Volume pure component molar

The adjustable parameters are related to pure component molar volumes and to characteristic energy differences as following... 

Input data Molecular structure pure-component molar volumes and viscosities at the mixture temperature. 

The van Laar, Wilson, and NRTL models require only binary mixture information to obtain values of the parameters, whereas the UNIQUAC model also requires pure component molar volumes as well as surface area and volume parameters. These latter parameters for the UNIQUAC model are usually obtained using a group contribution method in which a molecule is considered to be a collection of functional groups and the surface area and volume of the molecule are the sum of like quantities over all groups in the molecule. 

True mole fractions Z , molar concentrations C , and volume fractions ([) can be computed simply from pure component properties if one assumes that the excess molar volume V = 0. This assumption can be made initially so as to satisfy component volume and material balances exactly for each mixture. So, using the pure component molar volumes V at a given temperature, then V = Xh Q = x. j/V, and = ViQ, . 

Here we have used the facts that the pure-component molar volumes are independent of mixture composition (i.e., dVJdx )T,p = 0), and that for a binary mixture X2 = 1 — Xi, so (9jc2/ox i) = — 1. ... 

Therefore, given data for the volume change on mixing as a function of concentration, so that AmixY and the derivative 9(Aniixy)/9-ri can be evaluated at, r. we can immediately compute (V — V,) and (V — at this composition. Knowledge of the pure-component molar volumes, then, is all that is necessary to compute V i and Vi at the specified composition. vi. By repeating the calculation at other values of the mole fraction, the complete partial molar volume versus composition curve can be obtained. The results of this computation are given in Table 8.6-2. 

Value of partial molar volume at infinite dilution. tValiie of pure-component molar volume. 

The entries in Tables 8.6-2 and 8.6-4 are interesting in that they show that the partial molar volume and partial molar enthalpy of a species in a mixture are very similar to the pure component molar quantities when the mole fraction of that species is near unity and are most different from-the pure component values, at infinite dilution, that is, as the species mole fraction goes to zero. (The infinite dilution values in Tables 8.6-2 and... 

A partial molar property of a component in a mixture may be either greater than or less than the corresponding pure-component molar property. Furthermore, the partial molar property may vary with composidon in a complicated way. Show this to be the case by computing (a) the partial molar volumes and (b) the partial molar enthalpies of ethanol and water in an ethanol-water mixture. (The data that follow are from Volumes 3 and 5 of the International Critical Tables, McGraw-Hill, New York, 1929.)... 

Equation 9.1-4 indicates that the partial molar internal energy of species i in an ideal gas mixture t a given temperature is equal to the pure component molar,internal energy of that component as an ideal gas at the same temperature. Similarly, Eq. 9.1-5 establishes that the partial molar volume of species i in an ideal gas mixture at a given temperature and pressure is identical to the molar volume of the pure component as an ideal gas at that temperature arid pressure. 

Therefore, for a mixture in which the pure component and partial molar volumes are identical [i.e., V-, (T, P.x) =. v,-V,- (T, P) at all conditions], the fugacity of each species in the mixture is equal to its mole fraction times its pure-component fugacity evaluated at the same temperature and pressure as the /hixUire /, [T, P,x) — x fi T, P). However, if. as is generally the case, V-, Vj.-a hen /j and /, are related through the integral o er all pressures of the difference between the species partial molar and pure-component molar volumes. 

Here V is the mixture molar volume, Vi,2 the pure component molar volume, and VE the molar excess volume. No excess volumes were available for this system (II), requiring these measurements to be made as part of this study. 

If data are lacking for partial molar volumes, we might approximate them using the pure-component molar volumes then (11.1.6) becomes... 

The volume change of mixing of an ideal gas mixture shows a different behavior. The pure component molar volume can directly be read from the ideal gas equation of state ... 

Figure 1.5 shows the partial molar volumes of Ci and C3 vs. pressure in a mixture of C1/C3 with xc — 0.34 (mole fraction) and at T — 346 K. The mixture in the entire range of pressure is in the gas state (see Fig. 1.6). The molar volumes of pure Ci and C3 are also graphed in Fig. 1.5 at T = 346 K and different pressures. The partial molar volumes are calculated from the Peng-Robinson equation of state (1976), which wall be discussed in Chapter 3. The pure component molar volumes are from Starling (1973). The large difference between the partial molar volume and pure component molar volume provides strong evidence of the effect of mixing on the density.

Figure 1,5 Partial molar and pure component molar volumes of the C,/Cj system at 346 K — 0.34. 

PURE calculates pure liquid standard-state fugacities at zero pressure, pure-component saturated liquid molar volume (cm /mole), and pure-component liquid standard-state fugacities at system pressure. Pure-component hypothetical liquid reference fugacities are calculated for noncondensable components. Liquid molar volumes for noncondensable components are taken as zero. 

This simple mo l contiimes to ignore the possibility of volume changes on mixing, so for simplicity the molar volumes and are taken as those of the pure components. It should come as no surprise that in... 

For both polar and nonpolar nonhydrocaihon gaseous mixtui es at low pressui es, the most accurate viscosity prediction method is the method of Brokaw. The method is quite accurate but requires the dipole moment and the Stockmayer energy parameter (e/A ) for polar components as well as pure component viscosities, molecular weights, the normal boding point, and the hq-uid molar volume at the normal boding point. The Technical Data Manual should be consulted for the fidl method. 

Xi j = mole fraction of component or / in the liquid mixture V I = liquid molar volume of pure component or / at temperature T, mVkmol... 

For an ideal solution, the partial molal volumes equal the molar volumes of the pure liquid components. Denoting component the main components as 1 and the impurities as > 1, the volume becomes ... 

The observations on which thermodynamics is based refer to macroscopic properties only, and only those features of a system that appear to be temporally independent are therefore recorded. This limitation restricts a thermodynamic analysis to the static states of macrosystems. To facilitate the construction of a theoretical framework for thermodynamics [113] it is sufficient to consider only systems that are macroscopically homogeneous, isotropic, uncharged, and large enough so that surface effects can be neglected, and that are not acted on by electric, magnetic or gravitational fields. The only mechanical parameter to be retained is the volume V. For a mixed system the chemical composition is specified in terms of the mole numbers Ni, or the mole fractions [Ak — 1,2,..., r] of the chemically pure components of the system. The quantity V/(Y j=iNj) is called the molar... 

Abstract Isotope effects on the PVT properties of non-ideal gases and isotope effects on condensed phase physical properties such as vapor pressure, molar volume, heats of vaporization or solution, solubility, etc., are treated in some thermodynamic detail. Both pure component and mixture properties are considered. Numerous examples of condensed phase isotope effects are employed to illustrate theoretical and practical points of interest. 

The volume function then is homogeneous of the first degree, because the parameter X, which factors out, occurs to the first power. Although an ideal solution has been used in this illustration. Equation (2.31) is true of all solutions. However, for nonideal solutions, the partial molar volume must be used instead of molar volumes of the pure components (see Chapter 9). 

For many gaseous solutions, even if the gases are not ideal, the partial molar volumes of the components are equal to the molar volumes of the pure components at the same total pressure. The gases are said to obey Amagat s mle, and the volume change on mixing is zero. Under these conditions, the gaseous solution behaves ideally in the sense that it obeys the equation... 

---