Pure Component Behaviour

In a general case of a mixture, no component takes preference and the standard state is that of the pure component. In solutions, however, one component, termed the solvent, is treated differently from the others, called solutes. Dilute solutions occupy a special position, as the solvent is present in a large excess. The quantities pertaining to the solvent are denoted by the subscript 0 and those of the solute by the subscript 1. For >0 and x0-+ 1, Po = Po and P — kxxx. Equation (1.1.5) is again valid for the chemical potentials of both components. The standard chemical potential of the solvent is defined in the same way as the standard chemical potential of the component of an ideal mixture, the standard state being that of the pure solvent. The standard chemical potential of the dissolved component jU is the chemical potential of that pure component in the physically unattainable state corresponding to linear extrapolation of the behaviour of this component according to Henry s law up to point xx = 1 at the temperature of the mixture T and at pressure p = kx, which is the proportionality constant of Henry s law. 

Two different methods have been presented in this contribution for correlation and/or prediction of phase equilibria in ternary or mul> ticomponent systems. The first method, the clinogonial projection, has one disadvantage it is not based on concrete concepts of the system but assumes, to a certain extent, additivity of the properties of individiial components and attempts to express deviations from additivity of the properties of individual components and attempts to express deviations from additivity by using geometrical constructions. Hence this method, although simple and quick, needs not necessarily yield correct results in all the cases. For this reason, the other method based on the thermodynamic description of phase equilibria, reliably describes the behaviour of the system. Of cource, the theory of concentrated ionic solutions does not permit a priori calculation of the behaviour of the system from the thermodynamic properties of pure components however, if a satisfactory equation is obtained from the theory and is modified to express concrete systems by using few adjustable parameters, the results thus obtained are still substantially more reliable than results correlated merely on the basis of geometric similarity. Both of the methods shown here can be easily adapted for the description of multicomponent systems. 

With the relations given in Table 2.2-1 and the critical exponent values given in Table 2.2-2, the thermodynamic behaviour of a pure component close to the critical point can be described exactly, however further away from the critical point also the mean field contributions have to be taken into account. A theory which is in principle capable to describe... 

Type V fluid phase behaviour shows at temperatures close to 7C-A a three-phase curve hhg which ends at low temperature in a LCEP (h=h)+g and at high temperature in a UCEP (h+h) g The critical curve shows two branches. The branch h=g runs from the critical point of pure component A to the UCEP. The second branch starts in the LCEP and ends in the critical point of pure component B. This branch of the critical curve is at low temperature h=h in nature and at high temperature its character is changed into h=g- The h=h curve is a critical curve which represents lower critical solution temperatures. In Figure 2.2-7 four isothermal P c-sections are shown. 

Type IV fluid phase behaviour is a combination of type II and type V behaviour. These systems show two branches of the l2lig curve, three branches of the critical curve and three critical endpoints. At low temperature the P c-sections for this type of systems are similar to Figure 2.2-6, at temperatures close to the critical temperature of the pure component A PResections similar to Figure 2.2-7 are found. 

The enhancement factor contains three terms supercritical phase, ideal behaviour of the pure component 2 in the vapour phase at the sublimation pressure, and the Poynting factor that describes the influence of the pressure on the fugacity of pure solid 2. 

TypeL Non-ideal solutions of this type show small deviations from ideal behaviour and total pressure remains always within the vapour pressures of the pure components, as shown in figure (8), in which the dotted lines represent ideal behaviour. It is observed that the total pressure of each component shows a positive deviation from Raoult s law. However, the total pressure remains within the vapour pressures of the pure constituents A and B. 

Simulation data on mixture adsorption can be used to screen zeolites as adsorbents, but experimental data are necessary to validate the simulations and to accurately design the separation process. The first step of the process design is to obtain such data. However, the experimental assessment of multi-component adsorption equilibria and kinetics is not straightforward and is highly time-consuming. As a result, some theories have been developed that predict adsorption behaviour for a mixture based on the pure component equilibria [1,3]. The isotherm data have to be correlated before their use in a design model... 

Near Infra-Red spectroscopy is a non-intrusive technique that allows to monitor the composition of the gas phase (differentiate isomers) and its changes in a time resolved matmer. In the NIR spectra (figure 4) some small differences between iso-butane and n-butane can be observed. We can also observe that mixtures exhibit a spectral behaviour that is a linear composition of the pure component spectra. It is necessary to quantify the spectral differences of the two isomers, so that the composition of the mixtures can be determined by NIR spectroscopy. 

