Ideal binary system

Inequalities 54 and 56 follow from to each other on the basis of the reciprocity relationship 

Prigoginc and Defay (1954) have shown the validity of Equations 46 or 47 to cau.se the validity of Equations 39 and 40, henr , the diffusional stability condition (any of Equations 46, 47, 53-56) is a necessary and sufficient stability condition of the ono-phase state of multicomponent systems (including the metastable state). 

The state equation of an ideal gas is the well-known Clapeyron-Clausius equation 

For a one-Gompoiieiit sysleiii under isothermal conditions and without any phase transition, Equation 1.1.1-20 reduces to 

Substitution of V from Equation 1 into Equation 2 and integration of the latter from a certain initial state to the current state lead to 

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Examples of ideal binary systems ate ben2ene—toluene and ethylben2ene—styrene the molecules ate similar and within the same chemical families. Thermodynamics texts should be consulted before making the assumption that a chosen binary or multicomponent system is ideal. When pressures ate low and temperatures ate at ambient or above, but the solutions ate not ideal, ie, there ate dissimilat molecules, corrections to equations 4 and 5 may be made ... 

The extension of the simple ideal binary system considered in the preceding section to a nonideal multicomponent column is not diflicult. The only changes that have to be made to the basic structure of the solution algorithm arc ... 

The binary system which is easiest to describe is the so-called ideal binary system . As you can tell from the inverted commas, such a system does not really exist, but there are systems which come very close. In an ideal system the components in the S and L phase are completely miscible. In order to be so in the S phase, the substances need to be isomorphous, i.e. possess the same crystal structure. This is often accompanied by an analogous chemical structure. Some examples of these systems are silver (Ag) / gold (Au) and sodium nitrate (NaN03) / calcium carbonate (CaC03). 

A, B, C, and D have been calculated in the preceding example. The point A at 22.75 psia represents the computed bubble-point pressure for a solution whose mole fraction of C4H10 is 0.50. Point B represents the composition of the vapor at the bubble point. Similarly, the points C and D represent the bubble point and composition of the vapor at the bubble point for a solution whose mole fraction of C4Hio>is 0.75. The points E and jP. represent the vapor pressure of pure butane and pure propane, respectively, at 0° F. The line FACE is tile bubble-point line and the line FBDE is the dew-point line. It is obvious that a pressure-composition diagram for any ideal binary system could be calculated in this manner and would serve to describe the phase behavior quantitatively. 

The KBIs for ideal binary systems are given by the expressions [11] ... 

However, Matteoli and Lepori and Mateolli observed that An ij calculated with Eq. (18) has nonzero values for ideal binary systems, even though they are expected to vanish. It was also noted that there are many systems for which aU the Kirkwood-Buff integrals in binary systems are negative in certain ranges of composition. As a result, in such cases aU A , would be negative, and this is not plausible. 

FIGURE 12.5 Equilibrium y-x diagram for ideal binary system i-j. 

Operating Line and "Equilibrium" Curve. Both terms are of importance for the graphical solution of a separation problem, i.e., for the graphical determination of the number of stages of a cascade. This method has been developed for the design of distillation columns by MacCabe and Thiele and should be well known. For all cases, the operating line represents the mass and material balances. In distillation, the equilibrium curve represents the thermodynamical va-por/liquid equilibrium. For an ideal binary system, the equilibrium curve can be calculated from Raoult s law and the saturation-pressure curves of the pure components of the mixture. In all other cases, however, for example, for all membrane processes, the equilibrium curve does not represent a thermodynamical equilibrium at all but will represent the separation characteristics of the module or that of the stage. 

An ideal surface phase may be characterized by the criteria fi — 1 and Af = A°. It is obvious that these conditions imply that the surface phase is both uniform and ideal in the ordinary sense and in addition that t is a constant. From Eqs. (69) and (71), we may deduce that for an ideal binary system the following inequality always holds if yj > yl... 

Szapiio [207] derived an equation which can be used to calculate the composition of the liquid in the flask and of the reflux at the n-th plate as a function of pressure for ideal binary systems at full reflux. 

MCB forms ideal binary systems with both toluene and ethylbenzene and these are therefore suitable as a test mixture for columns. The toluene mixture is appropriate for columns of 5-20 actual trays and the ethylbenzene for 15-40 actual trays. The latter is also suitable for testing at pressures of 100 mm Hg and more. 

Example 8.5 1 I Constitutive flux equation for a non-ideal binary system For example, for a binary system, we have the following diffusion equations for the components 1 and 2, obtained from eq. (8.5-9) for i = 1 and 2 ... 

When A = 0 (that is ideal SYstem), the above equation reduces to the Maxwell-Stefan equation for ideal binarY SYStems. 

Fickian model. The Fickian model is a widely accepted model for diffusion, which means no one will laugh if you use it. It works well for ideal and close to ideal binary systems and can be used for nonideal binary systems if data are available. Most diffusivity data and correlations for mass-transfer coefficients are based on the Fickian model. This model is very difficult to use for nonideal ternary systems and can require negative diffusion coefficients to predict data. This model works well for dilute binary systems. 

Figure 1-19 shows the three diagrams for an ideal binary mixture (for example, a nearly ideal binary system is benzol-toluene). The pressure diagram for an ideal mixture may be described by Raoult s law. The partial pressuresp, (Xj),Piixi) and the overall pressure p(xi) are straight lines. 

Looking at the concentration dependence of the Gibbs energy, it is easier to understand the formation of two liquid phases. For an ideal binary system, the molar Gibbs energy at a given composition (see Chapter 4) can be calculated by... 

To calculate the vapor composition, it is necessary to develop an equilibrium relationship. For the distillation of an ideal binary system of components A and C, the equilibrium relationship is given by ... 

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