Equilibrium, chemical solution-vapour

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

Therefore it is the quantity p, which has been called the chemical potential of the electrolyte as a whole, which provides the criterion of phase equilibrium in the usual way. Similar considerations relate to a solution of an electrolyte (e.g. HCl) in equilibrium with its vapour ( 10 17). 

Chemical condensation This occurs when soluble corrosion products or atmospheric contaminants are present on the metal surface. When the humidity exceeds that in equilibrium with a saturated solution of the soluble species, a solution, initially saturated, is formed until equilibrium is established with the ambient humidity. The contaminants have already been detailed and of the corrosion products, obviously sulphates, chlorides and carbonates are most important in this context. However, in some cases there is a lack of reliable data on the vapour pressure exerted by saturated solutions of likely corrosion products. The useful data was summarised in Table 2.7. 

Problems with the determination of chemical equilibria in multiphase systems are solved in practice by assuming that the reaction takes place in any phase and all components are also equilibrated between phases. Accordingly, for a single reaction any of Eqns. (5.4-32) and (5.4-33) must be solved, while the relationships of Eqn. (5.4-31) must also be fulfilled. Since vapour-liquid equilibrium coefficients are functions of the compositions of both phases, the search for the solution is an iterative procedure. Equilibrium compositions are assumed, vapour-liquid equilibrium coefficients are then estimated, and new equilibrium compositions are evaluated. If the new equilibrium compositions are close to those assumed initially one may consider the assumed values to be the solution of the problem. Otherwise the evaluated compiositions are taken as the start for repetition of the procedure until a reasonable agreement between tissumed and evaluated comfiositions has been reached. 

Although crystals can be grown from the liquid phase—either a solution or a melt—and also from the vapour phase, a degree of supersaturation, which depends on the characteristics of the system, is essential in all cases for crystal formation or growth to take place. Some solutes are readily deposited from a cooled solution whereas others crystallise only after removal of solvent. The addition of a substance to a system in order to alter equilibrium conditions is often used in precipitation processes where supersaturation is sometimes achieved by chemical reaction between two or more substances and one of the reaction products is precipitated. 

Chemically bound water is most reasonably defined as including that present in interlayer spaces, or more firmly bound, but not that present in pores larger than interlayer spaces. As will be seen in Chapter 8, the distinction between interlayer space and micropores is not sharp water adsorbed on surfaces of pores further blurs the definition. From the experimental standpoint, the determination is complicated by the fact that the amount of water retained at a given RH depends on the previous drying history of the sample and on the rate at which water is removed. An approximate estimate is obtained by equilibrating a sample, not previously dried below saturation, with an atmosphere of 11% RH (F12,F13,F14). Saturated aqueous LiCl HjO gives the required RH (partial pressure of water vapour = 2,7 torr at 25°C). To achieve apparent equilibrium in a reasonable time (several days), the sample must be crushed and the system evacuated the salt solution should be stirred, at least intermittently. Young and Hansen (Y5) found the composition of the C-S-H in C3S paste thus... 

Equation (4) illustrates the application of the phase rule to equilibria between solids and solutions. Thus the number of variable concentrations in the equilibrium equation is exactly equal to the degrees of freedom / of the system, namely, the total number n of the molecular types taking part in the reaction less the number B of the substances present in the solid phase (f=n—B) n is also the number of the independent components of the system, which is equal to the total number of molecular types present (n-f sol vent), less the number of the chemical equations (1). The number of phases is P = B+2 (solution and vapour). Hence... 

The macroscopic chemical potentials and are therefore equal to the chemical potentials of the monomer molecules. This result is quite independent of any assumptions as to the mode of association. It is exact both for associated solutions and associated gases (such as acetic acid vapour), and depends only on the assumption that the complexes are in thermodynamic equilibrium with one another. 

