Correlation for the infinite-dilution activity coefficients of one binary

the last approach in the literature is given by Lobien and. Prausnitz ... function to describe solute-solventintermolecular forces. ... 3 kTa123. (15)...
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Ind. Eng. Chem. Res. 1992,31,420-424

420

Correlation for the Infinite-Dilution Activity Coefficients of One Binary Component from the Other Stefan0 Brandani, Vincenzo BrandaJ,* and Gabriele Di Giacomo Dipartimento di Chimica, Zngegneria Chimica e Materiali, Universitd de L'Aquila, 1-67040 Monteluco di Roio, L'Aquila, Italy

It is shown that for a variety of binary systems limiting activity coefficients can be related through pure-component properties and two adjustable binary parameters using a modified form of the scaled-particle theory. Calculated and experimental results are compared for 143 binary data points related to 32 pure components. The results of the proposed method are fiially compared with those of the method proposed by Wilson.

Introduction For a binary liquid mixture, infinite-dilution activity coefficients for both components are useful for determining the parameters of any two-parameter equation for the excess Gibbs energy. However, it often happens that measurement of one of these infinite-dilution activity coefficients is relatively easy while that of the other may be difficult. The problem, then, is to estimate the excess Gibbs energy of a binary liquid mixture over the entire range of compositions using only one measured value of the activity coefficient at infinite dilution. One possible solution to this problem, proposed by several investigators (e.g., Bruin and Prausnitz, 1971; Tassios, 1971), is to modify the expressions for the excess Gibbs energy, based on the local composition concept, in such a way that only one adjustable binary parameter is required to apply the model to the entire binary composition range. Another possibility is to predict one limiting activity coefficient from the other. A wide critical discussion of the methods proposed for the last approach in the literature is given by Lobien and Prausnitz (1982). A new method is presented here which relates infinitedilution activity coefficients through pure-component properties and two binary adjustable parameters. Our point of departure is the scaled-particle theory (Pierotti, 1976),modified with the introduction of binary adjustable parameters. Thermodynamic Framework At low pressures, the fugacity of component i in a binary liquid mixture can be expressed by the relationships f? = yixifl

which, for a binary mixture, gives 7: = H 1 , 2 / R

(7)

7; = H2,1/ps2

(8)

According to Pierotti (1976) and to Geller et al. (1976), Henry's constant is given by

where u1 is the molar volume of the solvent. Equation 9 assumes that the dissolution process can be carried out in two steps: in the first step, a cavity is made in the solvent to allow the introduction of a solute molecule; in the second step, the solute molecule interacts with the surrounding solvent. For the solute, the partial molar Gibbs energies g, and gi stand, respectively, for the first step (cavity formation) and for the second step (interaction). If the total pressure is low, scaled-particle theory gives for g,

4'-

18(L)1[ (2)- In (1- Y l ) (10) ~

1- Y1

where (11)

(1)

e

where is the vapor pressure of pure component i and Hi: is the Henry's constant of i in j . For the activity coefficients, the normalization conditions are lim y i = 1 (3)

where NA is Avogadro's number. To obtain an expression for gi, we assume some potential function to describe solute-solvent intermolecular forces. If we consider the interaction of a polarizable polar solute with a polarizable polar solvent, then, according to Pierotti (1976), a reasonable expression for the potential function r ( r ) is

r,-1

and lim y*i = 1 I2

(4)

where

4

Combining eqs 1 and 2, we obtain Taking the limit for x i

-

= y*iHij

0, eq 5 gives

(5)

From eq 12, Pierotti (1976) obtained

0888-5885/92/2631-0420$03.00/00 1992 American Chemical Society

Ind. Eng. Chem. Res., Vol. 31, No. 1,1992 421

Geller et al. (1976) used eqs 9,10, and 15 for correlating gas solubilites in terms of pure-component parameters only, making the simplifications 612

=

Ull

+ 422 2

= (€11€22)1/2 (17) In their correlation, the parameters for the solutes were determined independently and those for the solvents were adjusted to give the best fit for the gas solubility data at 25 OC. In our correlation for the infinite-dilution activity coefficients, we retain eqs 9,10, and 15, but we modify eqs 16 and 17 in this way: Q l l + 422 (1 + 512) 412 = 2 (19) €12 = ( ~ i i t 2 2 ) ~ / ~-( k11 2 ) In other words we assume that molecules are not hard spheres, but soft spheres. Moreover, we assume that the binary parameter tI2(the soft-core parameter) can be expressed as a function of the average polarizability and of the absolute difference of polarizabilities of the two components, according to €12

