Nonideal solutions vapor pressures

Now interpret phase X as pure solute then Cs and co become the equilibrium solubilities of the solute in solvents S and 0, respectively, and we can apply Eq. (8-58). Again the concentrations should be in the dilute range, but nonideality is not a great problem for nonelectrolytes. For volatile solutes vapor pressure measurements are suitable for this type of determination, and for electrolytes electrode potentials can be used. 

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. 

Pure-component vapor pressures can be used for predicting solu-bihties for systems in which RaoiilFs law is valid. For such systems Pa = Pa a, where p° is the pure-component vapor pressure of the solute andp is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

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).

Whenever the solute and solvent exhibit significant degrees of mutual attraction, deviations from the simple relationships will be observed. The properties of these nonideal solutions must be determined by the balance of attractive and disruptive forces. When a definite attraction can exist between the solute and solvent, the vapor pressure of each component is normally decreased. The overall vapor pressure of the system will then exhibit significant deviations from linearity in its concentration dependence, as is illustrated in Fig. 10B. 

The thermodynamic development above has been strictly limited to the case of ideal gases and mixtures of ideal gases. As pressure increases, corrections for vapor nonideality become increasingly important. They cannot be neglected at elevated pressures (particularly in the critical region). Similar corrections are necessary in the condensed phase for solutions which show marked departures from Raoult s or Henry s laws which are the common ideal reference solutions of choice. For nonideal solutions, in both gas and condensed phases, there is no longer any direct... 

An important attribute of Equation 5.16 is that the pressure exerted on both phases, Ptot, is common to both isotopomers. The important difference between Equations 5.16 and 5.9 is that the isotopic vapor pressure difference (P/ — P) does not enter the last two terms of Equation 5.16 as it does in Equation 5.9. Also isotope effects on the second virial coefficient AB/B = (B — B)/B and the condensed phase molar volume AV/V are significantly smaller than those on AP/P ln(P7P). Consequently the corrections in Equation 5.16 are considerably smaller than those in Equations 5.9 and 5.10, and can sooner be neglected. Thus to good approximation ln(a") is a direct measure of the logarithmic partition function ratio ln(Qv Q7QvQcO> provided the pressure is not too high, and assuming ideality for the condensed phase isotopomer solution. For nonideal solutions a modification to Equation 5.16 is necessary. 

In the case of nonideal solid solutions, the vacancies (or other point defects) by necessity interact differently with components A and B in their immediate surroundings. Therefore, the alloy composition near a vacancy differs from the bulk composition Nb. This is analogous to the problem of energies and concentrations of gas atoms dissolved in alloys under a given gas vapor pressure [H. Schmalzried, A. Navrotsky (1975)]. Let us briefly indicate the approach to its solution and transfer it to the formulations in defect thermodynamics. 

A better estimate of all attractive forces surrounding a molecule was found in the use of the solubility parameter [32,33], Hancock et al. [34] has reviewed the use of solubility parameters in pharmaceutical dosage form design. The solubility parameter is used as a measure ofthe internal pressures ofthe solvent and solute in nonideal solutions. Cosolvents that are more polar have larger solubility parameters. The square root ofthe cohesive energy density, that is, the square root of the energy of vaporization per unit volume of substance, is known as the solubility parameter and was developed from Hildebrand s Regular Solution Theory in the Scatchard-Hildebrand... 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

If the attraction between the A and B molecules is stronger than that between like molecules, the tendency of the A molecules to escape from the mixture will decrease since it is influenced by the presence of the B molecules. The partial vapor pressure of the A molecules is expected to be lower than that of Raoult s law. Such nonideal behavior is known as negative deviation from the ideal law. Regardless of the positive or negative deviation from Raoult s law, one component of the binary mixture is known to be very dilute, thus the partial pressure of the other liquid (solvent) can be calculated from Raoult s law. Raoult s law can be applied to the constituent present in excess (solvent) while Henry s law (see Section 3.3) is useful for the component present in less quantity (solute). 

Like gases, solutions can also be thought of as ideal. Raoult s law only works for ideal solutions. Ideal solutions are described as those solutions that follow Raoult s law. Solutions that deviate from Raoult s law are nonideal. What makes a solution deviate from ideal behavior The main reason is intermolecular attractions between solute and solvent. When the attraction between solute and solvent is very strong, the particles attract each other a great deal. This makes it more difficult for solute particles to enter the vapor phase. As a result, fewer particles will enter that state and the vapor pressure will be lower than expected. Remember, Raoult s law operates on the assumption that the reason for a decrease in the number of particles leaving the solution is that fewer can be on the surface in order to leave. If, in addition to this, the solute particles are also holding more tightly to the solvent particles, then fewer will leave the surface than expected. The most ideal solutions are those where the solvent and solute are chemically similar. 

