Argon molecular diameter

Figure A2.4.1. Radial distribution fiinction g(R ) for water (dashed curve) at 4 °C and 1 atm and for liquid argon (fiill curve) at 84.25 K and 0.71 atm as functions of the reduced distance R = R/a, where a is the molecular diameter from [1].

In a review of the motions of guest molecules in hydrates, Davidson (1971) indicated that all molecules between the sizes of argon (3.8 A) and cyclobutanone (6.5 A) can form si and sll hydrates, if the above restrictions of chemical nature are obeyed. Ripmeester and coworkers note that the largest simple structure II former is tetrahydropyran (THP) (C5H10O) with a van der Waals diameter of 6.95 A (Udachin et al., 2002). Closely following THP are m- and p-dioxane and carbon tetrachloride, each with a molecular diameter of 6.8 A (Udachin et al., 2002). Molecules of size between around 7.1 and 9 A can occupy sH, provided that the below shape restrictions are obeyed and a help gas molecule such as methane is included. 

Gas-viscosity measurements yield molecular diameters of 2.58 A (angstroms) for helium, 3.42 A for argon, and 4.00 A for carbon dioxide. With these values, calculate and c/i3 from Eq. (V-36), and calculate D i and Z i3 using Eq. (V-34). Compare with your experimental values. 

In speaking of sizes of atoms, we should keep in mind that the electron cloud does not end at any definite distance from the nucleus. As an experimental quantity the radius of the atom is found to depend a good deal on the environment of the atom during the measurement. The following values for the molecular diameter of argon are obtained by the method indicated ... 

Since argon and neon are both monoatomic gases, they have the same heat capacity, C = fH. The thermal conductivities at 20 °C are neon, 11.07mW/mK argon, 5.236 mW/m K. (a) Calculate the ratio of the molecular diameter of argon to that of neon, (b) Calculate the molecular diameter of neon. (Use the -j factor rather than the exact one.)... 

More profound study of the properties of argon based on a more realistic interaction energy leads to the conclusion that the molecular diameter, defined as the distance at which the intermolecular energy is zero, is about 3.4 A. Our rough estimate o = 3.2 A is as near to this as could be expected. 

Similar considerations apply to the prediction of the most likely location of the second minimum in the potential of mean force for the pair of Hsolute molecules. Consider two methane molecules (or neon, argon, etc.) in water. We have already noted that the first peak of gAA(R) is expected at Ri crA- The main reason is that R cta corresponds to the minimum of the direct pair potential between two solute molecules. For two spherical solutes in a normal solvent, the location of the second peak is expected at about R2 cta+(Tw In Sec. 4.11, we shall see that the simulated curve of the potential of mean force for methane in water has a second minimum either at ]l2 6 A or at J 2 7 A (with a choice of molecular diameters of 4.4 A and 2.8 A for methane and water, respectively). 

Argon at 27°C and atmospheric pressure has values of viscosity and thermal conductivity of 2.27 x 10 pascal-sec and 1.761 x 10 " Joules/(sec m °K) from each property respectively. Calculate molecular diameters and collision diameters, compare them, and evaluate. 

It must be noted, however, that the question of which temperature dependence for the molecular diameter one should employ in these computations is not yet settled. Only for hard spheres is the diameter of the particles a well-defined quantity and temperature independent. For simple fluids, say argon, methane, etc., one may reasonably argue that the effective hard-core diameter should be a decreasing function of the temperature. The physical idea is that as one increases the temperature, the kinetic energy of the particles increases. Hence, on the average, interparticle collisions would lead to more extensive penetration into the repulsive region of the pair potential for the two particles. Indeed, it has been demonstrated that if such a negative temperature dependence of is adopted,... 

Explain why the molecular diameter for argon, at 2.6 A, is about the same as that for moiecuiar hydrogen, at 2.4 A, even though hydrogen is a much smaiier atom than argon. 

Much can be explained by reference to the radial distribution function of liquid water (Fig. 2). The broken line is the radial distribution function of liquid water and the drawn out line is the radial distribution function of liquid argon. Both are normalized to the respective molecular diameters so that at R = 1 we find the nearest neighbor molecule, and so on. 

The laboratory layout consists of a molecular beam apparatus and a laser system. NaK clusters are created in an adiabatic coexpansion of mixed alkali vapour and argon carrier gas through a nozzle of 70 pm diameter into the vacuum. Directly after the nozzle the cluster beam passes a skimmer. Next, the laser beam coming from perpendicular direction irradiates the dimers and eventually excites and ionizes them. The emerging ions are extracted by ion optics, mass selected by QMS and recorded by a computer. 

Fig. 2.6. Schematic representation of a dry-box purification scheme. (A) Glove box (B) tank argon (C) purge line for pump container (D) gastight pump container (E), 2.7 ft /min graphite ring pump (F) bubbler (G) purification train consisting of Linde 13X and 4A Molecular Sieves, and Vermiculite-supported MnO at room temperature (see Chapter 3). In some installations an additional drying column follows the MnO column. Approximate column dimensions are 3-in. diameter by 4-ft length. (Unpublished design of T. L. Brown.)...

Catalysts Preparation. The silicoaluminophosphate (SAPO) molecular sieves employed in this study were synthesized in the laboratory of Professor Mark Davis in the Department of Chemical Engineering of the Virginia Polytechnic Institute, following the methods reported in U.S. Patent 4,440,871. The three different samples, distinguished by their microscopic structure, were the wide-pore SAPO-5, medium-pore SAPO-11, and the narrow-pore SAPO-34. Verification of their microscopic structure (through x-ray diffraction) and micropore diameters (by argon adsorption measurements) was performed at VPI. The SAPO molecular sieves were provided in the ammonium cation form. Ex situ calcination at 873 K for one hour in oxygen was performed on the SAPO samples prior to their use as catalysts for the propylene conversion. 

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