Table I. Pure-ComponentParameters and Average Absolute Percent Deviation on the Second Virial Coefficient Dataa no. component a aJk u p 1 water 1.48 341.1 3.400 1.85 2 hydrogen sulfide 3.92 252.3 4.287 O.Wb 3 carbon disulfide 8.47 430.2 5.037 0.00 4 carbon dioxide 2.65 256.9 3.698 0.00 5 carbon tetrachloride 10.5 465.9 5.964 0.00 6 chloroform 8.48 425.0 5.597 1.01 7 dichloromethane 6.49 394.1 5.137 1.60 8 methanol 3.26 500.5 4.473 1.70 9 l,l,l-trichloroethane 10.4 422.0 5.993 1.78 10 ethane 4.53 263.0 4.202 0.00 11 ethanol 5.12 501.6 4.999 1.69 6.18 322.9 4.487 O.Wb 12 propylene 6.41 370.4 5.372 2.88 13 acetone 14 1-bromopropane 9.38 350.4 5.487 2.18 15 propane 6.36 319.1 4.781 0.00 16 methyl acetate 6.96 461.6 5.507 1.72 17 n-propanol 6.95 471.0 5.389 1.68 6.98 485.8 5.556 1.66 18 2-propanol 19 furan 7.30 360.9 5.610 0.00 20 2-butanone 8.20 369.0 5.813 3.30 21 ethyl acetate 8.82 468.7 5.978 1.78 22 1-chlorobutane 10.1 410.6 6.087 2.05 8.78 543.3 5.911 1.66 23 n-butanol 24 sec-butanol 8.77 465.1 5.881 1.65 25 n-pentane 10.0 369.4 6.263 0.00 26 benzene 10.4 448.9 5.838 0.00 27 phenol 11.1 646.3 5.841 1.45 28 methylcyclopentane 11.0 422.6 6.311 0.00 29 n-hexane 11.9 401.4 6.653 0.00 30 n-perfluorohexane 11.8 583.9 5.857 0.00 31 toluene 12.3 518.6 6.201 0.00 32 n-heptane 13.7 448.8 6.924 0.00

AAF'D 14.7 7.5 5.3 5.2 5.0 6.0 2.4 15.5 0.5 4.9 9.6 5.9 2.0 10.9 6.6 0.6 6.6 15.2 5.0 4.2 5.2 3.2 6.8 10.3 7.3 2.5 5.7 1.9 12.0 6.1 12.8 5.9

'Units: CY, cm3 X e l k , K;U, A; p, D. AAPD,average absolute percent deviation on second virial coefficient data. All components with p < 1 were considered nonpolar and p was set to 0.

where

pZl=

lal - a21 x 1024

(22)

Determination of Pure-Component Properties The pure-component properties which are necessary for the correlation are vapor pressures, molar volumes, polarizabilities, dipole moments, and the parameters of Lennard-Jones or Stockmayer potentials. Vapor pressures and dipole moments were taken from Reid et al. (1977), except for carbon dioxide, whose vapor pressures were taken from Boublik et al. (1984); molar volumes were calculated by the modified Rackett equation (Spencer and Danner, 1972) with zRAvalues taken from Prausnitz et al. (1980). Polarizabilities were calculated according to Moelwyn-Hughes (1961), with the values of the refractive index and density taken from Riddick and Bunger (1970). The parameters of Lennard-Jones potential, for nonpolar compounds, and those of Stockmayer potential, for polar compounds, were calculated from the second virial coefficient data taken from Dymond and Smith (1980) and Cholinski et al. (1986), using recommended values or data set with the best accuracy. For nonpolar compounds, the fit of the second virial coefficient data was performed using the correlation derived by Brandani et al. (1987) from the data reported by Hirschfelder et al. (1954) for the Lennard-Jones potential. For polar compounds, we have derived a correlation of the reduced second virial coefficient reported by Hirschfelder et al. (1954) for the Stockmayer potential as a function of

