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**Unformatted text preview: **Chapter 11 Liquid-Liquid Equilibrium When two liquids are mixed, depending on the temperature and/or composition, either they are completely miscible in each other and form a single phase or, they are partially miscible (or, totally immiscible) in each other and form two separate phases. In the case of completely miscible, i.e., single phase systems, the equations developed in Chapter 6 are applicable. What we are interested in this chapter is the case when a liquid is partially miscible (or totally immiscible) in another liquid. First, the reason for making liquids partially miscible in each other will be investigated. Then, the procedure to determine the compositions in two separate liquid phases that are in equilibrium with each other will be described. Such equilibrium data are needed in various chemical and physical processes such as liquid-liquid extraction and tertiary oil recovery. 11.1 STABILITY OF MULTICOMPONENT LIQUID MIXTURES For thermodynamically allowable changes at constant temperature and pressure, the criterion ( dG ) T,P (11.1-1) indicates that all irreversible changes taking place at constant temperature and pressure must decrease the total Gibbs energy of the system. When the system reaches equilibrium, no further changes can occur and Gibbs energy reaches its minimum value. Let us consider mixing of two liquids, 1 and 2, at constant temperature and pressure. The Gibbs energy of this binary mixture is G mix = n 1 e G 1 + n 2 e G 2 + G mix (11.1-2) If the Gibbs energy of the mixture is lower than the summation of the Gibbs energies of pure components, then components 1 and 2 will be miscible (totally or partially) in each other. This statement is mathematically expressed as G mix < n 1 e G 1 + n 2 e G 2 (11.1-3) or, in other words, G mix < (11.1-4) which is the criterion for miscibility (partial or complete). The Gibbs energy of mixing is given by e G mix = e H mix | {z } A T e S mix | {z } B (11.1-5) Since mixing increases the degree of disorder within the system, the entropy change on mixing, e S mix , is always positive. Thus, the term B in Eq. (11.1-5) is always positive. The heat of mixing, e H mix , is related to the energetic e f ects. In order to make a mixture of 1 and 2 from 343 pure components, it is necessary to break 1-1 ( E 1 ) and 2-2 ( E 2 ) bonds and form 1-2 ( E 12 ) bonds. Depending on the magnitude of the interactions between like and unlike molecules, e H mix may take positive or negative values. Therefore, it is necessary to consider the following two cases. Case (i): Exothermic mixing ( e H mix < ) When e H mix < , interactions between unlike molecules are greater than those of like molecules, i.e., E 12 > E 1 + E 2 2 (11.1-6) In this case, e G mix is negative for all compositions of components 1 and 2. Therefore, liquids are completely miscible in each other and form a single phase. This situation is illustrated in Figure 11.1....

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