Diffusion of benzene

Example 37 Estimate the Diffusivity of Benzene Vapor Diffusing... 

Example 37 Estimate the diffusivity of benzene vapor diffusing into air at 30°C and 96.5 kPa total pressure. 

The main complication with this technique is that the mass transfer analysis is nontrivial. For example, the change of velocity as a function of the distance down the jet was not taken into account in modeling the system. The LJRR has been used to study the diffusivities of benzene and toluene in water [41] and cupric ion extraction [42,49]. 

MJ Hayes, GS Park. The diffusion of benzene in rubber. Trans Faraday Soc 52 949-955, 1956. 

Sastre, G., Catlow, C.R.A., and Corma, A. (1999) Diffusion of benzene and propylene in MCM-22 zeolite a molecular dynamics study. J. Phys. 

Diffusivity values are reported in a modified exponential form. For example, the experimentally determined diffusivity of benzene in water is 1.09x 10 cm /sec, but this value is reported as 1.09 (x 10 cm /sec). 

J. Quillet The thing that is not realized is that diffusion of benzene through rubber is about the same as benzene through benzene. The kinds of motion found in a liquid are in fact very similar to those found in a rubber. It s just that the translational motion of the large molecules is restricted. It is not too surprising that rubbers would show up in some cases as 1iquids. 

Investigation of Diffusion and Counter-diffusion of Benzene and Ethylbenzene in ZSM-5-type Zeolites by a Novel IR Technique... 

Fig. 3. Diffusion of benzene into H-ZSM-6 at various temperatures and for different pressure jumps.

Table 1 Diffusivities of benzene and ethylbenzene in fresh and coked H-ZSM-5...

The results of the inverse experiment, viz. counter-diffusion of benzene into H-ZSM-5, previously loaded with ethylbenzene from an ethylbenzene/helium stream at 415 K, are displayed in Fig. 6. 

On leaving their military bases in Czechoslovakia, the military of the old Soviet Union dumped all chemicals out onto the ground in an unbelievable show of disrespect. At one location, 50,000 kg of solvent was dumped out of a storage tank onto saturated soil. The solvent formed a pool on the surface that was visible for more than 2 weeks. As part of a hazard assessment, the Czech engineers need to know the total mass of benzene (one compound composing the solvent) that was evaporated into the air versus time for the 2-week period. Estimate and plot this mass. The mean depth of the pool just after the spill was 10 cm. Incorporate the diffusion of benzene into the saturated soil. Assume that there is no turbulence in the spilled pool. 

As an example, let us estimate the diffusivity of benzene in air. According to Table 18.3, the molar volume of benzene calculated from liquid density (89 cm3mol 1) and from the component method by Fuller et al. (90.8 cm3mor1) yield similar results. Incorporating these estimates into Eq. 18-44 yields ... 

Note that in this procedure the effect of molecular mean free path, that is, of molecular size is neglected. As an example we estimate diffusivity of toluene (Mk) uene = 92 gmol-1) from diffusivity of benzene (Afbenzene = 78 gmol-1) and get Dtoluene a (0.096 cm s-1) [92/ 78]-1/2 = 0.088 cm s-1. The experimental value is 0.086 cm s 1 (Gilliland, 1934). 

Possibly the earliest theoretical study of diffusion of aromatics in zeolites was published in 1987 by Nowak et al. (89), who considered diffusion of benzene and toluene in the pores of silicalite and theta-1. Theta-1 (90) has a unidimensional medium-sized pore opening bounded by 10-rings. In this study, only the straight channel of silicalite was considered, making the... 

On the basis of their 2H-NMR measurements for siliceous Y and NaY zeolites, the authors estimated the simulation time needed to observe cage-to-cage migration for an MD calculation for NaY zeolite. Their estimate of 200 ns is still beyond even the longest MD simulations on the most powerful machines. It is unsurprising, therefore, that more recent theoretical investigations into diffusion of benzene have used the more appropriate TST approach. 

The calculations led to predictions of adsorption sites for the nonpolar compounds that are in good agreement with those determined experimentally. The cation site is preferred over the window site. The activation barrier for movement between two cation sites was calculated to be 30 kJ/ mol and that for movement between a cation and a window site 43 kJ/mol. Experimental measurements of activation barriers to diffusion of benzene in faujasites are between 17 and 27 kJ/mol (24). The calculations provide strong support for the mechanism of surface-mediated diffusion for all guest molecules in the limit of infinite dilution and 0 K. The MEPs show that molecules slide along the wall of the supercage, with the plane of the aromatic ring almost parallel to the pore wall. 

As Figure 2 indicates, ion diffusivities were in the range of 10"7 to 10"6 cm2/sec at 18 °C. So were diffusivities of benzene and urea, but water diffusivity was somewhat higher, about 0.8-3.0 X 10 6 cm2/sec. The shape of the diffusivity curves for these molecules was about the same as that... 

Tab. 6.6 Comparison of diffusion of benzene molecules in DMPC as function of location and in tetradecane. Data taken from ref. 50...

The self-diffusion of benzene in PIB [36], cyclohexane in BR [37] and toluene in PIB [38-40] has been investigated by PFG NMR. In addition more recently Schlick and co-workers [41] have measured the self-diffusion of benzene and cyclohexane mixtures in polyisoprene. In the first reported study of this kind, Boss and co-workers [36] measured the self-diffusion coefficients of benzene in polyisoprene at 70.4 °C. The increase in Dself with increasing solvent volume fraction could be described by the Fujita-Doolittle theory which states that the rate of self-diffusion scales with the free volume which in turn increases linearly with temperature. At higher solvent volume fractions the rate of selfdiffusion deviates from the Fujita-Doolittle theory, as the entanglement density decreased below the critical value. 

So the apparent activation energy is also concentration-dependent If f(c) is a monotonically increasing function, ED will decrease continuously with increasing c. If f(c) is a monotonically decreasing function, ED increases continuously with c. For the diffusion of benzene in natural rubber the apparent activation energy decreases from 48 kj/mol at c = 0 to 35 kj/ mol at a volume fraction of 0.08. Ed/0 shows a discontinuity at transition temperatures. 

Figure 5 Natural logarithm of the room-temperature OHD-RIKES data for benzene. Note that the tail of the decay is linear, implying that the collective orientational diffusion of benzene is described well by a single-exponential decay, as would be expected for a symmetric-top liquid.

Figure 5 shows the Arrhenius plot of the diffusivities of aromatics. The diffusivities of benzene, toluene and / am-xylene, minimum molecule sizes of which are the same and are close to that of the pore diameter. Whereas, those of mefa-, or/Ao-xylene, which minimum molecule sizes are larger than the size of the pores, are almost 1/10 of the former group. This difference among the diffusivities is the reason why ZSM-5 shows shape selectivity. 

FIGURE 14.2 Molecular dynamics simulation of the diffusion of benzene within a hydrated lipid bilayer membrane. Benzene molecules are shown as Corey-Pauling-Koltun (CPK) models atoms in the phospholipid head groups are shown as ball and stick models and hydrocarbon chains and water molecules as dark and light stick models, respectively. (Reproduced with permission from Bassolino-Klinaas D, Alper HE, Stouch TR. Biochemistry 1993 32 12624-37.)... 

F. Jousse and S. M. Auerbach, /. Chem. Phys., 107, 9629 (1997). Activated Diffusion of Benzene in NaY Zeolite Rate Constants from Transition State Theory with Dynamical Corrections. 

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