Liquid equilibrium partially soluble

For systems of type II, if the mutual binary solubility (LLE) data are known for the two partially miscible pairs, and if reasonable vapor-liquid equilibrium (VLE) data are known for the miscible pair, it is relatively simple to predict the ternary equilibria. For systems of type I, which has a plait point, reliable calculations are much more difficult. However, sometimes useful quantitative predictions can be obtained for type I systems with binary data alone provided that... 

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

In order to define completely the solubility of a gas in a liquid, it generally is necessary to state the temperature, the equilibrium partial pressure of the solute gas in the gas phase, and the concentration of the solute gas in the liquid phase. Stric tly speaking, the total pressure on the system also should be stated, but for low total pressures, less than about 507 kPa (5 atm), the solubihty for a particular partial pressure of solute gas normally will be relatively independent of the total pressure of the system. 

The equilibrium adsorption characteristics of gas or vapor on a solid resemble in many ways the equilibrium solubility of a gas in a liquid. Adsorption equilibrium data are usually portrayed by isotherms lines of constant temperature on a plot of adsorbate equilibrium partial pressure versus adsorbent loading in mass of adsorbate per mass of adsorbent. Isotherms take many shapes, including concave upward and downward, and S-curves. Equilibrium data for a given adsorbate-adsorbent system cannot generally be extrapolated to other systems with any degree of accuracy. 

Reaction Conditions. Alcoholysis commonly takes place in one liquid phase, sometimes with one of the reactants being only partially soluble and going into solution gradually as the reaction proceeds. Unless an excess of one of the reactants is used, or unless one of the products is withdrawn from the reaction phase by vaporization or precipitation, the reaction does not proceed to completion but comes to a standstill with substantial proportions of both alcohols and both esters in equilibrium. The concentrations present at equilibrium depend on the characteristics of the alcohols and esters involved, but in most practical uses of the reaction, one or both of the devices mentioned are used to force the reaction toward completion. 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

Related Calculations. This illustration outlines the procedure for obtaining coefficients of a liquid-phase activity-coefficient model from mutual solubility data of partially miscible systems. Use of such models to calculate activity coefficients and to make phase-equilibrium calculations is discussed in Section 3. This leads to estimates of phase compositions in liquid-liquid systems from limited experimental data. At ordinary temperature and pressure, it is simple to obtain experimentally the composition of two coexisting phases, and the technical literature is rich in experimental results for a large variety of binary and ternary systems near 25°C (77°F) and atmospheric pressure. Example 1.21 shows how to apply the same procedure with vapor-liquid equilibrium data. 

I. 45 THE DISTRIBUTION OR PARTITION LAW It is a well-known fact that certain substances are more soluble in some solvents than in others. Thus iodine is very much more soluble in carbon disulphide, chloroform, or carbon tetrachloride than it is in water. Furthermore, when certain liquids such as carbon disulphide and water, and also ether and water, are shaken together in a vessel and the mixture allowed to stand, the two liquids separate out into two layers. Such liquids are said to be immiscible (carbon disulphide and water) or partially miscible (ether and water), according as to whether they are almost insoluble or partially soluble in one another. If iodine is shaken with a mixture of carbon disulphide and water and then allowed to settle, the iodine will be found to be distributed between the two solvents. A state of equilibrium exists between the solution of iodine in carbon disulphide and the solution of iodine in water. It has been found that when the amount of iodine is varied, the ratio of the concentrations is constant at any given temperature. That is ... 

Henry s law (i.e., c = po/H) relates the equilibrium oxygen solubility in the liquid (c ) to oxygen partial pressure in the gas (po) by the corresponding Henry s law constant (H). Because the liquid film mass transfer coefficient, l, is difficult to measure independently, kj a (i.e., times a) is used. It is a lumped parameter known as the volumetric mass transfer coefficient to characterize the overall mass transfer rate. 

To calculate phase equilibria for ternary mixtures of Type II, we require mutual solubility data for the two partially miscible bienries and vapor-liquid equilibrium data for the completely miscible binary. From such data we can obtain bienry parameters as required in some expression for molar excess Gibbs energy g for the ternary. 

