Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Mixtures ideal solutions

When a reaction occurs in an ideal system (i.e., in ideal gas mixture, ideal solution, or ideal adsorbed layer), then rs and r s in (44) are determined by simple mass action law. We shall call linear the stages whose rate, = rs - r s, depends linearly on the concentrations of intermediates (including free sites of the surface) the stages whose rate depends nonlinearly on the concentrations of intermediates (i.e., includes squares of concentrations of... [Pg.195]

An interesting question, which is closely related to the VPIE, is the deviation of isotopic mixtures from the ideal behavior. Isotopic mixtures, that is, mixtures of isotopic molecules (e.g., benzene and deuterated benzene), have long been considered as textbook examples of ideal solutions statistical theory predicts that mixtures of very similar species, in particular isotopes, will be ideal the only truly ideal solutions would thus involve isotopic species molecules which differ only by isotopic substitution... form ideal solutions except for isotope mixtures, ideal solutions will occur rather rarely we expect binary solutions to have ideal properties when the two components are isotopes of each other. ... [Pg.711]

Figure III-9u shows some data for fairly ideal solutions [81] where the solid lines 2, 3, and 6 show the attempt to fit the data with Eq. III-53 line 4 by taking ff as a purely empirical constant and line 5, by the use of the Hildebrand-Scott equation [81]. As a further example of solution behavior, Fig. III-9b shows some data on fused-salt mixtures [83] the dotted lines show the fit to Eq. III-SS. Figure III-9u shows some data for fairly ideal solutions [81] where the solid lines 2, 3, and 6 show the attempt to fit the data with Eq. III-53 line 4 by taking ff as a purely empirical constant and line 5, by the use of the Hildebrand-Scott equation [81]. As a further example of solution behavior, Fig. III-9b shows some data on fused-salt mixtures [83] the dotted lines show the fit to Eq. III-SS.
If an ideal solution is formed, then the actual molecular A is just Aav (and Aex = 0). The same result obtains if the components are completely immiscible as illustrated in Fig. IV-21 for a mixture of arachidic acid and a merocyanine dye [116]. These systems are usually distinguished through the mosaic structure seen in microscopic evaluation. [Pg.140]

Let us consider a mixture forming an ideal solution, that is, an ideal liquid pair. Applying Raoult s law to the two volatile components A and B, we have ... [Pg.6]

There is a parallel between the composition of a copolymer produced from a certain feed and the composition of a vapor in equilibrium with a two-component liquid mixture. The following example illustrates this parallel when the liquid mixture is an ideal solution and the vapor is an ideal gas. [Pg.429]

Since the 0 s are fractions, the logarithms in Eq. (8.38) are less than unity and AGj is negative for all concentrations. In the case of athermal mixtures entropy considerations alone are sufficient to account for polymer-solvent miscibility at all concentrations. Exactly the same is true for ideal solutions. As a matter of fact, it is possible to regard the expressions for AS and AGj for ideal solutions as special cases of Eqs. (8.37) and (8.38) for the situation where n happens to equal unity. The following example compares values for ASj for ideal and Flory-Huggins solutions to examine quantitatively the effect of variations in n on the entropy of mixing. [Pg.517]

One way to describe this situation is to say that the colligative properties provide a method for counting the number of solute molecules in a solution. In these ideal solutions this is done without regard to the chemical identity of the species. Therefore if the solute consists of several different components which we index i, then nj = S nj j is the number of moles counted. Of course, the total mass of solute in this case is given by mj = Sjnj jMj j, so the molecular weight obtained for such a mixture is given by... [Pg.543]

Mixtures. A number of mixtures of the hehum-group elements have been studied and their physical properties are found to show Httle deviation from ideal solution models. Data for mixtures of the hehum-group elements with each other and with other low molecular weight materials are available (68). A similar collection of gas—soHd data is also available (69). [Pg.9]

For ideal solutions (7 = 1) of a binary mixture, the equation simplifies to the following, which appHes whether the separation is by distillation or by any other technique. [Pg.84]

Equations for the mixture properties of an ideal solution foUow immediately. [Pg.497]

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,... [Pg.499]

Chlorobenzene mixtures behave in distillation as ideal solutions. In a continuous distillation train, heat may be conserved by using the condensers from some units as the reboilers for others thereby, saving process energy. [Pg.48]

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 ... [Pg.235]

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. [Pg.235]

Ideal solution behavior is often approximated by solutions comprised of molecules not too different in size and of the same chemical nature. Thus, a mixture of isomers conforms very closely to ideal solution behavior. So do mixtures of adjacent members of a homologous series. [Pg.520]

