Category: Liquid Phase Equilibria

P14.1. It has been suggested that the phase diagram of the hexane + furfural system can be adequately represented by the Margules one-parameter equation, where ln γi = xj2 · 800/T (K). Estimate the liquid-liquid mutual solubilities of each component in each liquid phase at 298 K. (ANS. ~10% each, by symmetry) P14.2. Suppose the solubility of water in ethyl…

Solid-liquid equilibria (SLE) calculations begin just as VLE and LLE calculations, by equating fugacities. From Eqn. 11.13, . The next step is to equate  and derive an equation to solve for temperature or composition depending on the problem statement. We have deliberately avoided substituting , however, as we did for VLE and LLE. This is because pure components below…

Numerical procedures using Excel and MATLAB are provided in online supplements. The Excel procedure extends Actcoeff.xlsx and explains details on setting up the macro or circular reference for binary or ternary mixtures. The MATLAB Rachford-Rice procedure can be extended more easily to multicomponent mixtures.

Referring back to Fig. 14.1, we may wish to find the combination of x1 and A12 where the system just begins to phase-split. This is known as a liquid-liquid critical point. If it is the highest T where two phases exist (called the UCST, upper critical solution temperature), then we must seek x1 where the concavity is equal to zero at only one composition…

Graphical representation of ternary LLE data is important for design of separation processes. For ternary systems, triangular coordinates simultaneously represent all three mole fractions, or alternatively, all three weight fractions. Triangular coordinates are shown in Fig. 14.6(a), with a few grid lines displayed. The fraction of component A is represented by lines parallel to the BC axis: Along , the composition…

Liquid-liquid mutual solubilities in partially miscible systems change with temperature at a given pressure. Whether the solubilities increase or decrease can be due to a number of factors including hydrogen bonding. When one species H-bonds and the other does not, then as the temperature is raised and hydrogen bonds are broken, the fluids become more “similar,”…

A special case of VLLE is obtained when one of the liquid-phase components is almost entirely insoluble in other components, and all other components are essentially insoluble in it, as occurs with many hydrocarbons with water. When a mixture forms two liquid phases, the mole fractions sum to unity in each of the phases. When…

Usually we require higher precision than obtained by graphing the Gibbs energy. Furthermore, we may encounter multicomponent mixtures, for which the extension of the above method is not straightforward. We can develop an entirely general method for computing the phase partitioning given relative activities in Eqn 14.1. In Fig. 14.4 are plotted the activities for the water +…

 shows the contributions to the Gibbs energy of a mixture for A12 = 3 of Fig 14.1. The pure component Gibbs energies do not contribute to the curvature in the Gibbs energy of a mixture, and therefore are not needed for LLE calculations—we need just ΔGmix. In principle, all that is required to make predictions of LLE partitioning…

Expressions for activity coefficients are the same for LLE as they are for VLE. The difference is that multiple liquid compositions can give the same activities or total pressure at a given temperature. This behavior is implied in Fig. 11.10, where we commented that the calculated lines indicate LLE. The time has come to analyze why…