Infinite dilution coefficient

Terminal activity coefficients, 7°, are noted in Figure 3. These are often called infinite dilution coefficients and for some systems are given in Table 1. The hexane—heptane mixture is included as an example of an ideal system. As the molecular species become more dissimilar they are prone to repel each other, tend toward liquid immiscihility, and have large positive activity coefficients, as in the case of hexane—water. 

Inferred petroleum reserves, 18 595 Infinite dilution coefficients, 8 743 Infinite heat-transfer surface area, 13 253 Infinity point, 14 611... 

The distribution coefficient A) is the ratio of activity coefficients and may be estimated from binary infinite dilution coefficient data. 

Binary interaction parameters (Ay) and infinite dilution activity coefficients are available for a wide variety of binary pairs. Therefore the ratio of the solute infinite dilution coefficient in solvent-rich phase to that of the second phase ( ) will provide an estimate of the equilibrium distribution coefficient. The method can provide a reasonable estimate of the distribution coefficient for dilute cases. 

Most methods for predicting D in concentrated solutions attempt to combine the infinite dilution coefficients )°2 and >21 in a simple function of composition. The simplest expression... 

Thus, the two infinite-dilution coefficients are calcnlated, and intermediate values of the coefficient... 

Let i be methanol and j be water. The infinite-dilution coefficient for methanol in water is computed using Equation (8.4). Values of terms are... 

Note For a simple molar average of infinite-dilution coefficients. 

After comparing a number of correlations for liquid-phase dlfiusivities, Reid et at.10 conclude (hat the Wilke-Clung correlation is to be preferred for estimating infinite-dilution coefficients of low-molecular-weight solutes in nonpolar and nonviscous solvents. For highly viscous solvents the Wilke-Chang corre-... 

Tsonopoulos and Pransnitz (27) have reported that the hydrocarbon infinite dilution coefficient, y00, is the appropriate quantity for correlating the aqueous solubilities of hydrocarbons. They, along with Leinonen et al. (23) and Pierotti et al. (28) have successfully correlated y00 with carbon number, molar volume, and degree of branching. Recently MacKay and Shiu (26) have correlated the hydrocarbon infinite dilution coefficients of 32 aromatic hydrocarbons (using the supercooled standard state) with carbon number. From this relationship, they derived a... 

The activity coefficient depends on tenperature, pressure, and concentratiom Excellent correlation procedures for activity coefficients such as the Margules, Van Laar, Wilson, NRTL, and UNIQUAC methods have been developed fPoling et al.. 2001 Prausnitz et al.. 1999 Sandipr 2008 Tpstpr and Modell. 1997 Van Ness and Abbott. 1982 Walas. 1985). The coefficients for these equations for a wide variety of mixtures have been tabulated along with the experimental data (see Table 2-2). When the binary data are not available, one can use infinite dilution coefficients fTable 2-2 Carlson. 1996 T pt... 

Activity-coefficient data at infinite dilution often provide an excellent method for obtaining binary parameters as shown, for example, by Eclcert and Schreiber (1971) and by Nicolaides and Eckert (1978). Unfortunately, such data are rare. 

Figure 4-11. Activity coefficients for noncondensable solutes at infinite dilution.

GAMMA calculates activity coefficients for N components (N 20) at system temperature. For noncondensable components effective infinite-dilution activity coefficients are calculated. 

Activity coefficients for condensable components are calculated with the UNIQUAC Equation (4-15)/ and infinite-dilution activity coefficients for noncondensable components are calculated with Equation (4-22). ... 

The value of coefficient depends on the composition. As the mole fraction of component A approaches 0, approaches ZJ g the diffusion coefficient of component A in the solvent B at infinite dilution. The coefficient Z g can be estimated by the Wilke and Chang (1955) method ... 

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

Absorption coefficient, linear decaidic a. K Aqueous solution at infinite dilution aq, CO... 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

Eor given biaary pair, two-phase behavior likely when infinite dilution activity coefficient of either component ia other component is >7.5. 

