Surface occupied by one molecule

As an example we shall take the case of palmitic acid on water at 16° C. The figure on p. 70, from Langmuir s paper, shows the compressive force (i.e. the difference, in dynes per cm., between the surface tension of pure water and of the oiled surface) as against the area occupied by one molecule, measured in Angstrom units. 

To estimate the surface tension we need to know the surface area occupied by one molecule. If the molecules form a cubic structure, the volume of one unit cell is a3, where a is the distance between nearest neighbors. This distance can be calculated from the density ... 

Kern and Findenegg measured the adsorption of n-docosane (C22H46) in heptane solution to graphite [403], They used a porous graphite with a specific surface area of 68 m2g 1 as determined from BET adsorption isotherms with N2. Tmax, which is assumed to correspond to monolayer coverage, is found to be 88.9 /.xmol/g. Can you conclude something about the structure of the adsorbed molecules What is the area occupied by one molecule compared to its size ... 

From the micelle size, the surface occupied by the hydrophilic part of one polyester molecule can be calculated, and thus the surface occupied by one carboxy group. This calculation is done assuming the density of the polyester in the micelle to be similar to bulk polyester and all the carboxy groups located on the micelle surface (conformation A and B given in Figure 2). 

From Figure l(the particle size vs neutralization degree a ) we can also calculate the surface a occupied by one molecule. The... 

Figure 4 shows an optimum balance exists when the polyester is neutralized with MDEA. For this system. Table VII gives the change of the specific surface for the latex and the corresponding surface occupied by one polyester molecule. 

Repeat Prob. 8-1 for the following data for the equilibrium adsorption of on the same silica gel at 110°C. The surface occupied by one benzene molecule is 34.8 X 10 cmT... 

Since very large surface areas are usually needed, the solids used should be highly porous.1 The extent of surface involved can be estimated from measurements of adsorptive capacity. With n-butyl amine as adsorptive,2 for an example, the total volume occupied by one molecule (as liquid) is 1.65 X 10-22 cm.3 The area occupied by one molecule is approximately the two-thirds power of the volume, or 3.0 X 10-16 cm.2 An efficient adsorbent in contact with a gas phase may hold a volume of adsorbate equal to as much as 1.0% of the particle volume (silica gel has an even larger capacity). One cm.3 of such an adsorbent would thus present a surface area of 18 square meters, equivalent to about 5.5 X 106 square feet per cubic foot of particle volume. The precise value of the surface area will vary with the adsorptive species used for the measurement (B12). 

Figure 5 shows the 7t-A isotherm of the mixed Langmuir monolayer composed of a] -trans-P-carotene with harium stearate (1 10) at the air/water interface. The n-A isotherm shows a steep rise at the surface pressure above 15 mN/m. This observation confirms that the molecules in the monolayer are closely packed at the surface pressure of 30 mN/m, the value which corresponds to the fabricating condition when transferring the monolayer to the glass substrate. The limiting area, which corresponds to the area occupied by one molecule at the air/water interface, can be extrapolated from the steep part of the n-A isothermtobe 32 /molecule (see broken... 

Eq. (3.3-18) is the famous BET equation, and it is used extensively for the area determination because once the monolayer coverage V is known and if the area occupied by one molecule is known the surface area of the solid can be calculated. 

Retter [82] has shown that from the temperature dependence of the pit width the surface concentration of the adsorbed molecules can be calculated. For the potential region of the cathodic capacitance pit of 9 mM adenosine in 0.5 M KCl with a Me Ilvaine buffer, pH 7, it was found that rj = 3.1 x 10" mol cm"-. This surface concentraion corresponds to an area of 0.55 nm- occupied by one molecule, i.e., to the perpendicularly adsorbed adenosine molecules. 

A plot of P/[V (Po — P)] versus P/Po allows one to determine Vm from the slope and intercept. Once known, this value may be converted to a specific surface area S, in m /g, if one knows the average area occupied by one molecule by the following equation ... 

The solute excess surface concentration T2L allows the determination of the area occupied by one solute molecule at the surface. F2t is the number of moles of the solute per rmit surface. Its reciprocal is the surface occupied by one mole of solute at the surface. The area occupied by one molecule of solute at the surface is obtained by... 

At pH 10.6, the surface of the substrate is negatively charged and sodium ions are adsorbed as counterions in the inner Helmholtz plane (IHP) of the electrical double layer (e.d.L). Adsorption of HDP gives a high-affinity isotherm, which reaches the plateau at equilibrium concentrations consistent with the critical micelle concentration (CMC) of HDPCl, 0.9 mmol/dm [36]. The adsorbed amount is 0.7 mmol/g at saturation, and the surface area occupied by one molecule is about 0.2 nm. This means that the adsorbed amount is somewhat higher than would be expected for close-packed monolayer coverage (0.3 nmVmolecule). 

The molecules are arranged in a quasicrystalline lattice stmeture devoid of defects. The face-centered-cubic (fee) lattice structure with a coordination number of z = 12 is used nearly exclusively in the literature and it is also adopted in this work (Fig. 31). The molecules are ahgned in sublayers parallel with the surface (Fig. 32a), within which they are fitted in a tight hexagonal pattern (Fig. 33). The cross-sectional area occupied by one molecule will be termed a site. ... 

