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Pa is the vapor pressure of the component A in its pure state. If Pb is the vapor pressure of pure B, and pb the partial pressure in the mixture, then pb = Pi>xb. This relationship is shown graphically in Fig. 3-1, where the abscissas are the mol per cent of the two components, A and By in the liquid portion. The ordinates are pressures, C being the vapor pressure of pure A, and D that of pure B. The lines AD and BC represent the partial pressures of the components over any mixture, while the line CD is the total pressure of the mixture.

Deviations from Raoult's Law. In view of the above assumptions as to equal molecular size, absence of association, etc., it is not surprising to find Raoult's law honored more in the breach than in the observance. Nonetheless mixtures of some organic liquids, such as benzene-toluene, deviate from it but little. The deviations of mixtures of hydrocarbons of the same series can usually be neglected for a great deal of engineering work, and even for mixtures of a number of series this is often true. For mixtures of aromatic and aliphatic compounds, however, the deviations are often large, though never of the order of magnitude of such mixtures as hydrochloric acid and water, and the like. Organic stereoisomers obey it very closely as would be expected from the considerations upon which it is based. However, the data for the great majority of other liquids, when plotted as shown in Fig. 3-1, deviate largely from the lines BC and AD. When very near points C and D, the deviation for any component is slight if that component is present in very large amount. This ordinarily is expressed by saying that in dilute solution Raoult's law applies to the solvent. Since the deviation from Raoult's law may be either positive or negative, great or small, this graphical generalization serves as a convenient standard of comparison.

Henry's Law. This relation is a modification of Raoult's law which applies to the vapor pressure of the solute in dilute solutions, just as Raoult's law applies to that of the solvent. Henry's law states that the partial pressure of the solute is proportional to its concentration in the solution. In analogy with Raoult's law it may be expressed by the equation

Fig. Raoult's law.

Mol percent A 100

3-1. Schematic diagram for

Fig. Raoult's law.

Mol percent A 100

3-1. Schematic diagram for

where pa = partial pressure of the solute xa = its mol fraction k = an experimentally determined constant Comparison with Raoult's law, pa = Paxaj shows that they differ only in the constant that determines the slope of the line. This constant is the vapor pressure of the pure component in the one case, while it must be experimentally determined in the other. A typical partial pressure curve for one component of a liquid mixture is shown in Fig. 3-2 where BD is the range over which Henry's law applies, while Raoult's law holds over the section EC, where C is the vapor pressure of pure A.

Dalton's Law. The most commonly used rule for relating the composition of the vapor phase to the pressure and temperature is Dalton's law (Ref. 8). It states that the total pressure is equal to the sum of the partial pressures of the components present, i.e.,

where pi, p2y pz = partial pressures of components 1, 2, and 3 w = total pressure For Dalton's law partial pressure is defined as the pressure that would be exerted by a component alone at the same molal concentration that it has in the mixture. If the perfect-gas laws apply to each of the components individually and to the mixture, it can be shown that the partial pressure of any component is equal to the mol fraction times the total pressure, i.e.,

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