Size of molecules

Boyle s law At constant temperature the volume of a given mass of gas is inversely proportional to the pressure. Although exact at low pressures, the law is not accurately obeyed at high pressures because of the finite size of molecules and the existence of intermolecular forces. See van der Waals equation. 

This observation that the length of the hydrocarbon chain could be varied from 16 to 26 carbon atoms without affecting the limiting area could only mean that at this point the molecules were oriented vertically. From the molecular weight and density of palmitic acid, one computes a molecular volume of 495 A a molecule occupying only 21 A on the surface could then be about 4.5 A on the side but must be about 23 A long. In this way one begins to obtain information about the shape and orientation as well as the size of molecules. 

MOPAC runs in batch mode using an ASCII input hie. The input hie format is easy to use. It consists of a molecular structure dehned either with Cartesian coordinates or a Z-matrix and keywords for the type of calculation. The program has a very versatile set of options for including molecular geometry and symmetry constraints. Version 6 and older have limits on the size of molecule that can be computed due to the use of hxed array sizes, which can be changed by recompiling the source code. This input format allows MOPAC to be run in conjunction with a batch job-queueing system. 

In 1906, Einstein worked out a theory of the viscosity of a liquid which contains, in suspension, spherical particles which are large compared with the size of molecules of the liquid. The predictions of the theory are found to be in good agreement with the measured values of the viscosity of liquids containing colloidal particles in suspension. The presence of these obstacles increases the apparent viscosity of the liquid, and Einstein found1 that the increment is proportional to the total volume v of the foreign particles in unit volume, that is to say, the sum of the volumes of the particles that are present in unit volume of the liquid thus,... 

Combining hindered diffusion theory with the diffusion/convection problem in the model pore, Trinh et al. [399] showed how the effective transport coefficients depend upon the ratio of the solute to pore size. Figure 28 shows that as the ratio of solute to pore size approaches unity, the effective mobility function becomes very steep, thus indicating that the resolution in the separation will be enhanced for molecules with size close to the size of the pore. Similar results were found for the effective dispersion, and the implications for the separation of various sizes of molecules were discussed by Trinh et al. [399]. 

The van der Waals equation adds two correction terms to the ideal gas equation. Each correction term includes a constant that has a specific value for every gas. The first correction term, a fV, adjusts for attractive intermolecular forces. The van der Waals constant a measures the strength of intermolecular forces for the gas the stronger the forces, the larger the value of a. The second correction term, n b, adjusts for molecular sizes. The van der Waals constant b measures the size of molecules of the gas the larger the molecules, the larger the value of b. 

In this chapter, some experimental tips on the synthetic studies of CPOs are reviewed. Because this class of materials has specific properties associated with the large size of molecules, several special methodologies should be dealt with, which are applicable to the dendrimers. 

In porous separators the pore radii are large compared to the size of molecules. Hence, interaction between the electrolyte and the pore walls has practically no qualitative effects on the ionic current through the separator the transport numbers of the individuaf ions have the same vafues in the pores as in the bulk electrolyte, hi swollen membranes the specific interaction between individuaf ions and macromofecufes is very pronounced. Hence, these membranes often exhibit sefectivity in the sense that different ions are affected differentfy in their migration. As a resuft, the transport numbers of the ions in the membrane differ from those in the efectrofyte outside the membrane. In the limiting case, certain types of ion are arrested completely, and the membrane is called permselective (see Chapter 5). 

Slowly tumbling large molecules, such as proteins, undergo rapid transverse relaxation, which causes line broadening in the NMR spectrum. This imposes an upper limit on the size of molecules whose structures can be usefully interpreted by NMR. Small molecules tumble at high rates and have much slower relaxation rates, and therefore a sharper well-resolved NMR spectrum. 

Ultra- filtration Water sample la filtered under pressure through a membrane that will pass molecular constituents below a certain size and retain those above that size. Large molecules Porosity of membrane daterminaa the size of molecules concentrated. Usually used for compounds > 1000 molecular weight. Can concentrate large sample volumes at low temperatures. 

API-MS quickly and reliably analyses any size of molecule in almost any matrix, without contamination or degradation. As it is usually not obvious which technique to use, it is therefore often worthwhile analysing the samples of interest with both ionisation techniques and making the final decision empirically. 

