Binaiy systems

The local-composition models have hmited flexibility in the fitting of data, but they are adequate for most engineering purposes. Moreover, they are implicitly generalizable to multicomponent systems without the introduction of any parameters beyond those required to describe the constituent binaiy systems. For example, the Wilson equation for multicomponent systems is written ... 

Vapor/liquid equilibrium (XT E) relationships (as well as other interphase equihbrium relationships) are needed in the solution of many engineering problems. The required data can be found by experiment, but such measurements are seldom easy, even for binaiy systems, and they become rapidly more difficult as the number of constituent species increases. This is the incentive for application of thermodynamics to the calculation of phase-equilibrium relationships. 

Moreover, Eq. (4-122), the Gibbs/Duhem equation, may be written for experimental values in a binaiy system as... 

The binary interaction parameters are evaluated from liqiiid-phase correlations for binaiy systems. The most satisfactoiy procedure is to apply at infinite dilution the relation between a liquid-phase activity coefficient and its underlying fugacity coefficients, Rearrangement of the logarithmic form yields... 

For a binaiy system comprised of species p and q, Eqs. (4-232), (4-312), and (4-315) may be written for species p at infinite dilution. The three resulting equations are then combined to yield... 

One advantage of this procedure is that kp and k are found directly from the pure-species parameters experimental data for the pq binaiy system, independent of the correlating expression used for G. ... 

Our primary interest in Eq. (4-324) is its apphcation to binaiy systems at infinite dilution of one of the constituent species. For this pur-... 

Cussler studied diffusion in concentrated associating systems and has shown that, in associating systems, it is the size of diffusing clusters rather than diffusing solutes that controls diffusion. is a reference diffusion coefficient discussed hereafter is the activity of component A and iC is a constant. By assuming that could be predicted by Eq. (5-223) with P = 1, iC was found to be equal to 0.5 based on five binaiy systems and vahdated with a sixth binaiy mixture. The limitations of Eq. (5-225) using and K defined previously have not been explored, so caution is warranted. Gurkan showed that K shoiild actually be closer to 0.3 (rather than 0.5) and discussed the overall results. 

For a binaiy system, r = Otg = L/Ot g. The symbol r applies primarily to the process, while Ot is oriented toward interactions between pairs of solute species. For each binaiy pair, fij = C( ji = l/Otiy. ... 

In case of binaiy systems, co-adsorption was performed using three different initial mixtures - being equimolar (Z/ = Zz = O.S) and rich in component 1 and 2 (respectively Z/ = 0.85 and Z = 0.15) - whose molar ratio were formerly checked. The selectivity of adsorbent rn/2) was either directly represented in an X-Y isobaric equilibrium diagram, or determined using the following equation, where Xi and K are die adsorbed and gas phase molar fraction of f component, and plotted versus total amount adsorbed Qtad-... 

Solution Since we have assumed the validity of Eq. (11.74), k - 1.0 throughout this problem. This, together with the fact that we are considering a binaiy system makes the solution simple enough that the steps can be explained as though carried out by hand calculations. 

Thus for binaiy systems, the partial properties are readily calculated directly from an expression for the solution property as a function of composition at constant T and P. The corresponding equations for multicomponent systems are much more complex, and are given in detail by Van Ness and Abbott.t... 

Solution Figure 13.1 shows a representative plot of M vs. Xi for a binaiy system. Valued of the derivative dMfdx- are given by the slopes of lines drawn tangent to the curve of M vs. x,. One such line drawn tangent at a particular value of x, is shown in Fig. 13.1. Its intercepts with the boundaries of the figure at x, = 1 and X = 0 are labeled J] and /2. As is evident from the figure, two equivalent expressions can be written for the slope of this line ... 

In the second method, several mixtures of known composition are formulated and placed in glass vials or ampoules. These are placed in a bath or oven and heated or cooled until two phases become one, or vice versa. In this way, the phase boundaries of a binaiy system may be determined. Again, impurities in the starting materials may affect the results, and this method does not work well for sparingly soluble systems or for systems that develop significant pressure. 

FIGURE S.2-S Common typas of equilibrium diagrams for binaiy systems. 

M1K Mikhailov, Yu.M., Ganina, L.V., Roshchupkin, V.P., and Shapaeva, N.V., Phase equilibrium and diffusion in binaiy systems based on nonyl aciylate, acrylic acid, and their homo- and copolymers, Polym. Sci., Ser. B, 49, 240, 2007. 

