Raoult s Law

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. 

Figure 4-4. Representation of vapor-liquid equilibria for a binary system showing moderate positive deviations from Raoult s law.

Figure 4 shows experimental and predicted phase equilibria for the acetonitrile/benzene system at 45°C. This system exhibits moderate positive deviations from Raoult s law. The high-quality data of Brown and Smith (1955) are very well represented by the UNIQUAC equation. 

Figure 5 shows the isothermal data of Edwards (1962) for n-hexane and nitroethane. This system also exhibits positive deviations from Raoult s law however, these deviations are much larger than those shown in Figure 4. At 45°C the mixture shown in Figure 5 is only 15° above its critical solution temperature. Again, representation with the UNIQUAC equation is excellent.

Figure 7 shows a fit of the UNIQUAC equation to the iso-baric data of Nakanishi et al. (1967) for the methanol-diethyl-amine system this system also exhibits strong negative deviations from Raoult s law. The UNIQUAC equation correctly re-... 

Raoult s law When a solute is dissolved in a solvent, the vapour pressure of the latter is lowered proportionally to the mole fraction of solute present. Since the lowering of vapour pressure causes an elevation of the boiling point and a depression of the freezing point, Raoult s law also applies and leads to the conclusion that the elevation of boiling point or depression of freezing point is proportional to the weight of the solute and inversely proportional to its molecular weight. Raoult s law is strictly only applicable to ideal solutions since it assumes that there is no chemical interaction between the solute and solvent molecules. 

Using the Gibbs-Diihem equation ((A2.1.27) with dT = 0, dp = 0), one can show that the solvent must obey Raoult s law over the same concentration range where Hemy s law is valid for the solute (or solutes) ... 

It should be noted that, whatever the fonu of Henry s law (i.e. in whatever composition units), Raoult s law must necessarily be expressed in mole fraction. This says nothing about the appropriateness of mole fractions in condensed systems, e.g. in equilibrium expressions it arises simply from the fact that it is a statement about... 

At the outset it will be profitable to deal with an ideal solution possessing the following properties (i) there is no heat effect when the components are mixed (ii) there is no change in volume when the solution is formed from its components (iii) the vapour pressure of each component is equal to the vapour pressure of the pure substances multiplied by its mol fraction in the solution. The last-named property is merely an expression of Raoult s law, the vapour pressure of a substance is pro-... 

Let us consider a mixture forming an ideal solution, that is, an ideal liquid pair. Applying Raoult s law to the two volatile components A and B, we have ... 

The naphthalene wUl dissolve in the liquid a-naphthol and, according to Raoult s law, the vapour pressure of the latter will be reduced. Hence a-naphthol will pass preferentially into the liquid phase and, if the external temperature is maintained at 95 5°, the ultimate result will be the complete melting of the solid a-naphthol since melting requires heat and no heat is imparted to the system, the temperature will fall. 

Raoult s law) Activity (referenced to Axial spin angular momentum cr, X... 

An ideal gas obeys Dalton s law that is, the total pressure is the sum of the partial pressures of the components. An ideal solution obeys Raoult s law that is, the partial pressure of the ith component in a solution is equal to the mole fraction of that component in the solution times the vapor pressure of pure component i. Use these relationships to relate the mole fraction of component 1 in the equilibrium vapor to its mole fraction in a two-component solution and relate the result to the ideal case of the copolymer composition equation. 

Finally, we note that Raoult s law (see Example 7.1) is a limiting law that is observed to apply in all solutions in the limit Xj 1 ... 

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). 

This is an expression of Raoult s law which we have used previously. Freezing point depression. A solute which does not form solid solutions with the solvent and is therefore excluded from the solid phase lowers the freezing point of the solvent. It is the chemical potential of the solvent which is lowered by the solute, so the pure solvent reaches the same (lower) value at a lower temperature. At equilibrium... 

At equilibrium, a component of a gas in contact with a liquid has identical fugacities in both the gas and liquid phase. For ideal solutions Raoult s law applies ... 

Complete separation of selenium from tellurium caimot be achieved owing to classical Raoult s law considerations and what appears to be the... 

For systems other than air—water vapor or for total system pressures different from 101.3 kPa (1 atm), humidity diagrams can be constmcted if basic phase-equihbria data are available. The simplest of these relations is Raoult s law, apphcable at small solute concentrations ... 

Of the assumptions inherent in this approximate relation, that of Hquid-phase ideaHty is usually least reaHstic. Therefore, the simplest generally useful special case of equation 222 is the modified Raoult s law expression ... 

When both phases form ideal thermodynamic solutions, ie, no heat of mixing, no volume change on mixing, etc, Raoult s law apphes ... 

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

To force the naturally more volatile component i overhead, the solvent should either behave essentially ideally with component j and cause positive deviations from Raoult s Law for component i (7 1 and 7 > 1), or behave essentially ideally with component i and cause negative deviations from... 

Raoult s Law for component j (7 1 and 7 < 1). Compounds of similar type and size, eg, pentane—hexane or methanol—ethanol, tend to behave ideally... 

Idea.1 Liquid Solutions. Two limiting laws of solution thermodynamics that are widely employed are Henry s law and Raoult s law, which represent vapor—Hquid partitioning behavior in the concentration extremes. These laws are used frequently in equiUbrium problems and apply to a variety of real systems (10). 

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 ... 

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