This study firstly aims at understanding adsorption properties of two HSZ towards three VOC (methyl ethyl ketone, toluene, and 1,4-dioxane), through single and binary adsorption equilibrium experiments. Secondly, the Ideal Adsorbed Solution Theory (IAST) established by Myers and Prausnitz [10], is applied to predict adsorption behaviour of binary systems on quasi homogeneous adsorbents, regarding the pure component isotherms fitting models [S]. Finally, extension of adsorbed phase to real behaviour is investigated [4]. 

Surfaces of binary liquid mixtures are the simplest Gibbs monolayers that exist. We are considering the surface tension y as a function of the mole fraction X = x. It runs from the value y for pure component 1 to y for pure 2. that is from X = 0 to X = 1. Often such curves cae convex with respect to the x-cuds (as curves 2 and 3 in fig. 4.1), Implying the tendency of the Interface to be richer in the component with the lower y. At the same time this is the most volatile component. Such convex behaviour is the rule for mixtures of simple molecules, like liquid Ar, CH4, N2, CO, etc. but has also been observed for binary mixtures of the Kr-ethene-ethane triod ) and for molten salt mixtures ). Concave curves (2 in the figure) require the surface to be enriched by the component with the higher y, but such... 

If we consider the v, x diagram at a temperature lying between the critical temperatures of the two pure components, then the behaviour shown in fig. 16.8 will be observed. The binodals become shorter and... 

We have shown above that the activity coefficients of the components of an azeotropic mixture may be calculated from a knowledge of the properties of the pure components, and the temperature and pressure of the azeotropic state. In this paragraph we shall investigate the prediction of states of uniform composition from a knowledge of the behaviour of the activity coefficients as functions of temperature and pressure. 

Assuming a four component mixture and simple two product splits. Fig. 1 shows all possible separation sequences into the pure components under the assumption of sharp splits. If the number of components is increased, an exponential growth of the number of sequences is observed (Fig. 2, sequences). This behaviour is well known [6] and can be described by... 

Mixtures of liquids exhibit ideal behaviour when their intermolecular forces are equal among and between themselves, their partial enthalpies are independent of concentration and equal to the molar enthalpies of the pure components. In this case they obey Raoult s law, which states that the partial vapour pressure of a component is proportional to its mole fraction in the liquid mixture ... 

In the AN+EAN solvent system, the addition of small quantities of ionic liquids results in the abrupt increase in values, which became constant on reaching to the value equivalent to pure EAN. In this case, the n values exhibit positive deviations from the ideal behaviour, while p values show synergistic effects on the property. The basicity of the pure components of the mixture has similar property values. In all explored mixtures, a values are higher than those of the pure solvents manifesting synergism on the acidity. In the mixture, x j =0.05, the n and P values are close to those of AN while the HBD value is higher than the one corresponding to EAN. 

The electrochemical behaviour of stainless steel has not been worked out completely, although the measured data are available. However, one aspect of the behaviour, based on the measured double layer capacity data, seems to be susceptible to interpretation. The capacity-potential curves are determined by the state of the metal surface and by the ionic environment. In this work, it has been assumed that the ionic environment is a constant. This means that the double layer capacity-potential curves should reflect the nature of the metal surface just as, say, an electron energy spectrum in surface science. Stainless steel has a complicated electrochemical behaviour. In previous work [22] an attempt has been made to compare the double layer capacity curves measured during dissolution and passivation of the stainless steel with that of the pure components. It seems that all the data in the high frequency regime can be fitted to eqn. (70) with the Warburg coefficient set equal to zero. 

Even if the behaviour is not first-order, the concept may still be useful. In the above example we see that the responses for formulations containing equal amounts of all but one components are not equal to the mean values of the responses for those 4 pure components. It may also be more interesting to compare the response at Xj = 0.6 and at = 0, and divide by the factor of the change in x-, that is 0.6. The results of this calculation are shown in table 9.12. 

Figure 5.3 presents the generic PVT relationship for a pure component in a 3D diagram. This representation captures both the temperature evolution of the phase boundaries at equilibrium, as well as their volumetric behaviour. The 2D representation for different cases is straightforward. 

The geometric properties of a RCM allow its simple sketch. Figure 9.5 shows the construction for the mixture methyl-isopropyl-ketone (MIPK), methyl-ethyl-ketone (MEK) and water. Firstly, the position of the binary azeotropes and of the ternary azeotrope is located. Then the boiling points for pure components and azeotropes are noted (Fig. 9.5a). The behaviour of characteristic points (node or saddle) is determined by taking into account the direction of temperatures. Finally, straight distillation boundaries are drawn by connecting saddles with the corresponding nodes (Fig. 9.5b). 

Flash points of mixtures cannot simply be deduced fi-om the data of the pure components. This is due to the quite complex relationship which describes the vapour pressure behaviour of mixtures. Only for the comparatively simple case of binary mixtures, algorithms are known which allow the caleulation of the flash-point with satisfying accuracy [e.g. 33]. 

---