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Correlation of the excess enthalpy data of J A
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ark in" at 38315 K (110 C) yields the values:
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Correlations of the excess enthalpy for the temperature range from 32315 to 38315 K (50 to 110 C) lead to infinite-dilution values of C ~ / x 1 x 2 R , which are nearly constant and equal to
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(2) = 72 x1x2R
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Equation (1460) may be directly applied with these data to estimate In yIm and In y," for temperatures greater than 36315 K (90 C) The van Laar equations [Eqs (1217)] are well suited to this system, and the parameters for this equation are given as
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A',, = In ypO
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Akl = In y,W
These data allow prediction of VLE by an equation of state at 36315 K (90 C) and at two higher temperatures, 42315 and 47315 K (150 and 200 C), for which measured VLE l ~ data are given by Barr-David and ~ 0 d ~ ePemberton and Mash report pure-species vapor
C Pemberton and C J Mash, Znt DATA Series, Sel: B, vol 1, p 66, 1978 reported in Heats ofMizing Data Collection, Chemistry Data Series, vol 111, part 1, pp 457-459, DECHEMA, Frankfumain, 1984 1 2 ~ Ban-David and B F Dodge, J Chem Eng Data, vol 4, pp 107-121, 1959 H
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CHAPTER 14 Topics in Phase Equilibria
pressures at 36315 K (90 C) for both ethanol and water, but the data of Barr-David and Dodge do not include these values They are therefore calculated from reliable correlations Results of calculations based on the PengRobinson equation of state are given in Table 143 Shown are values of the van Laar parameters Aiz and A;, , the pure-species vapor pressures PIsat P p t , and the equation of state parameters bi and qi, and root-mean-square (RMS) deviations between computed and experimental values for P and yl
Table 143 VLE Results for Ethanol(l)/Water(2)
TIK(tI"C)
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RMS %6P
RMS 6yl
***** Vapor-phase compositions not measured
The small value of RMS % 6 P shown for 36315 K (90 C) indicates both the suitability of the van Laar equation for correlation of the VLE data and the capability of the equation of state to reproduce the data A direct fit of these data with the van Laar equation by the gammalphi procedure yields RMS % 6 P = 0 1913The results at 42315 to 47315 K (150 and 200 C) are based only on vapor-pressuredata for the pure species and on mixture data at lower temperatures The quality of prediction is indicated by the P-x-y diagram of Fig 1410, which reflects the uncertainty of the data as well
143 EQUILIBRIUM AND STABILITY
Consider a closed system containing an arbitrary number of species and comprised of an arbitrary number of phases in which the temperature and pressure are uniform (though not necessarily constant) The system is initially in a nonequilibrium state with respect to mass transfer between phases and chemical reaction Changes which occur in the system are necessarily irreversible, and they take the system ever closer to an equilibrium state We imagine that the system is placed in surroundings such that the system and surroundings are always in thermal and mechanical equilibrium Heat exchange and expansion work are then accomplished reversibly Under these circumstances the entropy change of the surroundings is:
The final term applies to the system, for which the heat transfer d Q has a sign opposite to that of d Q,,,, and the temperature of the system T replaces T, because both must have the same , value for reversible heat transfer The second law requires:
1 3 ~ reported in Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, vol 1, part la, p 145, s DECHEMA, FrankfurtMain, 1981
143 Equilibrium and Stability
Figure 1410 P x y diagram for ethanol(l)/water(2) predicted values; the points are experimental values
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