Table 11. Parameters of the Correlation for the Six Classes of Systems systems 1 2 3 4 nonpolar-nonpolar j3 0.086 28 -0.023 40 0.001 12 0.55 6 0.29330 -0.10959 0.00779 0.35 nonpolar-polar j3 0.010 49 -0.023 53 0.001 70 1.66 6 0.06315 0.00172 -0.00120 2.00 polar-polar j3 0.01494 0.04789 -0.00481 0.40 6 -0.18095 -0.35000 0.07315 0.20 nonpolar-alcohol j3 0.073 59 -0.027 76 0.001 94 0.20 6 -0.04275 -0,00154 0.00030 0.20 polar-alcohol j3 0.05256 -0,02558 0.00385 2.00 6 -0.07809 -0,03499 0.00556 0.22 water-alcohol j3 -0.29512 -0.14137 0.03519 0.20 6 -0.40302 0.31951 -0.03549 0.23

the reduced temperature and the reduced dipole moment. This correlation reproduces tabulated data with an average percent deviation of 0.78%. Table I gives the pure-component parameters for 32 compounds and the average absolute percent deviation (AAPD) on second virial coefficient data. With the exception of water, methanol and 2-propanol, whose AAPD is about 15%, for the other compounds the AAPD is well below 10%.

Results and Discussion A total of 143 binary sets of data were compared in this study. The data were subdivided into six classes: nonpolenonpolar systems, polar-nonpolar systems, polarpolar systems, alcohol-nonpolar systems, alcohol-polar systems, and water-alcohol systems. The parameters of the correlation for the six classes are reported in Table 11. The results of comparison with measured data are summarized in Tables 111-VIII. Comparison is made on

422 Ind. Eng. Chem. Res., Vol. 31,No. 1,1992 Table 111. Predicted Infinite-Dilution Activity Coefficients for Nomolar-Nonwlar Binary systems' components 7; 7; A B T,K exptl exptl calc APD rep 2.1 1 1.71 1.67 1.50 26 29 346.0 14.0 1 1.74 1.50 1.27 26 32 348.0 0.0 1 1.42 1.42 1.32 31 32 377.0 3.1 1 1.35 1.31 1.82 32 26 333.0 1.8 1 1.68 1.71 1.49 26 29 348.0 0.7 1 1.16 1.03 1.17 28 29 343.0 12 10 183.0 1.14 1.10 1.10 0.0 1 32 5 323.0 1.17 1.12 1.11 0.7 1 29 30 298.0 8.41 17.8 17.6 1.0 1 29 30 318.0 6.05 13.1 13.2 1.0 1 2 4 273.0 2.02 2.80 2.79 0.3 1 15 4 277.4 2.08 2.02 2.03 0.3 1 26 3 298.0 1.56 1.38 1.38 0.0 1 19 5 303.0 1.33 1.35 1.36 0.4 1 32 26 331.2 1.76 1.33 1.29 3.2 2 32 26 350.0 1.59 1.33 1.16 12.7 2 5 26 293.2 1.13 1.10 1.09 1.0 3 0.0 4 26 25 320.0 1.52 1.79 1.79 'For 18 systems AAPD on 7; is 2.3, maximum error 14. bReferences listed in Table IX.

Table IV. Predicted Infinite-Dilution Activity Coefficients for Nonpolar-Polar Binary Systems' compone& 7; 7; A B T, K exptl exptl calc APD rep 1.68 47.8 1 3.71 3.22 20 29 333.0 3.02 12.8 1 3.49 3.46 20 32 333.0 5.00 7.94 58.9 1 4.71 25 13 315.0 4.81 4.81 5.60 16.4 1 13 318.0 29 5.58 3.22 3.63 12.7 1 32 13 323.0 3.53 4.75 34.5 1 2.89 29 20 333.0 3.29 2.81 14.6 1 2.68 32 20 362.0 1.34 1.61 1.93 19.8 1 13 340.0 26 1.52 1.65 1.83 10.7 1 13 318.0 26 3.03 2.18 28.0 1 1.97 13 318.0 5 1.66 1.48 1.00 39.7 3 29 331.8 6 1.78 1.66 6.5 4 1.85 6 29 348.0 0.2 2 1.70 1.70 1.59 26 13 304.0 1.57 1.66 1.83 10.0 2 26 13 314.4 1.63 2.02 24.0 2 1.54 26 13 330.0 2.15 3.00 2.33 22.2 2 5 13 318.2 2.80 2.37 15.3 2 2.15 13 324.0 5 3.66 3.63 0.9 3 6.23 13 31 238.2 4.30 1.47 65.9 3 4.38 20 29 298.1 2.16 2.69 24.4 4 3.03 13 5 304.0 3.78 7.19 7.66 6.5 5 3 13 319.0 2.82 2.31 18.1 5 2.04 5 13 328.6 18.4 5 6.12 7.24 6.41 29 13 301.5 'For 23 systems AAPD on 7; is 22.1, maximum error 65.9. References listed in Table IX.

