Curves, partial pressure vapor-composition

It is difficult to measure partial molar volumes, and, unfortunately, many experimental studies of high-pressure vapor-liquid equilibria report no volumetric data at all more often than not, experimental measurements are confined to total pressure, temperature, and phase compositions. Even in those cases where liquid densities are measured along the saturation curve, there is a fundamental difficulty in calculating partial molar volumes as indicated by... 

What about the upper curve Glad you asked (sigh.). The composition in the vapor is also related to Dalton s Law of Partial Pressures. For an ideal gas... 

Figure 3.10 shows the vapor pressure/composition curve at a given temperature for an ideal solution. The three dotted straight lines represent the partial pressures of each constituent volatile liquid and the total vapor pressure. This linear relationship is derived from the mixture of two similar liquids (e.g., propane and isobutane). However, a dissimilar binary mixture will deviate from ideal behavior because the vaporization of the molecules A from the mixture is highly dependent on the interaction between the molecules A with the molecules B. If the attraction between the molecules A and B is much less than the attraction among the molecules A with each other, the A molecules will readily escape from the mixture of A and B. This results in a higher partial vapor pressure of A than expected from Raoult s law, and such a system is known to exhibit positive deviation from ideal behavior, as shown in Figure 3.10. When one constituent (i.e., A) of a binary mixture shows positive deviation from the ideal law, the other constituent must exhibit the same behavior and the whole system exhibits positive deviation from Raoult s law. If the two components of a binary mixture are extremely different [i.e., A is a polar compound (ethanol) and B is a nonpolar compound (n-hexane)], the positive deviations from ideal behavior are great. On the other hand, if the two liquids are both nonpolar (carbon tetrachloride/n-hexane), a smaller positive deviation is expected.

For these data, assume the vapor phase an ideal gas and plot P vs. x, P vs. yu y,P vs. x, and y2 P vs. x,. Determine Henry s constant for each species from the partial-pressure curves. For each species, over what composition range does Henry s law predict partial pressures within 5 percent of the true values ... 

In both Figs. 22, A and B the uppermost curve gives the total vapor pressure as a function of the composition of the liquid. The corresponding curve as a function of the vapor composition will lie below it in each case, so that the vapor contains more of the constituent the addition of which causes an increase in the total vapor pressure. If an expression for the partial vapor pressure in terms of the mole-fraction composition of the liquid is available (of. 35d), an analogous expression for the vapor composition can be derived by utilizing the relationship based on the postulated ideal behavior of the vapor, i.e., that nJ/n2 is equal to pi/p2 ( 34e), where nJI and N2 refer to the respective mole fractions in the vapor phase. 

The isotherms are plotted on pressure-composition diagrams (Figures 1.3a and b). The curves calculated by Raoult s law are the broken straight lines. They are obtained simply by joining the pure-component vapor pressure points to the zero pressure point on the opposite side to get the partial pressure curves and by joining the two vapor pressure points to get the total pressure curve. The solid lines are obtained by simulation and represent expected behavior of the mixtures. The... 

Toluene and benzene form liquid mixtures that are practically ideal and closely obey Raoult s law for partial pressure. For the binary system of these components, we can use the vapor pressures of the pure liquids to generate the liquidus and vaporus curves of the pressure-composition and temperature-composition phase diagram. The results are shown... 

Sb. Vapor Pressure Curves for Nonideal Systems.—The general nature of the vapor pressure cuiwes showing positive and negative deviations are depicted in Fig. 22, A and B, respectively these results refer to a constant temperature. At any given composition, the slopes of the two partial vapor pressure curves are related by the Duhem-Margules equation. Thus, if the... 

For a maximum or minimum in the total vapor pressure curve, dP/dni must be zoro hence, by equation (35.4), either dps/dNi must be zero, or N pi must equal Nip. The former condition is unlikely, since it would mean that the partial vapor pressure would remain constant in spite of a change of composition, and so for a mairimum or minimum in the total vapor pressure curve NjPi = Nips or N1/N2 = pi/p. If the gases behave ideally, Pi/pt is equal to Ni/i, and the vapor will ve the same composition as the liquid in equilibrium with it, as stated above. 

In Fig. 23 there are shown the relative fugacity (or partial vapor pressure) curves for one constituent of the system quite similar curves will be obtained for the other. The points of horizontal inflection C will, of course, be identical, as regards temperature and composition of the liquid. Similarly, when the conditions are such that two liquid layers are formed, the points a, h and c, for a given temperature, will occur at the same compositions on the curves for the two constituents of the system. 

---