Raoult law activity coefficient

Estimate the vapor pressure of the two components in a regular solution for which cAh/(RT) = 1 and = 0.4 given that the vapor pressure of pure component A is 15.0 kPa and that of pure B, 20.0 kPa. Also calculate the Raoult law activity coefficients. Repeat the calculation for the case that cAh/(RT) = -1. 

Using Wilson s parameters for the carbon tetrachloride-acetonitrile system, estimate the Raoult law activity coefficients for each component in a equimolar solution. Then estimate the molar Gibbs energy of mixing. 

From the theory for regular solutions, the Raoult law activity coefficient for component B in a solution of A and B is... 

Calculate the Raoult law activity coefficients of both components and plot them as a function of the mole fraction of acetone. Determine the range of composition with respect to acetone that the solution can be regarded as regular. Calculate the enthalpy parameter for acetone-chloroform interactions on the basis of a one-parameter least-squares fit of the data in this range using an appropriate plot. 

Some organic compounds can be in solution with water and the mixture may still be a flammable mixture. The vapors above these mixtures such as ethanol, methanol, or acetone can form flammable mixtures with air. Bodurtha [39] and Albaugh and Pratt [47] discuss the use of Raoult s law (activity coefficients) in evaluating the effects. Figures 7-52A and B illustrate the vapor-liquid data for ethyl alcohol and the flash point of various concentrations, the shaded area of flammability limits, and the UEL. Note that some of the plots are calculated and bear experimental data verification. 

Figure 3 Acetone-chloroform solution Raoult s law activity coefficients solid curve ...

The factor yt is called an activity coefficient. Bnbblepointand dewpoint calculations made witli tliis equation are only a bit more complex than the same calculations made with Raoult s law. Activity coefficients are functions of temperature and liquid-phase composition, and ultimately are based on experiment (Sec. 12.1). For present purposes, the necessary values are assnmed... 

Table 1.4 Raoult Law and Henry Law Activity Coefficients for Dilute Solutions of Methanol in...

It should be noted that the values of quickly become non-unity and are greater than one. This is indicative of strong attractive solute-solvent interactions and negative deviations from Raoult law behavior. In the case of the methanol water system for which positive deviations from Raoult s law is observed (table 1.4), the Hemy law activity coefficients are less than one. 

Figure 14.4.3.2. The dependence of (A) subtilisin Carlsberg and (B) a-chymotrypsin substrate specificity for substrates 1 and 2 on the ratio of their Raoult s law activity coefficients. For the stractures of the substrates 1 and 2, and the solvents a through m in (A) and a to g in (B), refer to Ref 16. [Adapted, by permission, Ifom C.R. Wescott and A.M. Klibanov, Biotechnol. Bioeng., 56, 343(1997)].

Equation (1.5-21) is a genera/relationship between Heniy s Law and Raoult s Law activity coefficients for a component in a binary mixture. Farticu/ar expressions for 7 are obtained from particular expressions for7 which require a model for for their determination see Sections 1.4-1-1.4-3. To illustrate, suppose that g is described by the Porter equation, Eq. (1.4-14). Then, by Eqs. (1.5-21), (1.4-I5a), and (1.4-19a), we find the one-parameter expression... 

Use of Eq. (1.5-17) leqoires an expiesskm for a Hemy s Law activity coefficient y. Such expressions are usually developed from die conventional expressions for y, based on Raoult s Law standard states. For a single-solute-sii le-solvent mixture the connection betw die two is easily estaUisbed. By Eqs. (1.2.52), (1.2-38), and (1.4-5). we have... 

The problem of dissection of solvent effects thus reduces to the determination of rate constants in a series of solvents to obtain the 6AG " term, and the determination of values of AG° for the reactants by standard thermodynamic measurements. This paper is restricted to reactions in which the reactants are nonelectrolytes. For such compounds that are not too involatile, AG values can be obtained through measurements of Raoult s Law activity coefficients of the solute at infinite dilution in a series of solvents, or through the corresponding Henry s Law constants, equation and 6. 

Molar fraction of chloroform X,.h oroforn, Raoult s law activity ORaouh Raoult s law activity coefficient yRao it Henry s law activity Henry s law activity coefficient XHemy ... 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

A solution which obeys Raoult s law over the full range of compositions is called an ideal solution (see Example 7.1). Equation (8.22) describes the relationship between activity and mole fraction for ideal solutions. In the case of nonideal solutions, the nonideality may be taken into account by introducing an activity coefficient as a factor of proportionality into Eq. (8.22). 

Fig. 3. Binary activity coefficients for two component systems having (a) positive and (b) negative deviations from Raoult s law. Conditions are either...

In equation 21 the vapor phase is considered to be ideal, and all nonideaHty effects are attributed to the Hquid-phase activity coefficient, y. For an ideal solution (7 = 1), equation 21 becomes Raoult s law for the partial pressure,exerted by the Hquid mixture ... 

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

It follows that die separation of cadmium must be carried out in a distillation column, where zinc can be condensed at the lower temperamre of each stage, and cadmium is preferentially evaporated. Because of the fact that cadmium-zinc alloys show a positive departure from Raoult s law, the activity coefficient of cadmium increases in dilute solution as the temperature decreases in the upper levels of the still. The separation is thus more complete as the temperature decreases. 

For a minimum boiling azeotrope the partial pressures of the components will be greater than predicted by Raoult s Law, and the activity coefficients will be greater than 1.0. 

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