Vapor pressure ideal solutions

Raoult s law The vapor pressure of a substance in equi-Hbrium with a solution containing the substance is equal to the product of the mole fraction of the substance in the solution and the vapor pressure of the pure substance at the temperature of the solution. This law is not appHcable to most solutions but is often approximately applicable to a mixture of closely similar substances, particularly the substance present in high concentration. See drying equilibrium vapor pressure mole solution, ideal vapor pressure. 

Figure 12.15(a) is a plot of vapor pressure versus solution composition for an ideal two-component solution. 

Vapor Pressures of Solutions—The vapor pressure of a solution depends on the vapor pressures of its pure components. If the solution is ideal, Raoult s law (equation 14.3) can be used to calculate the solution vapor pressure. Liquid-vapor equilibrium curves showing either solution vapor pressures (Fig. 14-16) or solution boiling points (Fig. 14-17) as a function of solution composition... 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

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. 

We define Fj to be the mole fraction of component 1 in the vapor phase and fi to be its mole fraction in the liquid solution. Here pj and p2 are the vapor pressures of components 1 and 2 in equihbrium with an ideal solution and Pi° and p2° are the vapor pressures of the two pure liquids. By Dalton s law, Plot Pi P2 Pi/Ptot these are ideal gases and p is propor-... 

Vapor pressure lowering. Equation (8.20) shows that for any component in a binary liquid solution aj = Pj/Pi°. For an ideal solution, this becomes... 

The fugacity coefficient of thesolid solute dissolved in the fluid phase (0 ) has been obtained using cubic equations of state (52) and statistical mechanical perturbation theory (53). The enhancement factor, E, shown as the quantity ia brackets ia equation 2, is defined as the real solubiUty divided by the solubihty ia an ideal gas. The solubiUty ia an ideal gas is simply the vapor pressure of the sohd over the pressure. Enhancement factors of 10 are common for supercritical systems. Notable exceptions such as the squalane—carbon dioxide system may have enhancement factors greater than 10. Solubihty data can be reduced to a simple form by plotting the logarithm of the enhancement factor vs density, resulting ia a fairly linear relationship (52). 

If the hquid phase is an ideal solution, the vapor phase an ideal gas mixture, and the hquid-phase properties independent of pressure, then 7, = 1,... 

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 ... 

To understand the role of solute-solvent interac tions on solubilities and selectivities, it is instructive to define an enhancement factor, E, as the ac tual solubility, y9, divided by the solubility in an ideal gas, so that E = where P is the vapor pressure. This factor is a normahzed... 

Figure 6.5 Vapor pressures for x,c-C6HnCH +. v c-C(,Hi2 at T= 308.15 K. The symbols represent the experimental vapor pressures as follows , vapor pressure of c-C6Hi2 , vapor pressure of c-C6HnCHi , total vapor pressure. The dashed lines represent the ideal solution prediction.

Deviations in which the observed vapor pressure are smaller than predicted for ideal solution behavior are also observed. Figure 6.8 gives the vapor pressure of. (CHjCF XiN +. viCHCfi at T — 283.15 K, an example of such behavior,10 This system is said to exhibit negative deviations from Raoult s law. 

Consider an ideal binary mixture of the volatile liquids A and B. We could think of A as benzene, C6H6, and B as toluene (methylbenzene, C6H< CH ), for example, because these two compounds have similar molecular structures and so form nearly ideal solutions. Because the mixture can be treated as ideal, each component has a vapor pressure given by Raoult s law ... 

Benzene, C6Hh, and toluene, C(,H5CH5, form an ideal solution. The vapor pressure of benzene is 94.6 Torr and that of toluene is 29.1 Torr at 25°C. Calculate the vapor pressure of each of the following solutions and the mole fraction of each substance in the vapor phase above those solutions at 25°C ... 

Dichloroethane, CH.CHCh, has a vapor pressure of 228 Torr at 25°C at the same temperature, 1,1-dichlorotetrafluoroethane, CF.CCUH, has a vapor pressure of 79 Torr. What mass of 1,1-dichloroethane must be mixed with 100.0 g of 1,1-dichlorotctrafluoroethane to give a solution with vapor pressure 157 Torr at 25°C Assume ideal behavior. 