Experimentally deterrnined equiUbrium constants are usually calculated from concentrations rather than from the activities of the species involved. Thermodynamic constants, based on ion activities, require activity coefficients. Because of the inadequacy of present theory for either calculating or determining activity coefficients for the compHcated ionic stmctures involved, the relatively few known thermodynamic constants have usually been obtained by extrapolation of results to infinite dilution. The constants based on concentration have usually been deterrnined in dilute solution in the presence of excess inert ions to maintain constant ionic strength. Thus concentration constants are accurate only under conditions reasonably close to those used for their deterrnination. Beyond these conditions, concentration constants may be useful in estimating probable effects and relative behaviors, and chelation process designers need to make allowances for these differences in conditions. 

Hquid-phase activity coefficient (eq. 6) terminal activity coefficient, at infinite dilution constant in Wilson activity coefficient model (eq. 13)... 

Fiend s Constant. Henry s law for dilute concentrations of contaminants ia water is often appropriate for modeling vapor—Hquid equiHbrium (VLE) behavior (47). At very low concentrations, a chemical s Henry s constant is equal to the product of its activity coefficient and vapor pressure (3,10,48). Activity coefficient models can provide estimated values of infinite dilution activity coefficients for calculating Henry s constants as a function of temperature (35—39,49). 

For low miscibility, the solubiHty of a substance in water is often estimated as the inverse of the chemical s infinite dilution activity coefficient ... 

Once the composition of each equiHbrium phase is known, infinite dilution activity coefficients for a third component ia each phase can then be calculated. The octanol—water partition coefficient is directly proportional to the ratio of the infinite dilution activity coefficients for a third component distributed between the water-rich and octanol-rich phases (5,24). The primary drawback to the activity coefficient approach to estimation is the difficulty of the calculations involved, particularly when the activity coefficient model is complex. 

A sampling of appHcations of Kamlet-Taft LSERs include the following. (/) The Solvatochromic Parameters for Activity Coefficient Estimation (SPACE) method for infinite dilution activity coefficients where improved predictions over UNIEAC for a database of 1879 critically evaluated experimental data points has been claimed (263). (2) Observation of inverse linear relationship between log 1-octanol—water partition coefficient and Hquid... 

Rutan, The SPACE Predictor for Infinite Dilution Activity Coefficients, unpubhshed, presented at AlChE 1992 Annual Meeting, Nov. 3, Miami Beach, Fla. For information, write to Chades. A. Eckert, School of Chemical Engineering, Georgia Institute of Technology, Adanta, Ga. 30332-0100. 

The symmetrical nature of these relations is evident. The infinite-dilution values of the activity coefficients are In yF = Iri JT = B. 

The binary interaction parameters are evaluated from liqiiid-phase correlations for binaiy systems. The most satisfactoiy procedure is to apply at infinite dilution the relation between a liquid-phase activity coefficient and its underlying fugacity coefficients, Rearrangement of the logarithmic form yields... 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

Hayduk-Laudie They presented a simple correlation for the infinite dilution diffusion coefficients of nonelectrolytes in water. It has about the same accuracy as the Wilke-Chang equation (about 5.9 percent). There is no explicit temperature dependence, but the 1.14 exponent on I compensates for the absence of T in the numerator. That exponent was misprinted (as 1.4) in the original article and has been reproduced elsewhere erroneously. 

Concentrated, Binary Mixtures of Nonelectrolytes Several correlations that predict the composition dependence of Dab. re summarized in Table 5-19. Most are based on known values of D°g and Dba- In fact, a rule of thumb states that, for many binary systems, D°g and Dba bound the Dab vs. Xa cuiwe. CuUinan s equation predicts dif-fusivities even in hen of values at infinite dilution, but requires accurate density, viscosity, and activity coefficient data. 

Gordon Typically, as the concentration of a salt increases from infinite dilution, the diffusion coefficient decreases rapidly from D°g. As concentration is increased further, however, D g rises steadily, often becoming greater than D°g. Gordon proposed the following empirical equation, which is apphcable up to concentrations of 2N ... 

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