Membrane methods such as RO, MF, UF, and so on, are effective for removing certain sizes of molecules from contaminated water. However, energy is required for this removal technique. 

ROESY Rotating-frame Overhauser effect spectroscopy. A variation (one and two dimensional) on the nuclear Overhauser experiment (NOE). The techniques have the advantage of being applicable for all sizes of molecule. See Laboratory frame model. 

Size of molecules. Since the hydrogen molecule is smallest of all it will leak through permeable materials where methane and gasoline will not. 

The reason for the high selectivity of zeohte catalysts is the fact that the catalytic reaction typically takes place inside the pore systems of the zeohtes. The selectivity in zeohte catalysis is therefore closely associated to the unique pore properties of zeohtes. Their micropores have a defined pore diameter, which is different from all other porous materials showing generally a more or less broad pore size distribution. Therefore, minute differences in the sizes of molecules are sufficient to exclude one molecule and allow access of another one that is just a little smaller to the pore system. The high selectivity of zeolite catalysts can be explained by three major effects [14] reactant selectivity, product selectivity, and selectivity owing to restricted size of a transition state (see Figure 4.11). 

This determines the size of molecules that can be admitted and the rate at which different molecules diffuse towards the surface. Molecular sieves, with their precise pore sizes, are uniquely capable of separating on the basis of molecular size. In addition, it is sometimes possible to exploit the different rates of diffusion of molecules to bring about their separation. A particularly important example referred to earlier, concerns the production of oxygen and nitrogen from air. 

A word of caution on the use of the Schleyer-Mislow program BIGSTRN as obtained from QCPE may be appropriate. The default criteria for termination of the energy minimization loop, namely, 0.01 kcal/mol regardless of the size of molecule, is too loose. One can strengthen the criteria 100-fold with one of the options, with the inevitable consequence of prolonged computation time (29a). 

Knowing the framework type of a material, the size of molecules that can be adsorbed can be estimated. Kinetic diameters for various molecules [5-9] are given in Table 2.2. Thus neopentane (kinetic diameter of 0.62 nm) is expected to be adsorbed by NaX zeolite (FAU structure type) which has channels defined by 12-... 

The variety of the different framework structures result in different adsorbent characteristics acid strength, size of molecule adsorbed, adsorption/desorption rate of different molecules, capacity and stability. As a result, these differences characterize the adsorbent s selectivity to a specific molecule and adsorbent-adsorbate interactions. Take for example, the difference in selectivity of BaY and Ba-Mordenite [24] to p-xylene (PX), m-xylene (MX) and o-xylene (OX) ... 

According to the above mechanism, reverse osmosis separation is governed by two distinct factors, namely (i) an equilibrium effect which is concerned with the details of preferential sorption in the vicinity of the membrane surface, and (ii) a kinetic effect which is concerned with the mobilities of solute and solvent through membrane pores. While the former (equilibrium effect) is governed by repulsive and attractive potential gradients in the vicinity of the membrane surface, the latter (mobility effect) is governed both by the potential gradients (equilibrium effect) and the steric effects associated with the structure and size of molecules relative to those of pores on the membrane surface. 

Figure 3. Effect of solvent on the effective linear sizes of molecules in solution (Fuel 1982) (14) ...

Space filling van der Waals models (A3) are useful for illustrating the actual shape and size of molecules. These models represent atoms as truncated balls. Their effective extent is determined by what is known as the van der Waals radius. This is calculated from the energetically most favorable distance between atoms that are not chemically bonded to one another. 

In mobile phases that are good sample solvents, the retention mechanism of high molecular compounds can be explained on the basis of conventional theory of RPC or NPC gradient elution applying for small molecnles, considering the effect of increasing size of molecules on the values of the constants a, b, ko, and m of the retention equations— Equation 5.7, 5.10, or 5.11. 

The experimental of peptides or proteins depend more on the type of the column than on the gradient program and are constant within % at various gradient times. The variance in the (p is lower as the size of molecules increases. The values of (p are slightly higher with totally porous particles than with columns packed with superficially porous, nonporous particles and monolithic columns [97]. 

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