Raoult’s law and

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). 

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. 

To anticipate some of the results to be presented later, it is instructive to compute the equilibrium compn ofPETN at 1600°K. PETN is nearly oxygen-balanced and as will be shown later its Tfr- 1600°K. The empirical formula for PETN is CgHs On. Let X be the number of moles of C03 at equilibrium, and C, H, O the original gram atoms of carbon, hydrogen and oxygen respectively. Then from mass balance and Raoult s law... 

The reason for choosing a Henry s Law standard state can be seen by referring to Figure 6.13, which compares the Henry s law and Raoult s law standard states for CC14 in. yKC H O +. V2CCI4). At high, y2, Raoult s law... 

At this point, you re usually given the temperature versus mole fraction diagram for two miscible liquids (Fig. 140), and you re told it s a consequence of Raoult s Law. Well, yes. But not directly. Raoult s Law is a relationship of pressure, not temperature, versus mole fraction and Raoult s Law is pretty much a straight line. You don t need all your orbitals filled to see that you ve been presented with a temperature versus mole fraction diagram, there are two lines (not one), and neither of them are very straight. 

For the semi-batch stirred tank reactor, the model was based on the following assumptions the reactor is well agitated, so no concentration differences appear in the bulk of the liquid gas-liquid and liquid-solid mass transfer resistances can prevail and finally, the liquid phase is in batch, while hydrogen is continuously fed into the reactor. The hydrogen pressure is maintained constant. The liquid and gas volumes inside the reactor vessel can be regarded as constant, since the changes of the fluid properties due to reaction are minor. The total pressure of the gas phase (P) as well as the reactor temperature were continuously monitored and stored on a PC. The partial pressure of hydrogen (pnz) was calculated from the vapour pressure of the solvent (pvp) obtained from Antoine s equation (pvpo) and 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. 

The compositions of the vapor and liquid phases in equilibrium for partially miscible systems are calculated in the same way as for miscible systems. In the regions where a single liquid is in equilibrium with its vapor, the general nature of Fig. 13.17 is not different in any essential way from that of Fig. I2.9< Since limited miscibility implies highly nonideal behavior, any general assumption of liquid-phase ideality is excluded. Even a combination of Henry s law, valid for a species at infinite dilution, and Raoult s law, valid for a species as it approaches purity, is not very useful, because each approximates real behavior only for a very small composition range. Thus GE is large, and its composition dependence is often not adequately represented by simple equations. However, the UNIFAC method (App. D) is suitable for estimation of activity coefficients. 

Extensive, reviewed tabulated pollutant data also exist (see subsection Solubilities in Sec. 2 of this handbook). Any single tabulated Henry s law constant H is published with its measurement temperature, typically 20 or 25°C. The constant H for a subcritical pollutant (i.e., toluene) is proportional to its pure component vapor pressure Psat, and therefore H is an exponential function of temperature T. Using Henry s and Raoult s laws, a pollutant s constant H for a given ambient design temperature can be estimated by using its tabulated value and its vapor pressure, by extrapolating < 25°C over the ambient temperature range (4°C < T < 50°C), from T to T2 ... 

To derive the relationship between x p and jceq for an ideal solution, we first use Dalton s law of partial pressures and Raoult s law (7.45a, b) to write x p as... 

Using the phase diagram for water and Raoult s law, explain why salt is spread on the roads in winter (even when the temperature is below freezing). 

The Concept of Equilibrium Constants. If the solution is not ideal and Raoult s Law and Dalton s Law are not applicable it is necessary to make an empirical correction. For an ideal solution the relationship between the mole fractions of a given component in the liquid and vapor phases is given by... 

Henry s.Law and Raoult s Law are related in the following manner. Equation 1 is applicable to any component in an ideal solution. However, if the component in question is a gas dissolved in a liquid it is imlikely that the solution will exhibit ideal behavior. Consequently, under these conditions, equation 1 becomes... 

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 ... 

Application of Raoult s law to species i requires a value for Pf at tlie temperature of ap-plieation, and thus is not appropriate for a speeies whose eritieal temperature is less than the temperature of application. If a system of air in eontact with liquid water is presumed at equilibrium, tlien the air is saturated with water. The mole fraction of water vapor in tlie air is usually found from Raoult s law applied to the water with the assimiption that no air dissolves in the liquidphase. Thus, the liquid water is regarded as pure and Raoult s law for the water (species 2) becomes y2 = At 298.15 K (25°C) and atmospherie pressure, this equation yields ... 

Humidity, relating to the quantity of moisture in atmospheric air, is accurately given by equations derived from the ideal-gas law and Raoult s law for H2O. 

Eq. (4) is known as Henry s law, and solute is the Henry s law constant, which is less than Psoiute- Therefore, Henry s law applies to the solute in dilute solutions, and Raoult s law applies to solvent in dilute non-ideal solutions. Note the similarities between Eqs. (1) and (2) and between Eqs. (3) and (4) for the non-ideal dilute solution case. When the solution is ideal, Henry s law becomes identical to Raoult s law, and fsoiute becomes identical to f oiute- When the partial pressures of the solute and the solvent are directly proportional to their molefractions over the entire range, the solution is ideal. In a non-ideal solution, Raoult s law will apply to the solvent over the entire concentration range, whereas Henry s law will apply to the solute in a limited concentration range in which it is in a sufficiently diluted form. 

Comparing equations (2.19) and (2.20), it is clear that the Henry s law and Raoult s law expressions would become identical if k could be equated with 1 /p. Such an equating of terms is valid in the case of ideal solutions only, and in most solutions of gases in liquids, although k is constant, it is not equal to 1 /p. ... 

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