Diffusion of toluene

Estimate the diffusivity of toluene in water at 25°C using the Wilke-Chang and the Hayduk-Laudie relationships. Compare your result with measured values in Table 3.7. 

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). 

Larry Duda and Jim Vrentas were the first to systematically study the diffusion of small molecules in molten polymers, formulate a free volume-based theoretical model, and elucidate the sharp dependence of the diffusion coefficient on temperature and concentration.2 Figure 8.8 shows diffusivities of toluene in polystyrene as a function of concentration and temperature. The values were computed using the Vrentas and Duda (17) free volume model and, as shown, coincide well with available data. 

Consider the diffusion of toluene(l) present in trace amounts in a liquid mixture containing n-tetradecane(2) and n-hexane(3) at a temperature of 25°C. An effective diffusivity of the trace toluene defined by... 

TABLE 2.1 Effective Diffusivity of Toluene in a Liquid Mixture of n-Tetradecane-n-Hexane as a Function of the Mole Fraction of n-Tetradecane, X2... 

Figure 2.6. Effective diffusivity of toluene in a liquid mixture of n-tetradecane-n-hexane as a function of the mole fraction of n-tetradecane, X2.

Sorption isotherm data for the toluene/PVC system at 30°C are shown in Figure 3 (4). Here the Flory-Huggins equation with X = 0.75 describes the data fairly well over the whole range of activity. There is a suggestion of dual-mode behavior at low activity, but experiments in this range are limited by the very low diffusivity of toluene in glassy PVC. 

It is possible that the lower than required values of D2 reflect a problem with incorrect values of Q, which if too large would result in smaller values of D2. In an interferometric study of the diffusion of toluene in an uncrosslinked natural rubber sample, Mozisek (15) reported results for the mutual diffusion coefficient which were similar to the results of Hayes and Park. In the absence of thermodynamic data from Mozisek s work, correction factors calculated for the present work were applied to his data. The results are shown in Figure 7, which reproduces Mozisek s data along with the values for D2. The extrapolated value at 1, would exceed the self diffusion coefficient for toluene by about two orders of magnitude, similar to the discrepancy seen with Hayes and Park s data. This indicates that the fault with the results in the present case is not due to overly high values of the correction factors. Moreover, the method of calculating D from D12 has been confirmed experimentally by Duda and Vrentas (16) in a comparison of vapor sorption results for toluene diffusion in molten polystyrene with the values of D1 obtained directly using radio-labeled toluene. 

The diffusivity of toluene in air was determined experimentally by allowing liquid toluene to vaporize isothermally into air from a partially filled vertical tube 3 mm in diameter. At a temperature of 39.4°C, it took 96 x iff sec for the level of the toluene to drop from 1.9 cm below the top of the open tube to a level of 7.9 cm below the top. The density of toluene is 0.852 gm/cm , and the vapor pressure is 57.3 torr at 39.4°C. The barometer reading was 1 atm. Calculate the diffusivity and compare it with the value predicted from (16-3). Neglect the counterdiffusion of air. 

The sorption and diffusion of toluene through NR/linear low density polyethylene (LLDPE) blends at 35, 55 and 65 °C were investigated by Obasi et al. The molar percentage uptake (Qt) at any particular temperature plotted against the square root of time (y/t) showed initial increases in the mass of toluene sorbed until the maximum absorption was reached at which time, the mass of the absorbed toluene remained constant (Figure 22.2). 

S. Pickup and F. D. Blum. Self-diffusion of toluene in polystyrene solutions. Macromolecules, 22 (1989), 3961-3968. 

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