Fraction of Surface Covered

While a thermodynamic treatment can be developed entirely in terms of f(P,T), to apply adsorption models, it is highly desirable to know on a per square centimeter basis rather than a per gram basis or, alternatively, to know B, the fraction of surface covered. In both the physical chemistry and the applied chemistry of the solid-gas interface, the specific surface area is thus of extreme importance. 

Since S /S equals 6, the fraction of surface covered, Eq. XVII-4 can be written in the form... 

In the simplest case, for which all adsorption sites are equivalent and do not interact with each other, the fraction of surface covered by adsorbate. 

Variable Variable ft e t/t, reduced time, fraction of surface covered by adsorbed ... 

The rate of desorption of A, rdA, is proportional to the fraction of surface covered,... 

Let 0 and 02 be the fractions of surface covered by adsorption of A and B, respectively. Assuming that total area of surface for adsorption is 1 sq. cm, the surface portion remaining unaffected is = (1 — 0X — 02). 

Langmuir isotherm equation phys chem An equation, useful chiefly for gaseous systems, for the amount of material adsorbed on a surface as a function of pressure, while the temperature Is held constant, assuming that a single layer of molecules is adsorbed it is / = ap/ 1 + ap). where / is the fraction of surface covered, p is the pressure, and a is a constant. lar),myur Ts-3,th3rm i,kwa zh3n ) lanthana See lanthanum oxide. lan tha-na ... 

In this section a method for the direct calorimetric determination of heats of adsorption on evaporated metal films is described and results for the heals of adsorption of hydrogen on nickel, iron, and tungsten are reported. In all cases the heats of adsorption decrease with the fraction of surface covered in a mode that can satisfactorily be explained by interaction of adsorbed atoms. A criterion for mobility of the adsorbed atoms is developed... 

Values listed are fractions of surface covered in per cent at the specified temperatures and equilibrium pressures. 

Fraction of surface covered Molecular adsorption e.u. Dissociative adsorption Sd e.u. Associative adsorption SA e.u. ... 

By analogy, for the fraction of surface covered by two layers one may write... 

Equation (4.44) is used to calculate the fraction of surface unoccupied when W =W, that is, when just a sufficient number of molecules have been adsorbed to give monolayer coverage. LowelP has derived an equation that can be used to calculate the fraction of surface covered by adsorbed molecules of one or more layers in depth. Lowell s equation is... 

Equations (4.44) and (4.45) should not be taken to mean that the adsorbate is necessarily arranged in neat stacks of various heights but rather as an indication of the fraction of surface covered with the equivalent of i molecules regardless of their specific arrangement, lateral mobility, and equilibrium with the vapor phase. 

The number of sites on the metal surface pa- square centimeter can be taken as equal to the number of metal atoms per square centimeter (about 1.5 X 1015). Thus, the fraction of surface covered by water molecules, 0 turns out (by inserting the appropriate numerical values into this zeroth-approximation approach) to be about 0.7. 

Before we can calculate the sticking probability s and the fraction of surface covered 9 we must derive quantitative expressions for the processes just described. Let L be the number of nitrogen molecules entering the system per second through the leak. The number of molecules leaving the system per second through the pump = 3.8 X W paj,. The number of molecules removed from the volume per second by the filament = 3.8 X 10 pa/s. Let ci = the number of molecules per second accumulating in the volume V. Then ci = 3.2 X lO Vdp/dt. Except in the... 

Let a be the fraction of the surface covered with adsorbed gas. Then (1 — cr) is the fraction left uncovered. In view of the possibility that the surface is not homogeneous and that adsorption only occurs on active centres, fraction of surface covered must be understood to mean the fraction of the available surface which is actually covered. Thus, from the point of view of adsorption, the surface might be covered when certain patches only were completely occupied by adsorbed molecules, and the rest of the surface might be incapable of taking up gas at any pressure. 

In the simplest case, for which all adsorption sites are equivalent and do not interact with each other, the fraction of surface covered by adsorbate, covered related to the surfactant concentration, CSURF> the adsorption constant, in mol/m3, by the Langmuir adsorption isotherm ... 

A lightly sintered compact of monosized 20 nm diameter, Sb205-doped (1 wt%) tin oxide particles is conditioned in an enclosure so that the surface is atomically clean. With the compact held at 300 °C oxygen gas is steadily admitted to the enclosure and the electrical resistance of the compact monitored. At a stage in the process the resistance shows a marked increase. Estimate the fraction of surface covered by the chemically adsorbed species at this stage. [Answer 2%. Hint consider Eq. 4.49]... 

Adsorbed sulfur reduces the capacity of metals for adsorption of other molecules. H2 adsorption capacity is reduced in approximately direct proportion to the fraction of surface covered by sulfur. At low pressures CO adsorption is decreased by adsorbed sulfur. On the other hand, adsorbed sulfur can cause increased CO adsorption under conditions where metal carbonyls or subcarbonyls are stable. 

A second aspect of our procedure is illustrated in the case of low temperature isotherms, where P/P° values not negligibly small compared to unity are involved. In such cases, some degree of multilayer adsorption is to be expected, and must somehow be corrected for. Where the correction is small, it seems reasonable to make use of the BET treatment (I), from which it may be concluded that the actual fraction of surface covered, 0, is related to v/vm by ... 

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