Chern and Chen [30] studied the effect of the reactive surfactant, sodium dodecyl allyl sulfosuccinate, on the semibatch emulsion polymerization of n-butyl acrylate initiated by sodium persulfate. Sodium dodecyl allyl sulfosuccinate plays a similar role in the particle nucleation and growth stages to the conventional sodium dodecyl sulfate. The final number of latex particles per unit volume of water is proportional to the concentration of sodium dodecyl allyl sulfosuccinate in the initial reactor charge (the most important parameter with regard to particle nucleation) to the 0.72-0.80 power. The saturated particle surface area occupied by one molecule of sodium dodecyl allyl sulfosuccinate is 0.36 nm for the poly (n-butyl acrylate) particles prepared by the... 

A plot of PtV against P (or xtV against x) yields the monolayer capacity Vffi and to relate this to surface area it is necessary to know the area occupied by one molecule, a. 

In the Langmuir curve example we made an estimate of monoiayer, the total amount of nitrogen that would form a complete monolayer on the internal surface of the adsorbent. If we knew the surface area occupied by one molecule of adsorbed nitrogen, we could use it to estimate the total surface area of the solid. Make such an estimate as follows ... 

The calculation of data in Fig. 2 has been made by means of data collected in the handbook of Valenzuela and Myers [8], which includes more than 100 simple gas isotherms measured on adsorbents with known specific surface areas determined by the producers with the controlled BET method. The values were calculated from the BET surface area and from the cross-sectional area occupied by one molecule of the adsorptive investigated. The data in Fig. 2 represent 13 isotherms of ethane, ethylene, carbon dioxide, and propane measured on two activated carbons and silica gel at 10 temperatures below the critical temperatures. It is easy to see that in every case ... 

If the area occupied by one molecule of the adsorbed species is known, the surface area per unit mass 5g may be calculated from... 

It is useful to define the tenns coverage and monolayer for adsorbed layers, since different conventions are used in the literature. The surface coverage measures the two-dimensional density of adsorbates. The most connnon definition of coverage sets it to be equal to one monolayer (1 ML) when each two-dimensional surface unit cell of the unreconstructed substrate is occupied by one adsorbate (the adsorbate may be an atom or a molecule). Thus, an overlayer with a coverage of 1 ML has as many atoms (or molecules) as does the outennost single atomic layer of the substrate. 

Thus a substantial effort has been made by electrochemists to identify this species use of non-spectroscopic techniques to evaluate the number of surface sites occupied by each molecule of poison and the number of electrons required in its oxidation to CO2 led to a concensus view that it was COH. One of the first successful applica-... 

The use of MO theory to find deep minima in the So surface, or geometries of stable molecules, is well known. A simplified rule would be to choose the geometry so as to allow efficient overlap of valence orbitals of the constituent atoms in a way giving bonding orbitals for all available electrons from pairs or larger sets of suitably hybridized atomic orbitals. No atomic orbitals occupied by one electron should be left over dangling free and unable to interact with others, since that would give radicals, biradicals, etc. Chemical intuition allows one to proceed almost automatically in cases of molecules of familiar types. 

The determination of the specific surface area of a zeolite is not trivial. Providers of zeolites typically give surface areas for their products, which were calculated from gas adsorption measurements applying the Brunauer-Emmet-Teller (BET) method. The BET method is based on a model assuming the successive formation of several layers of gas molecules on a given surface (multilayer adsorption). The specific surface area is then calculated from the amount of adsorbed molecules in the first layer. The space occupied by one adsorbed molecule is multiplied by the number of molecules, thus resulting in an area, which is assumed to be the best estimate for the surface area of the solid. The BET method provides a tool to calculate the number of molecules in the first layer. Unfortunately, it is based on a model assuming multilayer formation. Yet, the formation of multilayers is impossible in the narrow pores of zeolites. Specific surface areas of zeolites calculated by the BET method (often termed BET surface area) are therefore erroneous and should not be mistaken as the real surface areas of a material. Such numbers are more related to the pore volume of a zeolite rather than to their surface areas. 

Gas adsorption (physisorption) is one of the most frequently used characterization methods for micro- and mesoporous materials. It provides information on the pore volume, the specific surface area, the pore size distribution, and heat of adsorption of a given material. The basic principle of the methods is simple interaction of molecules in a gas phase (adsorptive) with the surface of a sohd phase (adsorbent). Owing to van der Waals (London) forces, a film of adsorbed molecules (adsorbate) forms on the surface of the solid upon incremental increase of the partial pressure of the gas. The amount of gas molecules that are adsorbed by the solid is detected. This allows the analysis of surface and pore properties. Knowing the space occupied by one adsorbed molecule, Ag, and the number of gas molecules in the adsorbed layer next to the surface of the solid, (monolayer capacity of a given mass of adsorbent) allows for the calculation of the specific surface area, As, of the solid by simply multiplying the number of the adsorbed molecules per weight unit of solid with the space required by one gas molecule ... 

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