Mixture and Raoult’s law

Time out Vapor pressure data for pure components is available in the CRC handbook. C6, C7 and C8 form a nearly ideal mixture and Raoult s law applies ... 

There are many mixtures of liquids that do not follow Raoult s Law, which represents the performance of ideal mixtures. For those systems following the ideal gas law and Raoult s Law for the liquid, for each component. 

If the mixture follows Raoult s law, then the vapour pressure of a mixture may be obtained graphically from a knowledge of the vapour pressure of the two components. Thus, in Figure 11.6. OA represents the partial pressure PA of A in a mixture, and CB the partial pressure of B, with the total pressure being shown by the line BA. In a mixture of composition D, the partial pressure PA is given by DE, Pg by DF, and the total pressure P by DG, from the geometry of Figure 11.6. 

Figure 34.1 Binary Ideal liquid-liquid mixture in which the vapour behaves ideally and the liquid-liquid mixture obeys Raoult s Law.

The properties of mixtures of ideal gases and of ideal solutions depend solely on the properties of the pure constituent species, and are calculated from them by simple equations, as illustrated in Chap. 10. Although these models approximate the behavior of certain fluid mixtures, they do not adequately represent the -behavior of most solutions of interest to chemical engineers, and Raoult s law is not in general a realistic relation for vapor/liquid equilibrium. However, these models of ideal behavior—the ideal gas, the ideal solution, and Raoult s law— provide convenient references to which the behavior of nonideal solutions may be compared. 

In a limited sense solutions are homogeneous liquid phases eonsisting of more than one substanee in variable ratios, when for eonvenienee one of the substanees, whieh is ealled the solvent and may itself be a mixture, is treated differently from the other substanees, whieh are ealled solutes [1], Normally, the eomponent whieh is in exeess is ealled the solvent and the minor eomponent(s) is the solute. When the sum of the mole fraetions of the solutes is small eompared to unity, the solution is ealled a dilute solution A solution of solute substanees in a solvent is treated as an ideal dilute solution when the solute aetivity eoeffieients y are elose to unity (y=l) [1, 171], Solute/solvent mixtures A+ B that obey Raoult s law over the entire eomposition range from pure A to pure B are ealled ideal solutions. Aeeording to Raoult, the ratio of the partial pressure of eomponent AljpfO to its vapour pressure as a pure liquid (p ) is equal to the mole fraetion of A xa) in the liquid mixture, i.e. xa = Pa/Pa- Many mixtures obey Raoult s law very well, partieularly when the eomponents have a similar moleeular strueture e.g. benzene and toluene). 

Activity Coefficient a The efficient removal of volatile substances during edible oil deodorization depends not only on their vapor pressure but also on their concentration in the oil. The theoretical principle of the deodorization process has already been described in many publications (2-4). All calculations start from the basic laws of Raoult and Dalton, which are valid for ideal mixtures. However, in practice, the mixture of a fatty acid and a vegetable oil has a nonideal behavior. Consequently, a so-called activity coefficient a was introduced and Raoult s law may be written as follows ... 

Example. n-heptane and n-octane form a nearly ideal mixture. Use Raoult s law to construct a phase diagram at constant pressure (1 atm). 

At 353 K the vapour pressures of benzene and bromobenzene are 757 and 66 mmHg respectively. For an equimolar mixture fxA(l) = xB(l) = 0.5] calculate the total vapour pressure and the mole fraction of benzene in the vapour phases. Assume that the mixture follows Raoult s Law. 

An ideal mixture follows Raoult s law, and the relative volatility is the ratio of the vapor pressures. Thus... 

Equation (6-4) and Raoult s law apply for each of the three components in the mixture. Also, the mole fractions must add up to 1.0 in each of the two phases leaving the separator. The Mathcad program of Figure 6.3 is easily modified to include an additional component and solve for D, W, and the vapor and liquid compositions (see... 

Let us discuss the relationship of the preceding definition with Henry s and Raoult s laws, which are often used to define ideal solutions. Assuming that an ideal solution of i is in equilibrium with an ideal gas mixture, we have... 

