Adsorption constant pressure

Alternatively, data may be plotted as n versus T at constant pressure or as P versus T at constant n. One thus has adsorption isobars and isosteres (note Problem XVII-2). 

Gibbs adsorption isotherm can be written at constant pressure and temperature, dv=-9md7 -t 7 jdmj. 

Kinetic orders in CO oxidation on M/A1203 can be explained by the classical Langmuir-Hinshelwood expression for the rate equation, as a function of the rate constant k, the adsorption constants K and the partial pressures P ... 

Gas-liquid relationships, in the geochemical sense, should be considered liquid-solid-gas interactions in the subsurface. The subsurface gas phase is composed of a mixture of gases with various properties, usually found in the free pore spaces of the solid phase. Processes involved in the gas-liquid and gas-solid interface interactions are controlled by factors such as vapor pressure-volatilization, adsorption, solubility, pressure, and temperature. The solubility of a pure gas in a closed system containing water reaches an equilibrium concentration at a constant pressure and temperature. A gas-liquid equilibrium may be described by a partition coefficient, relative volatilization and Henry s law. 

The heat of adsorption at constant pressure, in which the gas is at constant pressure but not necessarily the equilibrium pressure. 

From experiments with the field emission microscope it is learned that for a system like oxygen on tungsten (a) the crystallographic plane of the tungsten has a marked influence on the adsorption properties (6) the heat of adsorption increases with the number of W atoms a particular 0 atom can contact (c) the heat of adsorption for the first layer, in which 0 atoms make first valence bonds with W atoms, is about 4 ev., for the second layer, in which 0 atoms make second valence bonds with W atoms, only about 2 ev. (d) at a constant pressure the rate of adsorption is constant until the first layer is complete, and for the second layer it is slower by a factor of 100 or more (e) beyond the second layer oxygen is adsorbed as admoles of O2, O4, Os. 

The relative adsorption constants for hydrogen, naphthalene, and diben-zothiophene have been estimated by determining how the rate constants, as described in Scheme 1, change as a function of the naphthalene concentration in HDS reactions of dibenzothiophene with NiMo/Al203 catalyst at 320°C and 2.5-MPa hydrogen pressure (21, 133, 134). The original data were used to determine the rate constants as described in Section IV, and the LHHW parameters were then estimated. The values obtained in this way are presented in Table XIX. These values should be considered only as estimates as data were limited, but the trends are believed to be valid. 

Freundlich Equation. This equation represents the variation of adsorption with pressure over a limited range, at constant temperature. 

The equation also applies to the adsorption of a gas on a solid. At low gas pressures, p. the equilibrium pressure of the gas can be substituted for a, the activity of the solute. The amount of gas adsorbed v/V is equivalent to the surface excess T, where v is equal to the volume of gas adsorbed per gram of solid and V is the molar volume of the gas. The total free energy change at constant pressure is E[Pg.1582]

An opposite effect is obtained with increasing hydrogen pressure in cyclohexane solvent. Due to the difference in the adsorption constant, PE is more easily displaced than AC by hydrogen, therefore yield in EB decreases as tne hydrogen pressure increases. 

Since the rate of hydrogenation is sensitive to operating conditions (temperature, pressure, catalyst quantity, solvent and agitation), relative rates determined in competitive hydrogenation of binary mixtures are considered to be more reliable than measuring individual rates50. Relative reactivities thus measured are determined by the ratio of rate and adsorption constants. 

Figure 9.3 Schematic drawing of calorimeters for measuring heats of adsorption under constant volume and constant pressure conditions. The active volume is filled with the adsorbent usually...

In practice, most calorimetric experiments are carried out under constant pressure. By moving the piston down, the pressure in the cell is increased and the heat release is measured. In this case the heat exchanged is equal to the integral enthalpy of adsorption ... 

Then according to thermodynamics one can obtain the change in the standard molar free energy (at constant pressure), in the enthalpy and in the entropy for adsorptional exchange (21) ... 

In the cases of Cr203, NiO, and Fe2Ch it was possible (24) to follow the kinetics of the adsorption of 02 at constant pressures around 6 cm. It was found that the uptake q followed the Elovich equation ... 

Using this equation, ln(r.) was evaluated at several temperatures at known coverages 6 = q/qx where qx is the equilibrium coverage at P0i = 6 cm.). The activation energy for adsorption, Ea, was evaluated from the ln(r,) vs. l/T plots, and it was found that at constant pressure the activation energy increased in a roughly linear fashion with coverage... 

A gas mixture consisting of two components is separated using one or more adsorption beds The beds are used in a cyclic process composed of steps involving column pressurization, depressurization (blowdown) and flow through the columns at constant pressure Analysis of such separation processes in terms of a cell model proceeds as follows ... 

The equations for a local equilibrium cell model of pressure swing adsorption processes with linear isotherms have been derived. These equations may be used to describe any PSA cycle composed of pressurization and blowdown steps and steps with flow at constant pressure. The use of the equations was illustrated by obtaining solutions for a single-column recovery process and a two-column recovery and purification process. The single-column process was superior in enrichment and recovery of the light component at large product cuts. The two-column process was superior at small cuts ... 

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