the basis that the infinite-dilution activity coefficient of component A is known. The infinite-dilution activity coefficient of component B is then predicted from the assumed value of t12and the calculated value of k12, and then a percentage error is calculated between measured and predicted ym values. While t12values are always negative, typical values of klz range between -0.24and 0.35, except for polar-polar and alcohol-polar systems where, for a few binary mixtures, kI2 reaches the value of 0.7. Measured infiiite-dilution activity coefficients are taken from literature data summarized in Table IX to data-set numbers in Tables 111-VIII. Table I11 shows predicted data from 18 data seta for nonpolar-nonpolar systems where the average absolute error is about 2% in 7;. Table IV summarim results from 23 data seta for polar-nonpolar systems, and the average

Table V. Predicted Infinite-Dilution Activity Coefficients for Polar-Polar Binary Systemsn componenta 7; 7; A B T, K exptl exptl calc APD rep 6 13 323.0 0.54 0.44 0.62 41.1 1 13 308.7 6 0.46 0.34 0.56 64.9 1 344.0 0.52 6 20 0.46 0.46 0.0 1 1.18 16 13 323.0 1.32 1.22 7.7 1 13 303.0 7 0.41 0.49 0.50 2.1 1 13 7 303.2 0.46 0.55 0.55 0.0 2 20 21 333.4 1.06 1.10 0.98 10.9 3 20 21 347.5 1.04 1.10 1.11 1.1 3 14 9 333.2 1.03 1.02 1.02 0.0 7 21 14 338.2 1.23 1.22 1.18 2.9 7 21 22 323.2 1.25 1.25 1.29 3.0 7 21 22 348.2 1.23 1.23 1.23 0.0 7 'For 12 systems AAPD on y; is 11.1, maximum error 64.9. References listed in Table IX.

Table VI. Predicted Infinite-Dilution Activity Coefficients for Nonpolar-Alcohol Binary Systemsn componenta 7; 7; A B T, K exptl exptl calc APD rep 29 8 318.0 37.0 30.3 49.0 61.8 1 29 11 335.0 9.39 19.3 24.1 24.9 1 29 11 344.0 8.94 20.7 19.3 7.0 1 32 11 323.0 10.1 15.3 18.9 23.9 1 8.85 10.2 32 11 343.0 11.6 14.2 1 32 11 333.0 12.4 16.4 16.4 0.0 1 4.81 12.6 12.3 32 23 323.0 2.3 1 6.23 12.1 9.16 24.3 1 26 8 328.0 3.39 6.05 3.81 37.0 1 26 8 373.0 3.90 7.24 6.56 9.4 1 26 11 347.0 5.26 10.5 20.0 90.1 1 26 17 313.0 2.95 6.17 7.59 23.1 1 26 17 348.0 5.10 13.3 13.3 0.0 1 31 11 308.0 4.81 9.58 8.38 12.6 1 31 11 328.0 2.53 3.25 31 23 384.0 4.17 28.4 1 8.17 14.6 12.2 5 8 328.0 16.6 1 4.62 17.6 13.9 5 11 318.0 21.2 1 4.39 12.6 9.32 5 11 338.0 26.1 1 5 17 308.0 3.67 15.6 16.0 2.3 1 3.00 12.2 12.0 1 1.4 5 23 308.0 2.59 12.4 8.39 32.3 1 5 23 323.0 3.39 1.95 1.95 0.0 1 27 26 343.0 4.44 10.6 11.2 5.7 1 26 11 318.0 4.40 7.72 7.16 7.2 2 26 11 346.4 12.09 49.7 45.9 7.7 2 32 11 293.2 2.03 3.72 9.58 157.6 2 32 17 303.2 1.99 3.29 7.12 116.5 2 32 17 318.2 32 17 333.2 1.93 2.90 5.50 89.7 2 9.05 18.1 17.7 2.3 2 29 11 348.2 18.3 29.7 19.4 34.6 3 8 32 323.2 25.2 24.6 2.6 3 8 32 333.2 15.6 23.6 28.0 18.8 3 8 32 343.2 13.2 310.3 49.5 11 25 8.70 9.33 7.2 3 11 25 324.2 33.0 8.30 8.02 3.3 3 12.0 17.3 20.3 17.1 3 11 32 323.2 333.2 11.0 16.0 15.6 2.4 3 11 32 343.2 10.2 14.7 12.3 16.3 3 11 32 9.80 13.3 10.0 24.8 3 11 32 353.2 8.78 3.14 3.03 3.6 3 17 5 343.6 6.23 3.66 3.69 0.8 3 17 31 338.2 298.0 49.0 16.0 18.0 12.5 4 11 32 6.34 14.3 125.8 6 17 32 333.2 16.0 8.95 5.89 7.69 30.6 6 17 32 353.2 9.30 5.13 5.13 0.0 6 23 32 353.2 5.62 4.76 3.64 23.4 6 23 32 373.2 OFor 45 systems AAPD on 7; is 26.0, maximum error 157.6. bReferences listed in Table IX.

