. The plant is then fiushed without the column to remove the solute solution. Afterwards, all solute is eluted from the column, collected, and analyzed to obtain the desorbed amount mdes.i- The equilibrium loading qi(Cfeed) for each component i can be calculated according to [Pg.384]

The experimental effort to include different concentrations is considerable but the obtained equilibrium values are typically rather reliable. [Pg.384]

Circulation method Another static method is based on a closed fluid circuit that includes the chromatographic column. A known amount m j of solute or a mixture of several solutes is injected into this circuit and pumped around until equilibrium is established. Samples are taken and analyzed to determine the resulting equilibrium concentration Ceq. The mass balance for the equilibrium loading accounts for the holdup of the complete plant  [Pg.384]


The calorific value is the heat produced by the combustion of a unit quantity of coal in a bomb calorimeter with oxygen and under a specified set of conditions (ASTM D-121 ASTM D-2015 ASTM D-3286 ISO 1928). For the analysis of coal, the calorific value is determined in a bomb calorimeter either by a static (isothermal) method or by an adiabatic method, with a correction made if net calorific value is of interest. The unit is calories per gram, which may be converted to the alternate units (1.0 kcal/kg = 1.8 Btu/lb = 4.187 kJ/kg). [Pg.131]

In principle, a continuous procedure can be used to construct the isotherm under quasi-equilibrium conditions the pure adsorptive is admitted (or removed) at a slow and constant rate and a volumetric or gravimetric technique used to follow the variation of the amount adsorbed with increase (or decrease) in pressure. A carrier gas technique, making use of conventional gas chromatrographic equipment, may be employed to measure the amount adsorbed provided that the adsorption of the carrier gas is negligible. In all types of measurement involving gas flow it is essential to confirm that the results are not affected by change in flow rate and to check the agreement with representative isotherms determined by a static method. [Pg.522]

Fig. 6.17 Principle of different static methods for isotherm determination. Fig. 6.17 Principle of different static methods for isotherm determination.
Besides this method of extrapolation towards c = 0, n = 0 of the static isotherm, it is possible to determine the Henry constant directly from the specific retention volume for zero sample size Vm if the elution time of the substance from the column does not depend on the sample size at a constant flow rate. In this case K s c,i = Vn,. [Pg.679]

Try to simulate mixture e q)eriments with single-component isotherms Determine component interactions only if necessary Check agreement between theoretical and e5q)erimental chromatograms Static methods... [Pg.380]

FIGURE 8.8. Comparison of (a) single-component equilibrium isotherms for C2H on 13X sieve and (b) binary isotherms for CO-CH4 on activated carbon, as determined by static and chromatographic methods. (From ref. 6, reprinted with permission.)... [Pg.234]

Examples of single-component and binary isotherms showing good agreement between the experimental isotherms determined by chromatographic and static methods are shown in Figure 8.8. It should be noted that this method is restricted to binary systems and cannot be easily extended to ternary or multicomponent mixtures. [Pg.235]

Static Involving Use of Adsorption Isotherms BRUNAUER, EMMETT, AND TELLER (B.E.T.). In this method tire surface area is not measured directly, but the number of molecules of the adsorbed substance required to give a monolayer (N) is determined. If the mean area per molecule (a) of the adsorbed substance is known by other means, the area of the solid may... [Pg.529]

Carbon monoxide chemisorption was used to estimate the surface area of metallic iron after reduction. The quantity of CO chemisorbed was determined [6J by taking the difference between the volumes adsorbed in two isotherms at 195 K where there had been an intervening evacuation for at least 30 min to remove the physical adsorption. Whilst aware of its arbitrariness, we have followed earlier workers [6,10,11] in assuming a stoichiometry of Fe CO = 2.1 to estimate and compare the surface areas of metallic iron in our catalysts. As a second index for this comparison we used reactive N2O adsorption, N20(g) N2(g) + O(ads), the method widely applied for supported copper [12]. However, in view of the greater reactivity of iron, measurements were made at ambient temperature and p = 20 Torr, using a static system. [Pg.259]

The time required to conduct an interfacial tension experiment depends largely on the properties of the surfactants and less on the chosen measurement method. A notable exception is the drop volume technique, which, due to the measurement principle, requires substantial ly more time than the drop shape analysis method. Regardless of the method used, 1 day or more may be required to accurately determine, e.g., the adsorption isotherm (unit D3.s) of a protein. This is because, at low protein concentrations, it can take several hours to reach full equilibrium between proteins in the bulk phase and those at the surface due to structural rearrangement processes. This is especially important for static interfacial tension measurements (see Basic Protocol 1 and Alternate Protocols 1 and 2). If the interfacial tension is measured before the exchange of molecules... [Pg.645]

Ikeda et al. (1984b) plotted Eq. (4.42) by determining the equilibrium concentrations from adsorption isotherms for S(H), S(NH4), and NH4, and using the pH value to determine [H+]. This plot shows good linearity (Fig. 4.11), which confirms that the mechanism hypothesized in Eq. (4.40) is operational. The kv and k- values for Eq. (4.42) can then be calculated from the slope and intercept of Fig. 4.11, and the kinetic Keq can be determined from the ratio kjk x (Table 4.2). It is important to notice that the values calculated kinetically and statically (equilibrium method) are similar, which indicates that the rate constants one calculates from p-jump experiments are chemical kinetics rate constants. These data also verify... [Pg.83]