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. [Pg.1274]

The fugaeity in Equation 2-39 is that of the eomponent in the equilibrium mixture. However, fugaeity of only the pure eomponent is usually known. It is also neeessary to know something about how the fugaeity depends on the eomposition in order to relate the two, therefore, assumptions about the behavior of the reaetion mixture must be made. The most eommon assumption is that the mixture behaves as an ideal solution. In this ease, it is possible to relate the fugaeity, f, at equilibrium to the fugaeity of the pure eomponent, f, at the same pressure and temperature by... [Pg.66]

V = V . In such a case, V can be obtained directly from the ideal gas law, without recourse to measurement, and hence, the volumetric composition can be readily computed. On the other hand, in non-ideal (i.e., real) mixtures and solutions,... [Pg.326]

Therefore, it is a sufficient condition for ideal solution behavior in a binary mixture that one component obeys Raoult s law over the entire composition range, since the other component must do the same. [Pg.277]

Equation (7.6) is the starting point for deriving equations for Amix2[j[, the change in Zm for forming an ideal mixture. For the ideal solution, 7r.( = 1 and equation (7.6) becomes... [Pg.326]

The excess molar thermodynamic function Z is defined as the difference in the property Zm for a real mixture and that for an ideal solution. That is,... [Pg.328]

The extent of deviation from ideal solution behavior and hence, the magnitude and arithmetic sign of the excess function, depend upon the nature of the interactions in the mixture. We will now give some representative examples. [Pg.330]

In our discussion of (vapor + liquid) phase equilibria to date, we have limited our description to near-ideal mixtures. As we saw in Chapter 6, positive and negative deviations from ideal solution behavior are common. Extreme deviations result in azeotropy, and sometimes to (liquid -I- liquid) phase equilibrium. A variety of critical loci can occur involving a combination of (vapor + liquid) and (liquid -I- liquid) phase equilibria, but we will limit further discussion in this chapter to an introduction to (liquid + liquid) phase equilibria and reserve more detailed discussion of what we designate as (fluid + fluid) equilibria to advanced texts. [Pg.412]

Since Raoult s law activities become mole fractions in ideal solutions, a simple substitution of.Y, — a, into equation (6.161) yields an equation that can be applied to (solid + liquid) equilibrium where the liquid mixtures are ideal. The result is... [Pg.419]

The reason is that classical thermodynamics tells us nothing about the atomic or molecular state of a system. We use thermodynamic results to infer molecular properties, but the evidence is circumstantial. For example, we can infer why a (hydrocarbon + alkanol) mixture shows large positive deviations from ideal solution behavior, in terms of the breaking of hydrogen bonds during mixing, but our description cannot be backed up by thermodynamic equations that involve molecular parameters. [Pg.497]

Such a rough comparison of real mixtures with ideal solutions is definitely not perfect but it allows the authors of [230] to proceed using conventional theory. The general conclusion following this comparison is that the quantum. /-diffusion model just slightly differs from its... [Pg.184]

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 ... [Pg.459]

Which of the following mixtures would you expect to show a positive deviation, negative deviation, or no deviation (that is, form an ideal solution) from Raoult s law Explain your conclusion, (a) methanol, CH3OH, and ethanol, CH3CH2OH (b) HF and H20 (c) hexane, C6H14, and H20. [Pg.471]

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... [Pg.999]

As previously noted, the equilibrium constant is independent of pressure as is AG. Equation (7.33) applies to ideal solutions of incompressible materials and has no pressure dependence. Equation (7.31) applies to ideal gas mixtures and has the explicit pressure dependence of the F/Fq term when there is a change in the number of moles upon reaction, v / 0. The temperature dependence of the thermodynamic equilibrium constant is given by... [Pg.236]

If the reaction mixture can be considered to be an ideal solution, the activity coefficients are... [Pg.271]


See other pages where Mixtures ideal solutions is mentioned: [Pg.214]    [Pg.6]    [Pg.7]    [Pg.497]    [Pg.520]    [Pg.542]    [Pg.52]    [Pg.80]    [Pg.82]    [Pg.268]    [Pg.271]    [Pg.272]    [Pg.424]    [Pg.662]    [Pg.999]    [Pg.803]    [Pg.227]    [Pg.236]   
See also in sourсe #XX -- [ Pg.21 ]

See also in sourсe #XX -- [ Pg.21 ]




SEARCH



Ideal mixtures

Ideal solution

Mixtures solutions

Solute mixtures

Solution ideal solutions

© 2024 chempedia.info