Molecular diameters, table

The pore size of Cs2.2 and Cs2.1 cannot be determined by the N2 adsorption, so that their pore sizes were estimated from the adsorption of molecules having different molecular size. Table 3 compares the adsorption capacities of Csx for various molecules measured by a microbalance connected directly to an ultrahigh vacuum system [18]. As for the adsorption of benzene (kinetic diameter = 5.9 A [25]) and neopentane (kinetic diameter = 6.2 A [25]), the ratios of the adsorption capacity between Cs2.2 and Cs2.5 were similar to the ratio for N2 adsorption. Of interest are the results of 1,3,5-trimethylbenzene (kinetic diameter = 7.5 A [25]) and triisopropylbenzene (kinetic diameter = 8.5 A [25]). Both adsorbed significantly on Cs2.5, but httle on Cs2.2, indicating that the pore size of Cs2.2 is in the range of 6.2 -7.5 A and that of Cs2.5 is larger than 8.5 A in diameter. In the case of Cs2.1, both benzene and neopentane adsorbed only a little. Hence the pore size of Cs2.1 is less than 5.9 A. These results demonstrate that the pore structure can be controlled by the substitution for H+ by Cs+. 

Table 4.26 Values of average velocity u, molecular diameter a, mean free path X., and average time between collisions t for some gas molecules...

When the molecular diameter approaches the channel opening of a ZSM-5 zeolite, the diffusion coefficient can drop by nine orders of magnitude between normal hexane and 1,3,5-trimethylbenzene, and can drop by three orders of magnitude between p-xylene and o-xylene (table 11.4). 

Rankine has made numerous accurate measurements of -q and calculated the molecular diameters from them. For calculating the number of molecules entering into collision in a gas it is therefore convenient to use Rankine s tables of a and the expression V 2uo2un2. 

The question of molecular diameters is also dealt with by Sutherland, who gives a table of values. 

Since all molecular diameters and velocities are of the same order of magnitude, and since the rates of different chemical reactions at a given temperature vary by many powers of ten, the absolute rate of a reaction is principally determined by the exponential term e ElRT. Thus the higher the value of E, the higher should be the temperature at which the reaction can obtain a given speed. This conclusion is strikingly verified, as shown by the following table. 

From data like these for SF6 a collection of diffusion coefficients (Figure 4), activation enthalpies, and pre-exponential factors (Table I) have been assembled. It was necessary to assume a value of the jump distance which seemed intuitively appropriate, the molecular diameter, for use in Equation 1. 

Table 2.4 shows the ratio of molecular diameter to cavity diameter for guests in structures I and II. The corresponding data for structure H is given in Table 2.7, and the data for cyclopropane and trimethylene oxide (which form both si and sll) are also provided. 

We can use Eq. (4.23) to calculate the magnitude of the pre-exponential factor and compare it to experimental data. Molecular diameters d (or dB) may, e.g., be estimated from gas viscosity data based on the standard model of the kinetic theory of gases, or from an analysis of the elastic scattering of molecules (see Section 4.1.3). Some values are given in Table 4.1 and are typically around 2-3 A. Table... 

The nature of the perfume material. Molecules with a large molecular diameter diffuse far less rea< than smaller ones, and polar materials (with relatively high water solubility) less readily than nonpoh ones (compare Table 13.8). 

The values of molecular diameters for simple molecules are given in Table 9-4. There is a linear ralationship between log D0 and Eq ... 

The available data show a somewhat scattered correlation between the energy of activation and the diameter of the gas molecule, varying between the first and the second power of the molecular diameter of the penetrant molecule. In our experience the best correlation is obtained if En is assumed to be proportional to second power of the collision diameter (see Fig. 18.2, where the data of Table 18.3 for the collision diameters are used). If nitrogen is taken as the standard gas for comparison, we can use the product... 

The close agreement between the corresponding values of wp and w in Table 12.5 is probably deceptive. It must be re-emphasized that it is unlikely that the Kelvin equation provides a reliable basis for the calculation of pore widths of around six molecular diameters. Also, as pointed out in Chapter 7, the application of the standard statistical multilayer thickness correction may be an oversimplification. For these reasons, the values of pore widths in Tables 12.4 and 12.5 should be regarded as apparent rather than real pore sizes. 

Typical molecular diameters and mean free paths at atmospheric pressure and a temperature of 15 °C are given in Table 3.3 for different gases. 

The basic molecular characteristics of these species are reflected by the potential parameters given in Table I. Thus, the energy parameter c (proportional to the component critical temperature) increases from carbon dioxide to water, while the parameter a (molecular diameter) is the highest for acetone. 

Typical values of b and D for a range of membranes are given in Table 9.10 together with some other parameter values. The range in D values reflects differences in membrane quality, the smallest D values being formed in high quality membranes. The diffusion coefficients become smaller in the same order as the kinetic molecular diameter (see Table 9.6) increase. The large differences in the D values indicate that the pore diameter is of the order of the molecular diameters (0.4-0.5 nm). 

Table 2.2. Molecular diameters, mean free path and velocities of some gases...

The table shows the remarkable decrease in the micropore diffusivity of a gas when its molecular diameter approaches that of the zeolite pore. The temperature coefficients of and Dm are given by the Arrhenius relationship [ >s, Dm = D exp(— // 7)] because these diffusions are activated processes. E is the activation energy for the diffusion process and D° is a constant. These diffusivities can also be complex functions of adsorbate loadings and compositions. ... 

From Table 2 it appears that on passing from carbon black and aerosil to carbosil the thickness of the solvation shell of benzene increases and the hydration film decreases. The studies of changes of chemical potential of water molecules at the adsorbent/bonded wa-ter/ice interface depending on water layer thickness are presented in another paper [57]. For the initial silica the surface effect is confined to the adsorbent water monolayer. Poor carbonization of aerosil surface causes the increase of water layer thickness to 40-50 molecular diameters. With the increase of carbon constituent part on the complex adsorbent surface, the thickness of interfacial water layer decreases to 15 molecular diameters. 

Some molecular properties of polar solvents are summarized in table 4.3. The dipole moment and molecular polarizability are the molecular parameters which lead to the solvent permittivity. The other parameters listed are the molecular diameter and the Lennard-Jones interaction energy, Elj. These are of interest in assessing the role of van der Waals forces in determining the properties of a polar liquid. 

We now proceed to explain in detail how the molecular constants enumerated in the preceding section can be determined experimentally. There is first the molecular volume, the determination of which, when neutral molecules are in question, can be effected by the methods of the kinetic theory of gases, already referred to in Chapter I (viscosity, free path, diffusion and direct measurement by molecular rays). The following table shows some molecular diameters so determined, in Angstroms ... 

Table 14.2 Ratios of molecular diameters (obtained from von Stackelberg and Muller 1954) to hydrate cavity diameters for various gases, including those commonly found in natural gas hydrate (from Sloan 1998). = indicates the cavity occupied by a single guest.

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