Table I lists experimental results, comprising derived values of the fugacity of benzene at known total molarity in the aqueous phase, [B], and known molarity of 1-hexadecylpyridinium chloride [CPC] or sodium dodecylsulfate [SDS]. Fugacities have been calculated from total pressures by subtracting the vapor pressure of the aqueous solution in the absence of benzene from the measured total pressure and correcting for the small extent of nonideality of the vapor phase (15, 22). Results are given for temperatures varying from 25 to 45°C for the CPC systems and 15 to 45°C for the SDS systems.

In this definition, the activity coefficient takes account of nonideal liquid-phase behavior for an ideal liquid solution, the coefficient for each species equals 1. Similarly, the fugacity coefficient represents deviation of the vapor phase from ideal gas behavior and is equal to 1 for each species when the gas obeys the ideal gas law. Finally, the fugacity takes the place of vapor pressure when the pure vapor fails to show ideal gas behavior, either because of high pressure or as a result of vapor-phase association or dissociation. Methods for calculating all three of these follow. 

This equation is good for ideal solutions. For an ionic surfactant solution, the solution is nonideal even at very low surfactant concentration and gives a highly nonlinear dependence of osmotic pressure on concentration. This is expected because ionic surfactants have a high affinity for the interfaces of solution-vapor, solution-solid, and solution-membrane as well as for themselves (i.e., micellization). 

The effect of solvent can be represented without too much additional difficulty for the case of dilute solutions which are nonideal." For such solutions, Henryks law is obeyed with reasonable accuracy, i.e., the solubility of the vapor is proportional to its concentration in solution. For purposes of comparison with our preceding work we can express the vapor pressure of the solute in terms of the deviations of the system from Raoult s law ... 

A very important feature of nonideal solutions is their departure from Raoult s Law in later sections we shall repeatedly examine and make use of the information provided here. Positive and negative departures from Raoult s Law for a binary solution are schematically illustrated in Fig. 3.3.1. Attention is directed to the following facts (a) If one component exhibits a positive (negative) departure from Raoult s Law, the other must do likewise a proof for this statement is to be furnished in Exercise 3.3.2. (b) As the mole fraction x, of component i (i = 1,2) approaches unity (i.e., as the solution becomes very dilute by virtue of a large excess of component i as solvent), the partial pressure P, of the solvent closely approaches the value specified by Raoult s Law as x, 1, Pi —XiPf, where P is the partial pressure of pure i. (c) As the mole fraction of component i approaches zero (i.e., when component i as solute is present at close to infinite dilution) the vapor pressure of the solute does not generally follow Raoult s Law,... 

It is found empirically that the vapor pressure of component 2 nonideal solution may be specified by P2 = 2x2 — x )P2- (a) Determine its activity coefficient relative to the standard state, (b) Find an analytic expression for P in terms of x. (c) Plot out the partial pressures as a function of composition and note their shape. 

FIGURE 11.10 In an ideal solution, a graph of solvent vapor pressure Pi versus mole fraction of solvent Xi is a straight line. Nonideal solutions behave differently examples of positive and negative deviations from the ideal solution are shown. The vapor pressure of pure solvent is P°. 

FIGURE 11.15 Vapor pressures above a mixture of two volatile liquids. Both ideai (biue lines) and non-ideai behaviors (red curves) are shown. Positive deviations from ideal solution behavior are illustrated, although negative deviations are observed for other nonideal solutions. Raoult s and Henry s laws are shown as dilute solution limits for the nonideal mixture the markers explicitly identify regions where Raoult s law and Henry s law represent actual behavior. 

At sufficiently low mole fraction X2, the vapor pressure of component 2 (even in a nonideal solution) is proportional to X2 ... 

But this is not the entire story. As we saw with heats of solution, if the solution is not ideal, the intermolecular forces between molecules will be changed. Either less energy or more energy will be required for molecules to break the intermolecular bonds and leave the surface of the solution. This means that the vapor pressure of a nonideal solution will deviate from the predictions made by Raoult s law. We can make a general prediction of the direction of the deviation based upon heats of solution. If the heat of solution is negative, stronger bonds are formed, fewer molecules are able to break free from the surface and there will be a negative deviation of the vapor pressure from Raoult s law. The opposite will occur for a positive heat of solution. 

The deviation of vapor pressure from Raoult s law can be represented graphically by comparing the mole fractions of solvents with their vapor pressures. Graph 1 below shows only the partial pressure of the solvent as its mole fraction increases. As predicted by Raoult s law, tire relationship is linear. Graph 2 shows the vapor pressure of an ideal solution and the individual partial pressures of each solvent. Notice that the partial pressures add at every point to equal the total pressure. This must be true for any solution. Graph 3 and 4 show the deviations of nonideal solutions. The straight lines are the Raoult s law predictions and the curved lines are the actual pressures. Notice that the partial pressures still add at every point to equal the total pressure. Notice also that a positive heat of solution leads to an increase in vapor pressure, and a negative heat of solution, to a decrease in vapor pressure. 

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