Ideal-liquid mixture

In Equation (15), the third term is much more important than the second term. The third term gives the enthalpy of the ideal liquid mixture (corrected to zero pressure) relative to that of the ideal vapor at the same temperature and composition. The second term gives the excess enthalpy, i.e. the liquid-phase enthalpy of mixing often little basis exists for evaluation of this term, but fortunately its contribution to total liquid enthalpy is usually not large. 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Benzene and toluene form an ideal liquid mixture. A mixture composed of 50 mol % benzene is used in a chemical plant. The temperature is 80°F, and the pressure is 1 atm. 

Since the mole fractions are qnantities that are smaller than nnity, their logarithms are negative, AmSab is positive, and AmGab is negative, the process of mixing being a spontaneons process under the usual conditions. Eqnations (2.14) and (2.15) snffice to define an ideal (liquid) mixture. 

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. 

Ideal Liquid Mixtures. Raoult s Law. Ideal Liquid Mixture of Involatile B and Volatile A... 

This serves to define an ideal liquid mixture of such a system, stated simply ... 

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... 

The condition (compare Frame 32, section 32.2) that the liquids form an ideal liquid mixture is that their vapour pressure P (Figure 33.1(b)) must be such that Raoult s Law (Frame 32, equation (32.8) for solvent and involatile solute) is obeyed. In its extended form, for the present case of two volatile liquids A and B, this latter Law takes the extended form ... 

In this frame we consider, in some further detail the pressure-composition properties of a binary ideal liquid mixture at constant temperature, T, as defined in Figure 34.1. Here we assume that both components are in the liquid phase and that they are volatile and miscible (dissolve in each other (Frame 33)). Whilst the treatment here is not exhaustive it is intended to give the reader some insight into how to apply the principles developed so far to the ideal vapour and ideal liquid phases of a system. 

Binary Ideal Liquid Mixture. Dependence of Vapour Pressure,... 

Figure 34.2 Pressure-composition diagram for binary ideal liquid mixture. Dependence of P on mole fraction (xA,xB) of liquid present. Note. Liquid B is more volatile than liquid A since PB > PA - it exerts a higher (saturated) vapour pressure.

Figure 34.4 Pressure-composition diagram for Ideal Liquid Mixture of toluene and benzene showing liquid and vapour compositions. The region of the plot enclosed and labelled liquid + vapour corresponds to the area of stability of both liquid and vapour.

General Principles of Equating Chemical Potentials for Components in Different Phases at Equilibrium the Ideal Liquid Mixture Consisting of Liquid Phases... 

Consider now a more complicated system, as is shown in Figure 35.6. Here the mixture of liquids present obey Raoult s Law (Frames 32, equation (32.8) and 33, equation (33.6)) and hence they constitute an ideal liquid mixture. On the basis of this law, for each component, i ... 

Figure 35.6 (a) Ideal liquid mixture, at equilibrium at temperature, 7, containing a component, i, which exerts a partial pressure. Pi, in the vapour phase and which, in the liquid phase behaves ideally, so that Raoult s law holds p = x,.P. (b) Shows the system (a) under conditions where x) = 1 (i.e. i is the sole component). The vapour pressure is then equal to P. ... 

In equation (35.16), Frame 35 we saw that for a multicomponent ideal liquid mixture (Frame 35, Figure 35.6(b) containing a number of components, then for each component i ... 

The factor that makes an ideal dilute solution different from an ideal liquid mixture is the fact that the solute (in this case A) follows Henry s Law (Frame 33, section 33.2) which takes the form ... 

Chemical Potential, ai liquid mixture) for a Rea (Non-Ideal) Liquid Mixture. Activity, a... 

We begin by restating the equation (35.16), Frame 35 that we established to hold for the pure liquid solvent in an ideal liquid mixture, this time writing /u.(i)(Ilqmd mixture) as (ldeai liquid mixture) Thg chemical potential, /x(i)(Klealhqmdmlxture), for an jdeai liquid mixture is then ... 

In real (non-ideal) liquid mixtures quite often equation (39.1) is simply not valid. Nor is the one (i.e. equation (36.8), Frame 36) holding for the solute in ideal dilute solution, which took the form ... 

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 39.2 The graphs show plots of (a) /r(i)

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