Maximum molecular diameter

Maximum molecular diameter The longest dimension of a molecule. 

It is obvious that the barbital molecule included shallowly in the 3 CyD(2) can not escape easily because of the existence of the shifted 3 CyD(l ) as depicted in Fig. 3 (b). As the maximum molecular diameter of barbital molecule is larger than the minimum cavity diameter of 3-CyD, a barbital molecule buried in the dimeric 3 CyD also can not escape from the crystalline state. So barbital molecules are bound very tightly by 3-CyDs. However, when the crystals are dissolved in aqueous medium and the matrix structure of 3-CyD is broken, the barbital molecules included only at their ethyl groups are easily released. 

A tank of chlorine contains 1000 kg of chlorine at 50 bar gauge (1 bar = 100,000 Pa). What is the maximum hole diameter (in mm) in this tank that will result in a downwind concentration equal to the ERPG-1 at a downwind distance of 300 m Assume 1 atm, 25°C, a molecular weight of chlorine of 70.9, and that all the liquid chlorine vaporizes. 

Densities of molecules adsorbed on surfaces are in moles per unit area, which we win give the symbol rij for species j. Typical units of nj are moles per cm. There is a maximum density rijo of molecules packed in a two-dimensional layer on a flat surface when all molecules touch or reach Hquidlike or soHdlike densities. We call this density a monolayer, whose density is approximately the inverse of the square of the molecular diameter, which is less than 1 x lO molecules/cm2 for all molecules (Figure 7-21). We wiU find it convenient also to define a coverage of adsorbed molecules as the fraction of the monolayer density dj,... 

Figure 7.17 Left Fluctuating density in a liquid phase near a solid surface, relative to the bulk density p0. The first maximum occurs at the hard-sphere contact distance from the surface, at r = a the molecular diameter. Right Pair potentials for two molecules in the liquid calculated from p(r) - p0exp[-w/kT]...

Microfiltration with inorganic membranes is a promising alternative. As early as 1964 porous silver membranes (composed of permanently molecular bonded pure silver particles) in the disk form were commercially available. Silver membranes with a maximum pore diameter of 1.2 pm were tested successfully on the pilot scale for cold sterilization of beer to remove any organisms that can cause spoilage in closed... 

Numerical evaluation of the Kassel integral permitted a comparison between theoretical and experimental fall-off behaviour . With an average molecular diameter of 5.5 A the calculated rate coefficient-azoethane pressure curve showed the best agreement with experiment at an effective number of oscillators of 18, somewhat less than half of the maximum 2N— 6. Because of the complexity of the reaction the experimental curve is probably in error, rendering comparison unreliable. Similar calculations for azomethane using the earlier uninhibited kinetic data showed best agreement with experiments at a molecular diameter of 4.7 A and an effective number of oscillators of 12, one half of the total normal modes of vibrations. 

Hansen and Verlet [156] observed an invariance of the intermediate-range (at and beyond two molecular diameters) form of the radial distribution function at freezing, and from this postulated that the first peak in the structure factor of the liquid is a constant on the freezing curve, and approximately equal to the hard-sphere value of 2.85. They demonstrated the rule by application to the Lennard-Jones system. Hansen and Schiff [157] subsequently examined g r) of soft spheres in some detail. They found that, although the location and magnitude of first peak of g r) at crystallization is quite sensitive to the intermolecular potential, beyond the first peak the form of g(r) is nearly invariant with softness. This observation is consistent with the Hansen-Verlet rule, and indeed Hansen and Schiff find that the first peak in the structure factor S k) at melting varies only between 2.85 n = 8) to 2.57 (at n= ), with a maximum of 3.05 at n = 12. 

Since the effective pore size is estimated from the molecular diameter of globular proteins which are retained 90% by the membrane, it is obvious that larger pores do exist. The measurement of a membrane s bubble point (see the section on the bubble point test in Chapter 2) permits calculation of the maximum pore size in the skin of the membrane. 

Kinetic molecular diameter This estimates the maximum diameter if the molecule were a spherical. 

Pzlp = os(z). the wall-molecule distribution function see Chapter 3, Section 3.4). In Figure 6.17a, the density profile at a vapor-liquid interface is represented a relatively smooth density curve is found, which reflects that some molecules are allowed to stick out beyond the limit (in a statistical sense) of the liquid phase. When a hard wall is present, the situation is quite different if it is assumed to be ideally smooth, as in Figure 6.17b, it (along with the liquid molecular interactions) forces the liquid molecules to order into quasi-discrete ordered layers, but this order lasts only for a distance of a few molecular diameters, after which the disordered nature of the liquid prevails. The density at the wall position is zero, and at a distance rjl, a maximum in p is observed, corresponding to the first liquid layer this density, p, is known as the contact value of the density. The midplane density p may or may not approach the bulk density, depending on the wall-wall distance d. Experiments have shown that for water in the presence of mica surfaces, there are about four quasi-ordered water layers, covering a distance of about 1 nm from... 

Calculate the approximate maximum rate for a gaseous bi-molecular chemical reaction at 0.50 atm and -20°C, given that the molecular diameter (s) is 3.0 x 10 m and the average speed of a molecule (c) is 481 ms" How long would it take to consume the reacting gases at this rate (Compare the answers with the solutions to Exercise 3.5.)... 

Figure 1. (a) General form of the intermolecular pair potential, as a function of separation, r. The parameter a, defined by = 0, corresponds to the molecular diameter e, is the maximum value of tj>. (b) Schematic of a possible sequence of collisions between three molecules, 1,2, and 3, for three times t = 0, t, t". 

Always starting from his principle of the three membranes and the idea that most of the interior is not formed of pure water, he calculates, by the same process, the thickness of the latter, knowing the proportion of water in the solution, and finds this thickness equal to 1/17577 inch (approximately 1/670 of a millimetre) however, as its bubbles have their maximum diameter, so that they burst and are reduced in a kind of dust if one continues to blow, he concludes that, until this limit of thinness only, the water molecules can remain united, and that thus the diameter of one of these molecules does not exceed the value above. He deduces from the same method still that the diameter of the molecules of oil is not higher than 1/303851 of an inch (cqtproximately 1/12000 millimetre). Leidenfrost thus had the idea to seek upper limits of molecular diameters. 

Alternatively, the results can be represented by plotting p(r) against r, which shows the peaks more clearly. The curve obtained is shown in Fig. 1.5(b), where Po is the mean number density of molecules in the liquid. The p(r) curve starts from zero and rises sharply at a finite value of r as a consequence of the molecular repulsions. It then passes through a maximum and oscillates about the value po, tending to the value Po at large values of r. The first maximum corresponds to the shell of nearest neighbours and gives the approximate molecular diameter. 

Kelvin lengths are typically twice the diameter of the molecules in a liquid (Table 5.1). It is questionable if at such length scales the liquid behaves like a continuum. Experiments with the SPA showed that the discrete molecular nature of the liquid does not seem to play a crucial role down to dimensions of 0.8 nm for hexane and 1.4nm for water, or even lower [506, 507, 534]. Molecular dynamics simulations of two silica surfaces, interacting across a water bridge agreed with predictions using Kelvin s equation [542]. Monte Carlo simulations of the interaction between a sphere and a flat surface in a vapor showed that either the adhesion force increases with humidity or the force versus humidity curve shows a maximum [543, 544]. Such simulations are, however, limited to sphere sizes of the order of at most few 10 molecular diameters. They complement continuum theory, which is applicable only for larger particle radii. 

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