Chemical equilibrium in homogeneous systems—Dilute solutions—Applicability of the Gas Laws—Thermodynamic relations between osmotic pressure and the lowering of the vapour pressure, the rise of boiling point, the lowering of freez ing point of the solvent, and change in the solubility of the solvent in another liquid—Molecular weight of dissolved substances—Law of mass action—Change of equilibrium constant with temperature and pressure... 

Let p0V(P) be the chemical potential of the solvent vapour. We shall admit that the solute is not volatile and therefore that the chemical potential of the solvent is represented by the same function in both cells. Under these conditions, the liquid-vapour equilibrium implies the equalities... 

S-IO C above that of the experiment. The sampling point was 3-5 mm from the solution surface. About 3-5 sec before sampling the stirrer was stopped to avoid splashing of the syringe needle. The proposed technique [39] was tested on the reduction of some alkyl halides with sodium borohydride in dimethylformamide. It was shown that the kinetic curves derived as a result of chemical freezing of samples practically coincided with those obtained by analysis of an equilibrium vapour phase. The technique is recommended for studying processes with a half-time of transformation exceeding lOmin. 

Gas-liquid and vapour-liquid equilibria display similarities, but also significant differences. Let s consider a component i in a gaseous mixture dissolved in a solvent, at equilibrium at constant temperature. If the solution is very diluted and there is no chemical reaction, then the Henry law expresses a simple proportionality between the solute partial pressure pi and its molar fraction in liquid x, ... 

The uncontrolled spread (dispersion) of organic chemicals results from their mobility (determined by their chemical structure), the nature of their applications and the physicochemical conditions at the place where they are used. Increasing concentrations of halogenated hydrocarbons in the atmosphere would be impossible without the high volatility (vapour pressure) of these substances. Similarly, bioaccumulation factors of up to 100 000 (PCBs in oysters) (Fbrstner, 1995) can only occur because the chemicals concerned are highly lipophilic and the equilibrium of their distribution between water and fat is very much on the side of the solution in fat. 

Henry s law describes the partitioning of a chemical between a gaseous phase (e.g. air) and a liquid phase (e.g. water), stating that the solubility of a gaseous compound in that liquid is proportional to its partial pressure above the solution. The proportionality factor obtained for equilibrium conditions is represented by the Henry s law constant. It is expressed either as H (Pa mVmol), the ratio of the partial pressure in the vapour phase p in Pa) and the concentration in water (5 in mol/m ), or as H (dimensionless), the ratio of the concentrations (mol/m )in air and water ... 

The impact of these liquid phase reactions on the phase equilibrium properties is thus an increased solubility of NH3, CO2, H2S and HCN compared with the one calculated using the ideal Henry s constants. The reason for the change in solubility is that only the compounds present as molecules have a vapour pressure, whereas the ionic species have not. The change thus depends on the pH of the mixture. The mathematical solution of the physical model is conveniently formulated as an equilibrium problem using coupled chemical reactions. For all practical applications the system is diluted and the liquid electrolyte solution is weak, so activity coefficients can be neglected. 

As mentioned in 7 3 it is always possible to discuss the equilibrium of a reaction in solution in terms of the partial pressures in the saturated vapour above the solution (provided that this vapour is a perfect mixture). However, for many purposes it is more useful to express the equilibrium constant of a liquid phase reaction directly in terms of the composition of the liquid. This is done by substituting in equation (10 1) any of the appropriate expressions for the chemical potential of a component of a solution which have been developed in the last two chapters. It will save space if the equations are developed in a general form applicable to a non-ideal solution. The limiting forms of these expressions appljdng to reaction equilibrium in an ideal solution may be obtained by putting the activity coefficients equal to unity. 

In 10 10 it was shown that the equilibrium of an electrol3rte in a saturated solution with its pure solid phase depends on /e, the chemical potential of the electrolyte as a whole. Similar considerations apply to the equilibrium of a volatile electrolyte, such as hydrochloric acid, with its vapour. 

Let fi be the chemical potential of hydrogen chloride in the vapour phase. For equilibrium with the solution... 

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