Wilke-Chang relationship

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. 

Several relationships are widely used to calculate values of Di lI10 for organic compounds in water and air. One of the most commonly used empirical correlations for predicting the water-phase diffusivity is the Wilke-Chang [23] equation ... 

This relationship is clearly related to equation (15.18) in particular. The term in log is of note. In the original reference [3] very limited justification for its inclusion was made. Furthermore, the values of quoted in Reference [3] were obtained from then unpublished work, and effectively have the nature of an empirical correction, which in itself is not a major problem in the utility of the model. However, when the work was published the values of the parameter were quite different [12], yet this error in the Wilke-Chang equation has not been corrected in the literature, to the authors knowledge. 

In the absence of a rigorous theory for diffusion in liquids, a number of empirical relationships have been proposed, one of which we mention briefly. For a binary mixture of solute A in solvent B, the diffusion coefficient D°AB (cm2 s1) of A diffusing in an infinitely diluted solution of A in B can be found with the Wilke-Chang correlation ... 

Although the B and C terms exhibit opposite relationships with analyte diffusion, the C-term relationship is mainly of interest because resistance to mass transfer is the dominant form of band-spreading at the faster velocities that are desired. Equations (17-9) and (17-10) imply that speeding up diffusion will increase mass transfer and help decrease plate height. The Wilke-Chang equation [9] shows that diffusivity is directly proportional to temperature and inversely proportional to viscosity ... 

This relationship between the permeability values of several compounds (P) and the partition coefficient of these compounds between the IL phase immobilized in the membrane and the feed/receive phase (K) has been observed by several authors [34,71], finding that the increase in the K values for the compounds was reflected in an increase in the P values. A mathematical correlation between these parameters has been established by de los Rfos et al. [35], being the diffusion coefficient into the IL phase calculated by the empirical Wilke-Chang equation, with the bulk diffusion coefficient defined as... 

Equation 2.10, which is a simplified form of the Wilke-Chang equation [11], shows the relationship between temperature and diffusion. In this equation. S is a constant that depends bothonthe solvent and the analyte molecule. For those who are interested in the quantitative relationship, the diffusion coefficient is inversely proportional the molar volume to the power ofO.6, so approximately to the square route of molecular mass (depending on detailed molecular structure, in particular for macromolecules). In this example, neither the solvent nor analyte is altered, and thus it can be directly concluded how the temperature influences the diffusion 2.10. It shows the linear increase of with increasing temperature, but at the same time we have to consider the decrease in viscosity, which is also a function of temperature, thus increasing the diffusion coefficient even more. 

The relationship described in Equation 5.24 is not dimensionally consistent therefore accurate estimates of aqueous diffusivity will only be obtained if the values of the parameters used have the specified units. The Wilke-Chang correlation provides estimates with average errors of 10%. 

The gas A must transfer from the gas phase to the liquid phase. Equation (1) describes the specific (per m2) molar flow (JA) of A through the gas-liquid interface. Considering only limitations in the liquid phase, this molar flow notably depends on the liquid molecular diffusion coefficient DAL (m2 s ). Based on the liquid state theories, DA L can be calculated using the Stokes-Einstein expression, and many correlations have been developed in order to estimate the liquid diffusion coefficients. The best-known example is the Wilke and Chang (W-C) relationship, but many others have been established and compared (Table 45.4) [28-33]. 

Wilke and Chang (1955) developed an empirical relationship that was based on the temperature and viscosity characterization of the Stokes-Einstein relationship. It deviates from the equivalent diameter characterization by using another parameter, and incorporates the size of the solvent molecule and a parameter for polarized solvents. It is the most generally used of the available equations (Lyman et al., 1990) and is given as... 

The theoretical approaches described in the foregoing equations have not been successful in predicting the diffusion coefficients. Thus, semiempirical relationships on the basis of the Stokes-Einstein equation have been developed. Wilke and Chang modified Equation (6.23), and their equation is good only for dilute concentrations of un-ionized solutes, as given by ... 

Wilke and Chang [7] modified fhis relationship to develop a dimensional relationship for the dilute case, i.e., low concentrations of i in j ... 

Wilke and Chang, 1955 (32) studied the diffusivity of both iodine and toluene in alkanes and included in their analysis other systems from the literature. They investigated the influence of solvent properties, such as, viscosity, molar volume, molecular weight and heat of vap>orization and found a linear relationship between Log (Dpg/T) and Logp with a slope of (0.5). They examined also the influence of solute properties, by collecting diffusion data for a variety of solutes in the solvents, water, methanol, ethanol, hexane, toluene and carbon tetrachloride and they observed a linear relationship between Log (Dpg/T) and log V, the slope being (-0.6). They proposed the following equation... 

As with diffusion in air, semiempirical relationships between the properties of diffusing species and water can be used to obtain estimates of molecular diffusivity. One of the most commonly used approaches for estimating diffusion coefficients for nonionic species in liquids at dilute concentrations is that of Wilke and Chang (1955). This method incorporates the dependence on temperature and viscosity the theoretical derivations obtained with a solvent association parameter and explicit dependence on the molar volume of the diffusing species... 

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