Raoult s law applies to the vapor pressure of the mixture, so positive deviation means that the vapor pressure is higher than expected for an ideal solution. Negative deviation means that the vapor pressure is lower than expected for an ideal solution. Negative deviation will occur when the interactions between the different molecules are somewhat stronger than the interactions between molecules of the same... 

The activities of the various components 1,2,3. .. of an ideal solution are, according to the definition of an ideal solution, equal to their mole fractions Ni, N2,. . . . The activity, for present purposes, may be taken as the ratio of the partial pressure Pi of the constituent in the solution to the vapor pressure P of the pure constituent i in the liquid state at the same temperature. Although few solutions conform even approximately to ideal behavior at all concentrations, it may be shown that the activity of the solvent must converge to its mole fraction Ni as the concentration of the solute(s) is made sufficiently small. According to the most elementary considerations, at sufficiently high dilutions the activity 2 of the solute must become proportional to its mole fraction, provided merely that it does not dissociate in solution. In other words, the escaping tendency of the solute must be proportional to the number of solute particles present in the solution, if the solution is sufficiently dilute. This assertion is equally plausible for monomeric and polymeric solutes, although the... 

Relative lowering of the solvent s vapor pressure. The equilibrium vapor pressure of the solvent over a dilute ideal solution p obeys the equation... 

Solid-Fluid Equilibria The solubility of the solid is very sensitive to pressure and temperature in compressible regions, where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature often exhibit fairly simple linear behavior (Fig. 20-19). To understand the role of solute-solvent interactions on sofubilities and selectivities, it is instructive to define an enhancement factor E as the actual solubihty divided by the solubility in an ideal gas, so that E = ysP/Pf, where P is the vapor pressure. The solubilities in CO2 are governed primarily by vapor pressures, a property of the solid... 

The dissolution of a solute into a solvent perturbs the colligative properties of the solvent, affecting the freezing point, boiling point, vapor pressure, and osmotic pressure. The dissolution of solutes into a volatile solvent system will affect the vapor pressure of that solvent, and an ideal solution is one for which the degree of vapor pressure change is proportional to the concentration of solute. It was established by Raoult in 1888 that the effect on vapor pressure would be proportional to the mole fraction of solute, and independent of temperature. This behavior is illustrated in Fig. 10A, where individual vapor pressure curves are... 

Fig. 10 Dependence of vapor pressure of a solution containing a volatile solute, illustrated for (A) an ideal solution and (B) a nonideal solution and shown as a function of mole fraction of the solute. Individual vapor pressure curves are shown for the solvent (0) the solute ( ), and for the sum of these (X).

Equations 63, 68, and 70). Note that if YA = 0-9, the free energy of solvation would be less negative by only 0.07 kcal/mol. Thus, when the solution is nearly ideal (y A 1). the free energy of solvation is primarily determined by the vapor pressure. 

The vapor pressure of an ideal solution is 450. mm Hg. If the vapor pressure of the pure solvent is 1000. mm Hg, what is the mole fraction of the nonvolatile solute ... 

Background If a nonvolatile solid is dissolved in a liquid, the vapor pressure of the liquid solvent is lowered and can be determined through the use of Raoult s Law, Pi = X 0. Raoult s Law is valid for ideal solutions wherein AH = 0 and in which there is no chemical interaction among the components of the dilute solution (see Figure 1). 

Not all solutions obey Raoult s law. Any solution that follows Raoult s law is an ideal solution. However, many solutions are not ideal solutions. A solution may have a vapor pressure higher than predicted by Raoult s law. A solution may have a vapor pressure lower than predicted by Raoult s law. Solutions with a... 

A solution of pentane, C5Hi2, in carbon tetrachloride, CCI4, is nearly ideal. The vapor pressure of pentane is 450 mm Hg at 20°C, and the vapor pressure of carbon tetrachloride is 87 mm Hg at this temperature. What is the mole fraction of carbon tetrachloride in the vapor over an equimolar solution of these two liquids ... 

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