The (integral) enthalpy of mixing or the (integral) enthalpy of solution of a binaiy system is the amount of heat which must be supplied when mole of pure solvent A and ns mole of pure polymer B are combined to form a homogeneous mixture/solution in order to keep the total system... 

Since 6 2 = 2B j B Bjj, the details of the compositioo dependmce of and are directly influenced by the magnitude of the interaction coefliciem B.i. The eflect is iii rat i in Fig. 1.3-1, which shows values of versus y, computed from Eq. (1.3-23a) for a representative binaiy system for which the pure-conqKinent virial coefficients are B = -1000 em /nufl and = -2000 cmVmol. The temperature is 300 K and the pressure is 1 bar, die curves correspond to diflenmt values of B,2, which range from -500 to -2500 cm /mol. All curves approach asymptotically the pure-component value 4>, = 0.9607... 

The essential features of vapor-liquid equilibrium (VLE) behavior are demonstrated by the simplest case isothermal VLE of a binaiy system at a temperature below die critical temperatures of both pure components. For this case ( subcritical VLE), each pure couqionent has a well-defln vapor-liquid saturation pressure Ff , and VLE is possible for the fiiU range of liquid and vsqior compositions X/ and y,. Figure l.S-1 illustrates several pes of behavior riiown by such systems. In each case, the upper solid curve ( bubble curve ) represents states of saturated liquid the lower solid curve ( dew curve") represents states of saturated vapor. 

Figure l.S-la is for a system that obeys/biou/r s Low. The significant feature of a Raoult s Law system is the linearity of the isothermal bubble curve, expressed for a binaiy system as... 

FIGURE 5.2-4 Pressure-contposition equilibrium diagram for a binaiy system. 

According to the Gibbs phase rule, temperature and pressure of a CEP are unique for binaiy systems and, thus, are independent of the overaJl composition of the sample, see section 2. For the ternary systems examined, a dependency of the CEP data from the mole fraction of CO2 (xco2) could not be determined, as has been suggested by Patton et al. [4]. The differences were all found to be within the experimental error, see below. Note also that fluid three-phase behavior only occurs in a small range of xco2 ( 3 mole%). However, in order to avoid any influence whatsoever, for each ternary system examined, samples were prepared at constant CO2 mole fractions of 0.95 to 0.%. 

Peihaps the most important teim in Eq. (S.2-3) is the liquid-phase activity coefficient, and methods for its prediction have been developed in many fomis and by many woricers. For binaiy systems the Van Laar (Eq. (1.4-18)], Wilson [Eq. (1.4-23)], NRTL [Eq. (1.4-27)], and UNIQUAC [Eq. (1.4-36)] relationships are usefiil for predicting liquid-phase nonidealities, they require some experimental data. When no data are available, and an approximate nonideality correction will suffice, the UNIFAC approach (Eq. (1.4-31)], which utilizes fiinctional group contributions, may be used. For special cases involving regular solutions (no excess entropy of mixing), the Scatchard-Hildebrand method provides liquid-phase activity coefficients based on easily obtained pure-component properties. 

Equation (7.1-16) reduces to two qtecial cases of molecular diffusion which are customarily considered. In equumAal counierdiffiision, component A diffuses through component B, which is diffusing at the same molal rate as A relative to stationaiy coordinates, but in the opposite direction. This process is offen approximated in the distillation of a binaiy system. In unimolal unidirectional diffusion, only one molecular species—component A—diffuses through component B, which is motionless relative to stationaiy coordinates. This type of transfer is approximated frequently in the operations of gas absorption, liquid-liquid extraction, aiid adsorption. 

For binaiy systems. Fig. 1.6-1, shows these two extremes. In Fig. 1.6-la, there are two possible solid phases one of ffiese is pure solid 1 and the other is pore solid 2. The curve on the left gives the solulrility of solid 2 in liquid 1 the curve on the right gives the solubility of solid I in liquid 2. These soluMlity curves intersect at the eutectic point. The curve on the left is the coexistence line for solid 2 and the liquid mixture the curve on the right gives the coexistence line for solid I and the liquid mixture. At the eutectic point, all three phases are at equilibrium. For this type of system, there is no difference between freezing temperature and melting temperature. 

Srinivas, C. Venkateshwara Rao, M. Prasad, D- L. Vapor-liqmd eqi bna in the binaiy systems fomed by methanol with 1,2-dichloroethane, 1,1,1-trichloroethane and i,l,2,2-tetrachloroethane at 96.7 kPa Fluid Phase Equilib. 1991,61, 285-297... 

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