At time t = 0 the sample is put into contact with the supply of liquid hydrocarbon (n-hexane or benzene) in equilibrium with the gas and is then placed quickly in the magnet. The liquid phase is either pure or consists of a mixture such that the two partial presstnes of the gases are equal to 60 mbar (assuming that the mixture obeys Raoult s law). To distinguish the hydrocarbons when they are mixed, one is perhydro and the other perdeutero. 

In ternary systems, the phase equihbrium can also be calculated from Dalton s and Raoult s laws. The following holds for ideal mixtures ... 

Many or even most liquid mixtures encountered in industrial practice exhibit a nonideal equihbrium behavior. In high-pressure systems both the vapor phase and the liquid phase can deviate fiom Dalton s and Raoult s laws (e.g., Prausnitz et al. 1998). In low-pressure systems deviations from Raoult s law prevail. The fundamental principles for formulating the thermodynamics of nonideal systems are presented in Chap. 2. 

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... 

Boiling lines and dew lines for an ideal mixture at a given pressure p may be derived from Dalton s and Raoult s laws to give... 

Following is the composition of a liquid alcohol mixture to be fed to a distillation tower at 101.32 kPa methyl alcohol (x = 0.30), ethyl alcohol (xb = 0.20), n-propyl alcohol (x = 0.15), and -butyl alcohol (xp = 0.35). Calculate the following assuming that the mixture follows Raoult s law. 

Equations (1.2-59), (1.2-W), and (l.4-l)-(1.4-4) are valid regardless of the standard-stale conventions adopted for the components of the mixture. If Raoult s Law standard stales are used for all conqxMients (the usual procedure), then... 

The vapor composition in equilibrium with the liquid usually has a different composition than the liquid. For ideal gas and liquid mixtures the equilibrium relations are given by combining Dalton s and Raoult s laws. 

The important models with which we are concerned are the perfect gas, the perfect gas mixture and the ideal solution (gaseous, liquid or solid). These may be defined in either of two ways which are entirely equivalent (1) in terms of limiting experimental laws such as the gas equation and Raoult s law (2) in terms of expressions for the chemical potentials of the various components. These expressions are as follows ... 

Figure 9.8 Fugacity of ethanol in a gas phase equilibrated with a binary liquid mixture of ethanol (A) and H2O at 25 °C and 1 bar. Open circles experimental noeasure-ments. The dashed lines show Henry s law behavior and Raoult s law behavior.

For the rare case of an ideal mixture, the forces of attraction between solute and solvent equal the attractive forces in the mixture. Then Raoult s law, Eq. (3.3.6), is even valid for a high dilution, and the vapor pressure of the pure solute pA,sat (also denoted as equals Ha,x ... 

In deriving Raoult s law (Equation 1.27), the imphed assumption was that all components are condensable that is, their critical temperature is higher than the mixture temperature. If a component s critical temperature is below the mixture temperamre, it does not condense at that temperature as a pure component. There would be no vapor pressure for that component at the system temperature and Raoult s law would not apply. The gas component could nonetheless exist as a solute in... 

Benzene-Toluene-Xyiene Example. Consider the rectification of a mixture containing 60 mol per cent of benzene, 30 mol per cent of toluene, and 10 mol per cent of xylene into a distillate or product containing not over 0.5 mol per cent of tolueM, f id a bottoms or residue containing 0.5 mol per cent of benzene.V reflux ratio 0/D equal to 2 will be used, and the feed will enter preheated so that the change in mols of overflow across the feed plate will be equal to the mols of feed. The usual simplifying assumptions will be made, and Raoult s law will be used. The distillation will be carried out at 1 atm. abs. pressure. 

The design becomes somewhat more complex when a mixture of compounds is involved. However, the components of the mixture are usually mutually soluble in the liquid phase, and, as a first approximation for related solvents, it can be assumed that the mixture follows Raoult s law, i.e., the partial pressure of each component in the product gas will be equal to the vapor pressure of the pure component at the gas outlet temperature times its mole fraction in the liquid phase. For more precise calculations and more complex liquid mixtures, it is necessary to use vapor-liquid equilibrium (VLB) data for the specific system. The estimation and correlation of VLB data are discussed in various chemical engineering texts, such as Perry s Handbook (Perry et al., 1984), Reid and Sherwood (1966), and Prausnitz (1969). 

---