Real ideal mixture

For a real vapor mixture, there is a deviation from the ideal enthalpy that can be calculated from an equation of state. The enthalpy of the real vapor is given by... 

A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. 

Figure 9 provides a comparison of the predictions of empirical methods with Wormald s data for a 50/50 mole percent mixture of steam and methane. As can be seen, the frequently used artifices of calculating mixture enthalpies by blending the pure component enthalpies at either total or partial pressures are very inaccurate. Likewise, the assumption of ideal gas enthalpy for the real gas mixture, equivalent to a zero enthalpy departure on the diagram, is an equally poor method. 

PHYSICAL NATURE OF CHEMICAL POTENTIAL IN IDEAL AND REAL GAS MIXTURES... 

Following the philosophy of Section 5.8.1, it is also possible (if uninformative) to express /jlt for real gas mixtures in a form that mimics the ideal gas expression (6.57), namely,... 

Two further crude approximations have been used for the virial equation of state. The first is that the virial coefficients combine linearly. This combination of constants results in an equation of state that is additive in the properties of the pure components. In such a mixture Dalton s and Amagat s laws still hold, and the mixture may be called an ideal mixture of real gases. The assumption is probably the crudest that can be used and is... 

We shall discuss first the concept of the ideal liquid mixture (section 32.2) [i.e. one whose vapour pressure characteristics are such that they follow Raoult s Law (see below)] and contrast this with a real liquid mixture [i.e. one where non-ideal behaviour is exhibited and for which Raoult s Law is no longer obeyed]. We can then compare this concept of an ideal and real liquid mixture with that of ideal and real gases (Frame 31) showing that the ideas are fairly similar in nature and that parallels can be drawn and applied to their distinction and also that their definitions refer to limiting laws which apply. 

Here Raoult s law acts as the limiting demarcation criterion between ideal and real or non-ideal liquid mixtures. As Figure 32.4(a) indicates, in practice, non-ideal (real) liquid mixtures do not show linear behaviour but their vapour pressure deviates from (i.e. above or below) the line AB. 

Ideal Liquid Mixtures Real Liquid Mixtures... 

What we would like to be able to do is to determine for a real (i.e. non-ideal) liquid mixture what effective concentration we need to use in order to adapt the ideal equation (39.1) to give the same chemical potential as the real liquid mixture. Now, for gases, we have established (Frame 38) that ... 

Figure 39.4 shows that if = 1 then a = X (i.e. the effective mole fraction corresponds to the actual mole fraction as made up) then we have ideal behaviour. As discussed before (Frame 33, Figure 33.2) both positive and negative deviations from ideality can occur in real liquid mixtures. 

Activity as a function was introduced by Lewis in 1908, and a full description was given by Lewis and Randall [74] in 1923. The activity a of a substance i can be defined [75.76] as a value corresponding to the mole fraction of the substance i in the given phase. This value is in agreement with the thermodynamic potential of the ideal mixture and gives the real value of this potential. 

For an ideal mixture, the enthalpy of mixing is zero and so a measured molar enthalpy of mixing is the excess value, HE. The literature concerning HE -values is more extensive than for GE-values because calorimetric measurements are more readily made. The dependence of HE on temperature yields the excess molar heat capacity, while combination of HE and GE values yields SE, the molar excess entropy of mixing. The dependences of GE, HE and T- SE on composition are conveniently summarized in the same diagram. The definition of an ideal mixture also requires that the molar volume is given by the sum, Xj V + x2 V2, so that the molar volume of a real mixture can be expressed in terms of an excess molar volume VE (Battino, 1971). 

The new reference state reduces to GV in the limiting case of an ideal mixture, but also satisfies the volume conservation condition. The following differences exist between the ML and SR excesses the ML excesses have non-zero values if either the partial molar volumes differ from the ideal ones or D = + Xi d a.yi/dxi)pj 7 1, where P represents the pressure and y- is the activity coefficient of component v, the SR excesses have non-zero values only if D 1. The present reference state is a hypothetical one similar to the ideal state, in which the molar volume, the partial molar volumes and the isothermal compressibility are the real ones. 

The conventional method based on eq 1 provides umeason-able results, such as nonzero excesses (or deficits) for single components, all negative excesses for an ideal binary mixture A—B when aU three KBIs are negative, and all negative excesses in some concentration ranges for some real binary mixtures. 

As to liquid mixtures, it is even more difficult to predict the p-V-T properties of liquid mixtures than of real gas mixtures. Probably more experimental data (especially at low temperatures) are available than for gases, but less is lcnown bburth estimation of the p-V T properties of liquid mixtures. For compounds with like molecular structures, such as hydrocarbons of similar molecular weight, called ideal liquids, the density of a liquid mixture can be approximated by assuming that the specific volumes are additive ... 

In Section 3.1.3.1., it was shown that the ideal mixing of components is connected neither with volume contraction nor with volume dilatation. However, in real binary mixtures, positive as well as negative deviations from the ideal behavior can be observed. The dependence of molar volume on composition is usually expressed in the polynomial form... 

Note that this is not a theoretical ideal gas. We take the limit P —> 0 for a real gas mixture. Uy R) is the pair potential for the ij pair. We assume that the pair potential has a square-well form, i.e.,... 

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