So far we have considered liquid-liquid equilibrium only for binary mixtures. We next consider multicomponent mixtures. When two solvents are partially miscible (rather than immiscible), their mutual solubility will be affected by the addition of a third component. In this case the equilibrium conditions are... 

The discussion in this section has been concerned with the distribution of a solute between two liquid, phases whose equilibrium is unaffected by the added solute. This will occur if the amount of added solute is very small, or if the solvents are essentially immiscible at all conditions. However, if the amount of dissolved solute is so large as to affect the miscibility of the solvents, the solute addition can have a significant effect on the solvents, including the increase (salting in) or decrease (saltin out) of the mutual solubility of the two solvents, as was discussed in Sec. 11.2. It is important to emphasize that such situations are described by the methods in Sec. 11.2 as a multicomponent liquid-liquid equilibrium problem, in contrast to the procedures in this section, which are based on the assumption that the partial or complete immiscibility of the solvents is imaffected by the addition of the partitioning solute. 

In this chapter we consider several other types of phase equilibria, mostly involving a fluid and a solid. This includes the solubility of a solid in a liquid, gas, and a supercritical fluid the partitioning of a solid (or a liquid) between two partially soluble liquids the freezing point of a solid from a liquid mixture and the behavior of solid mixtures. Also considered is the environmental problem of how a chemical partitions between different parts of the environment. Although these areas of application appear to be quite different, they are connected by the same starting point as for all phase equilibrium calculations, which is the equality of fugacities of each species in each phase ... 

The partial derivative is obtained from parameters found by regressing vapor-liquid equilibrium (VLE) data for the solvent mixture. The estimated solubilities are not very sensitive to these parameters. There are multiple ways to obtain the Ay values. One is to use data from solute solubilities in the pure solvents and regress the parameters A°2 and A separately. Then,... 

A similar example of a promising application of solar heat for intensified process systems is pervaporation. In pervaporation, a selective membrane is used as barrier between two phases, the liquid feed and the vapour permeate. The process depends on the sorption equilibrium and the mobility of the components through the membrane and is rather independent of the vapour liquid equilibrium. The desired component, which is in liquid form in the feed, permeates through the membrane and evaporates while passing the membrane, because the partial pressure of the permeating component is kept lower than the equilibrium vapour pressure [21]. Permeabilities depend on the solubility and diffusion rates through the membrane. 

Based on solute solubility considerations, a chemical reaction in a SILP catalyst system can be assessed. Thus, a higher substrate solubility directly leads to a faster reaction rate and therefore to a faster conversion. Figure 9.11 shows the results of propene hydrogenation in four different SILP catalyst systems at 303 K. The conversion X (r = ) is plotted over the reaction time. The data points describe the experimentally measured conversions from batch experiments, and the drawn lines characterize the calculated conversion. For the calculated conversions, the vapor/liquid equilibrium (Eq. (9.1)) of all substrates and the product and the kinetics Eq. (9.13) are solved simultaneously. Reasonably, the partial reaction orders and... 

In general, O2 solubility in aqueous solution is governed by Henry s law, which states that at a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. For O2 solubility, Henry s law can be put into mathematical terms (at constant temperature) as... 

Simple extensions to cases where liquids A and B are only partially soluble and where solid C is distributed between the equilibrium layers are readily visualized. For example, in the configuration shown in Fig. 2.17, the situation is fundamentally similar to that in Fig. 2.16, except that the... 

Liquid/liquid extraction is a process that involves mass transfer between two immiscible or partially miscible liquids. The separation from a homogeneous liquid solution occurs by adding a liquid component, insoluble or partially soluble in the solution, the solvent, in which the component to be extracted from the solution, the solute, is preferably soluble. The solute diffuses in the solvent with a characteristic velocity until it reaches the equilibrium concentrations in each of the phases formed. This separation process is based on the distribution of the solute between the two phases and partial miscibility of the liquids. 

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