Phase equilibrium less liquid phases

The effect of external pressure on the rates of liquid phase reactions is normally quite small and, unless one goes to pressures of several hundred atmospheres, the effect is difficult to observe. In terms of the transition state approach to reactions in solution, the equilibrium existing between reactants and activated complexes may be analyzed in terms of Le Chatelier s principle or other theorems of moderation. The concentration of activated complex species (and hence the reaction rate) will be increased by an increase in hydrostatic pressure if the volume of the activated complex is less than the sum of the volumes of the reactant molecules. The rate of reaction will be decreased by an increase in external pressure if the volume of the activated complex molecules is greater than the sum of the volumes of the reactant molecules. For a decrease in external pressure, the opposite would be true. In most cases the rates of liquid phase reactions are enhanced by increased pressure, but there are also many cases where the converse situation prevails. 

It should be mentioned that DSC and NMR do not measure the same parameters, and in this way, these techniques are complementary. DSC is a dynamic method, which gives information about the transitions between different phases of lipids, whereas NMR allows quantitation of liquid and solid phases at equilibrium. Indeed, NMR and DSC methods give different values for the solid fat index (SFI) (Walker and Bosin, 1971 Norris and Taylor, 1977) NMR values are much lower than those given by DSC below 20°C. For example, for milk fat at 5°C, DSC and NMR indicate 78.1% and 43.7% solid fat, respectively. The observed difference can be explained by the presence of an amorphous phase which, due to its melting enthalpy, is seen as a solid by the DSC method. Using time-domain NMR, Le Botlan et al. (1999) showed that in milk fat samples, an intermediate component exists between the solid and liquid phases, constituting about 6% of an aged milk fat. 

V = TOTAL MOLES OF VAPOR AT EQUILIBRIUM CONDITIONS Ni = 1 )LES FRACTION OF COMPONENT i IN THE FEED STREAM Li = TOTAL MOLES OF COMPONENT i IN THE LIQUID PHASE Vi = TOTAL MOLES OF COMPONENT i IN THE VAPOR PHASE... 

The principle of Le Chatelier-Braun states that any reaction or phase transition, molecular transformation or chemical reaction that is accompanied by a volume decrease of the medium will be favored by HP, while reactions that involve an increase in volume will be inhibited. Qn the other hand, the State Transition Theory points out that the rate constant of a reaction in a liquid phase is proportional to the quasi-equilibrium constant for the formation of active reactants (Mozhaev et al., 1994 Bordarias, 1995 Lopez-Malo et al., 2000). To fully imderstand the dynamic behavior of biomolecules, the study of the combined effect of temperature and pressure is necessary. The Le Chatelier-Braim Principle states that changes in pressure and temperature cause volume and energy changes dependent on the magnitude of pressure and temperature levels and on the physicochemical properties of the system such as compressibility. "If y is a quantity characteristic of equilibrium or rate process, then the influence of temperature (7 and pressure (P) can be written as ... 

Using Le Chatelier s principle, one can qualitatively predict the effect of pressure on an equilibrium melting point. The increase in pressure results in a decrease in the volume of the system. For most materials, the specific volume of the liquid phase is less than that of the solid phase, so that an increase in pressure would have the effect of shifting the equilibria to favor the solid phase. This shift will have the observable effect of raising the melting point. For those unusual systems where the specific volume of the liquid exceeds that of the solid phase, then the melting point will be decreased by an increase in pressure. 

The introductory Section 3.1.2.5 in Chapter 3 identifies the negative chemical potential gradient as the driver of targeted separation, and the relevant species flux expression is developed in Section 3.1.3.2 (see Example 3.1.9 also). Section 3.1.4 introduces molecular diffusion and convection and basic mass-transfer coefficient based flux expressions essential to studies of distillation and other phase equilibrium based separation processes. Section 3.1-5.1 introduces the Maxwell-Stefan equations forming the basis of the rate based approach of analyzing distillation column operation. After these fundamental transport considerations (which are also valid for other phase equilibrium based separation processes), we encounter Section 3.3.1, where the equality of chemical potential of a species in all phases at equilibrium is illustrated as the thermodynamic basis for phase equilibrium (Le. = /z ). Direct treatment of distillation then begins in Section 3.3.7.1, where Raouit s law is introduced. It is followed by Section 3.4.1.1, where individual phase based mass-transfer coefficients are reiated to an overall mass-transfer coefficient based on either the vapor or liquid phase. 

In Figure 14-23, the solid and vapor chemical potentials do not change with the addition of a solute to the liquid phase. However, adding solute to the liquid does lower the chemical potential of the liquid solvent. Hence, to re-establish equilibrium, the S-L and the L-V curves shift to respectively lower and higher T. This can be thought of as an example of Le Chatelier s principle. 

TRIPLE POINT. The temperature and pressure at which the solid, liquid, and vapor of a substance are in equilibrium with one another. Also applied to similar equilibrium between any three phases, Le., two solids and a liquid, etc. The triple point of water is +0.072 C at 4.6 mmHg it is of special importance because it is the fixed point for the absolute scale of temperature. 

Section 8.2.1 was concerned with equilibrium between a condensed phase and the vapour. It is often necessary, however, to estimate the effect of pressure on equilibria between two condensed phases. For example, the melting point of sodium at one atmosphere pressure is 97.6°C. Can it be used as a liquid heat transfer medium at 100°C, at a pressure of 100 atm, or will it solidify It is known that the liquid is less dense than the solid, and this argues that high pressures will encourage solidification. This is another aspect of Le Chatelier s work, which we can now quantify. This and similar problems may be solved by the Clapeyron equation, which we shall now derive. 

Only a brief outline of the effects of pressure on rates and equilibria is given here since the subject is amply documented elsewhere. " It has long been appreciated that the position of a chemical equilibrium may be shifted by the application of external pressure in reactions in both the liquid and the gaseous phase. This shift in equilibrium favours the direction of the reaction which results in the smaller volume this is an application of the Le Chatelier s principle. In gas-phase reactions the term volume denotes the total volume of the system in dilute solutions the term volume denotes the algebraic sum of the partial molar volumes of the individual reagents and products. The thermodynamic relationship which summarizes this effect is... 

Coming again to the diagram, we know that the vaporisation (change of liquid to vapour) is accompanied by absorption of heat. Hence, if heat is given to the system (as along OA), then according to Le Chatelier s principle, the equilibrium will shift in that direction in which heat is absorbed, i.e., more liquid will pass into vapour. Thereby, the pressure of the system wiU increase. The curve OA extends to the point A, which is critical temperature (374°C) of liquid water, beyond which only one phase, i.e., vapom will exist. 

Curve CE is known as melting point or fusion curve of monoclinic sulphur. The two phases in equilibrium along it are monoclinic and liquid sulphur. The system is univariant. The ciu-ve CE shows the effect of pressure on the melting point of monoclinic sulphur. As this curve slopes sU tly away from the pressure axis, it means that the melting point of monoclinic sulphur increases with an increase of pressure. This is in accordance with Le Chatelier s principle as melting of monoclinic sulphur is accompanied by a sligd t increase of volume. 

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