Collision, diameter number

In liquids the interactions between neighboring molecules are considerably more complicated than in gases. The resultant broadening obliterates the fine line structure seen in gas spectra, leaving only broad band profiles. There are many possible contributors to this broadening. In some cases, adequate approximation is obtained by assuming that the band contour is established by collisions. Ramsay (1952) has noted that substitution of appropriate molecular density and collision diameter numbers in the collision broadening formula results in realistic band widths for certain liquid-phase systems. In such systems, the bands typically show an approximately Lorentzian profile. Approximate deconvolution of inherently broadened liquid-phase spectra may therefore be obtained on the basis of the assumption of Lorentzian shape (Kauppinen et al., 1981). 

In SI units, T>jk is measured in m2/s. Consistent units in the first expression are ks = 1.38066 x 10-23 J/K is the Boltzmann constant, mjk is the reduced molecular mass (kg), p is the pressure (N/m2), T is temperature (K), and ajk is a reduced collision diameter (m). The second expression in Eq. 3.95 replaces the Boltzmann constant and the molecular mass with the gas constant R = 8.31451 J/g-mol K and the reduced molecular weight Wjk (g/mol), which requires Avogadro s number A. Assuming that Wjk is given in g/mol, the divide by 1000 is required to maintain SI units. The reduced mass and collision diameter are given as... 

Compute the fall-off curve using QRRK theory. For this calculation, assume a collision diameter of 4.86 A. Assume that the average energy transfer per N2-C-C5H5 collision is -0.69 kcal/mol (needed to calculate the parameter /5 used in the model). Take the number of oscillators to be, v = actual, with the frequency calculated above. Assume the reaction barrier to be E0, given above. 

Taking the collision diameter to be 400 pm, calculate the collision number, Z, for collisions between the molecules CH2=CH-CH=CH2 and CH2=CH-CHO at 500 K, and from this find the pre-exponential factor, A. 

The superlinear density dep>endence of the simulation results for listed in Table IV is well accounted for by the estimate of the Enskog enhancement factors of the Br-Ar pair. For a packing fraction of 0.01, this factor is close to 1. At this density Nordholm et al. evaluate a Br2-Ar collision frequency from analysis of the time variation of the Br2 internal energy of 2.0 x 10 which is comparable to a value of 1.5 x 10 estimated from a collision diameter fferj.Ar = Br.Ar + The collision number Nyj for V-T transfer is kg/Z and is 65 at low density. We conclude that at low densities where collisions are well resolved, the model of this work and the simulations give similar collision numbers. 

According to quantum mechanics, isolated molecules do not have a finite boundary, but rather fade away into the regions of low electron density. It has been well established, however, from properties of condensed matter and molecular interactions, that individual molecules occupy a finite and measurable volume. This notion is at the core of the concept of molecular structure. 33 A number of physical methods yield estimations of molecular dimensions. These methods include measurements of molar volumes in condensed phases, critical parameters (lattice spacings and bond distances), and collision diameters in the gas phase. 34 From these results, one derives values of atomic radii from which a number of empirical molecular surfaces can be built. Note that the values of the atomic radii depend on the physical measurement chosen. 35-i37... 

Z, the collision number, is calculable to within a power of ten. There is a little ambiguity in the definition of what constitutes the collision diameter, but this is not very serious. With regard to the factors of orientation and internal phase, unless the reaction is one of extremely simple molecules, then only rough guesses can be made as to the magnitude of P. 

Experimental values of can be compared with Eq. (4-23) by obtaining at a given temperature directly from experiment and from (rfln/ )/ [d(l/T)]. A preliminary value of n is then selected which is less than the maximum possible value of 6(s — 2), where s is the number of atoms in the (nonlinear) decomposing molecule. The hard-sphere collision diameter is estimated from viscosity measurements or similar sources. Now if, in Eq. 

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