Packing efficiency calculating

The volume of one atom is firr3 and the volume of the cell is s3. Calculate the packing efficiency of... 

Volume additivity methods generally do not take into account crystal packing efficiency or molecular conformation effects and thus will afford identical calculated densities for positional and conformational isomers and for compounds that possess different multiples of the same functional group composition. As an example, a volume additivity calculation predicts that l,3,5-trinitro-l,3,5-triazacyclohex-ane (RDX), l,3,5,7-tetranitro-l,3,-5,7-tetraazacyclooctane (a-HMX), and /3-HMX all will possess the same crystal density, 1.783 g/cm [32]. In fact, the experimentally observed densities of these three compounds differ markedly (i.e., 1.806 [33], 1.839 [34], and 1.902 [35], respectively). 

Our interest is in the order of magnitude of these quantities, so we need not worry about the cross-sectional shape or the surface packing efficiency of the water molecules in these calculations. tThis manner of referencing is used for equations occurring in the same chapter. 

Like their random-packing efficiency model (above), the Bravo, Fair et al. structured-packing model is based on the two-film theory. The HTU is calculated from the mass transfer coefficients and interfacial areas using Eqs. (9.23) and (9.24). The HETP can be calculated from the HTU using Eqs. (9.12) and (9.13). The mass transfer coefficients are evaluated from... 

Engineers will find detailed information on key fractionation concepts. .. column process design and shortcut calculations. .. tray design and operation. .. tray efficiency. .. packing design and operation. .. packing efficiency and scaleup. .. packing capacity and pressure drop. .. and much more. 

The extent to which the total pore volumes can be utilised depends not only upon molecule sieving but also on the packing efficiency of the guest in the pores. In analcime oily small polar molecules (H2O or NH3) can enter because the interstices which make up the pore volume are too small and the windows are very narrow. Even for H2O and NH3 rather high temperatures are needed for equilibration in a reasonable time, and N2 areas calculated from water uptake are meaningless because N2 is not sorbed at -1958C. At high... 

A quantitative measure of how efficiently spheres pack into unit cells is called packing efficiency, which is the percentage of the cell space occupied by the spheres. Calculate the packing efficiencies of a simple cubic cell, a body-centered cubic cell, and a face-centered cubic cell. Hint Refer to Figure 11.22 and use the relationship that the volume of a sphere is where r is the radius of the sphere.)... 

The main conclusion of the calculations summarized here is that the packing efficiency (as determined by the shape of the chain contour and the mobility of chain segments) is an extremely important physical factor in determining the permeability. This conclusion is also supported by positron annihilation studies of the microstructure of polymers in... 

This isomerism conveniently illustrates the small energy difference there is between the a and /3 forms (the packing efficiency is similar with calculated densities of 1.635 and 1.66 gem-3 respectively). 

In Sample Problem 12.4, we use the density of an element and the packing efficiency of its crystal structure to calculate its atomic radius. Variations of this approach are used to find the molar mass and as one of the ways to determine Avogadro s number. 

An atom is assumed to be spherical, so the volume of an atom is (4/3)7rr. The volume of a cubic unit cell is a a is the length of the cube edge). The packing efficiencies are calculated below ... 

Traditional methods to estimate solid-phase density from molecular structure are primarily based on a simple summation of appropriate atomic or group volumes. The basic disadvantage of these group or volume additivity procedures is that they disregard crystal-packing efficiency and molecular conformation. Thus, conformational isomras, or even different compounds with the same functional group composition, wiU aU be calculated to have the same density. To solve this problem, Ammon and coworkers have developed a scheme to estimate molecular densities by predicting possible crystal... 

Finally, we calculate the packing efficiency by dividing the volume occupied by atoms by the volume of the cubic unit cell, a ... 

Determine the packing efficiency by calculating the fraction of space occupied by atoms in a body-centered cubic metal. 

The plate number calculated from a non-retained peak is a measure of the column packing efficiency, whereas in the case of peaks eluted later, mass-transfer processes also contribute to the plate number. As a general rule, N is higher for retained compounds because their relative band broadening by extracolumn volumes (see Section 2.6) is lower than for the early eluted peaks. 

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