In this paper solubility measurements of synthetic and natural dyestuffs are presented using VIS-spectroscopy. The investigations concentrate on two different methods. I. P-carotene was measured as a function of temperature and pressure in near- and supercritical C02 (289 to 309 K, 10 to 160 MPa) and CC1F3 (297 to 326 K, 12 to 180 MPa), respectively, using a static method. II. Additionally, the solubilities of l,4-bis-(n-alkylamino)-9,10-anthraquinones (with n-alkyl = butyl, octyl) were determined with a dynamic method in temperature and pressure ranges from 310 to 340 K and 8 to 20 MPa, respectively this method permits a continuous purification from better soluble impurities as well as the measurement of solubilities at the same time. For both anthraquinone dyestuffs intersection points of the solubility isotherms were found in the plot of concentration versus pressure. This behavior can be explained by a density effect. [Pg.259]

The measurements of external and internal specific surface area have already been discussed in Chapter 1, Section 1.1.3. The principles and the isotherm equation of the BET method to measure external specific surface area, including macro- and mesopores, have been presented in Chapter 1, Section 1.3.4.1.5. The external specific surface area is usually determined by nitrogen gas adsorption at the temperature of liquid nitrogen. Both static (one-point) and dynamic (five-point) methods are applied. The calculations are made by Equation 1.75 (Chapter 1), using one or five different pressure values. The external specific surface area is calculated from the maximum number of surface sites, that is, monolayer and the cross-sectional area of nitrogen molecules. [Pg.211]

Two kinetic (CMS-Kl, CMS-K2) and one equilibrium (CMS-R) carbon molecular sieves, used originally for separation of gaseous mixtures, were investigated. The adsorption Nj isotherms at 77 K, in static conditions where obtained. In the case of the two first sieves the adsorption was so low that the calculation of parameters characterizing the texture was impossible. The volume of nitrogen adsorbed on the sieve CMS-R is remarkable From obtained results parameters characterizing micropore structure according to Dubinin -Radushkevich equation and Horvath - Kawazoe method were determined. [Pg.225]

For description of textural properties of carbonaceous adsorbents, adsorption/desorption isotherms of vapours and gases in static conditions as well as mercury porosimetry are used. The latter method often leads to destruction of porous structure of investigated materials while the usage of the former one is affected by the specific properties of molecular sieves described above. Taking into account these limitations, in this work the authors have made an attempt of determination of porous structure of carbon molecular sieves with the used of the pycnometric technique. [Pg.226]

The specific surface excess isotherms for binary liquid mixtures benzene + n-heptane and benzene + 2-propanol were measured by static immersion method [8] The concentrations of equilibrium solutions were determined using HP 5890 gas chromatograph from Hewlett-Packard. The initial mixtures over the whole concentration range served for detector calibration, The surface excess of a given component was calculated from the relation ... [Pg.348]

Figure 2. Sorption Isotherm of Com Starch Determined at 25°C by Static Method. Figure 2. Sorption Isotherm of Com Starch Determined at 25°C by Static Method.
Metal accessibility was determined by the H2-O2 titration method in a static volumetric equipment. Hydrogen preadsorbed at 500°C was titrated at 25°C by oxygen. Isotherms have been determined in the 0-50 torr range. Extrapolation to the original values was used to calculate the number of exposed atoms. [Pg.329]

The primary use of isotherm data measurements carried out on single-component elution profiles or breakthrough curves is the determination of the single-component adsorption isotherms. This could also be done directly, by conventional static methods. However, these methods are slow and less accurate than chromatographic methods, which, for these reasons, have become very popular. Five direct chromatographic methods are available for this purpose frontal analysis (FA) [132,133], frontal analysis by characteristic point (FACP) [134], elution by characteristic point (ECP) [134,135], pulse methods e.g., elution on a plateau or step and pulse method) [136], and the retention time method (RTM) [137]. [Pg.122]

Although direct measurement of reactant temperatures have enabled more quantitative assessment of such reactions, precise tests of thermal explosion theory require a reaction for which the mechanism and Arrhenius parameters are sufficiently well established to give accurate estimates of rates under explosive conditions. Typically the reaction rates involved will be around ten times those determined by static kinetic methods. In addition the thermal conductivity of each gas mixture used and the stoicheiometry and heat of reaction must be known. Pritchard and Tyler suggest the thermal isomerization of methyl isocyanide as a suitable candidate. They report temperature-time records for diluted mixtures in which temperature excesses of 70—80 K occur without explosion. However, the roll-call of missing data—improved heats of formation, isothermal kinetic data at higher temperatures, thermal conductivity measurements up to 670 K, and the recognition and elucidation of side reactions (if any) indicate the extent of further investigations necessary if their proposal is to be fully realized. [Pg.340]


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