absolute error is about 22% in 7:. Table V summarizes resulta from 12 data seta for polar-polar systems, and the average absolute error is about 11% in 7;. This demon-

Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 423 Table VII. Predicted Infinite-Dilution Activity Coefficients for Polar-Alcohol Binary Systemsa componenta 7; 7; A B 2'. K exDtl exDtl calc APD 1.77 4.2 1.85 1.73 8 13 323.0 19.7 1.76 1.41 1.64 8 13 333.0 85.7 1.76 0.25 1.63 13 11 322.0 2.81 35.0 1.72 2.08 20 11 349.0 6.4 2.40 2.55 2.64 8 21 333.0 7.1 2.35 2.18 2.65 8 21 344.0 1.88 1.12 40.3 2.33 11 21 347.0 2.01 19.1 1.89 1.69 17 21 360.0 1.61 0.0 1.67 1.61 18 21 351.0 1.23 0.15 88.1 1.26 20 24 363.0 2.80 1.19 57.7 3.03 8 16 323.0 4.8 1.78 1.87 13 8 323.2 2.06 11.0 2.85 2.54 3.49 8 323.2 21 1.92 0.37 80.8 2.22 13 11 327.4 2.52 26.1 1.90 2.00 8 13 313.2 1.91 0.0 1.91 1.80 8 13 323.2 1.56 17.4 1.89 1.73 8 13 333.2 4.25 29.1 3.29 2.77 21 11 313.2 3.46 22.8 2.82 2.53 21 11 333.2 16.8 2.44 2.85 2.25 21 11 353.2 2.30 7.3 1.90 2.14 21 11 373.2 ~~

~~

rep 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 3

"For 21 systems AAPD on 7; is 27.6, maximum error 88.1 *References listed in Table IX. Table VIII. Predicted Infinite-Dilution Activity Coefficients for Alcohol-Water Systems' componenta 7; 7; A B 2'. K exDtl exDtl calc APD 19.7 5.42 4.35 2.35 1 11 323.0 1.6 5.21 5.29 2.49 1 11 323.0 i 23 378.0 3.71 54.6 47.9 12.3 67.8 67.4 3.98 40.5 1 23 376.0 18.5 47.0 3.98 39.7 1 24 333.0 39.5 25.5 3.35 42.1 1 24 353.0 7.4 31.3 3.67 33.8 1 24 335.0 32.4 4.2 3.53 33.8 1 24 350.0 35.3 10.0 3.42 32.1 1 24 367.0 5.06 9.4 4.62 1 313.0 20.9 17 3.60 1.87 48.1 1 333.0 16.8 17 0.61 81.2 3.25 1 369.0 14.3 17 4.03 22.4 3.29 23 1 343.2 68.03 3.13 3.67 17.2 23 1 353.2 48.53 5.1 2.97 3.12 23 1 372.2 27.11 3.27 4.03 23.1 1 343.2 67.8 23 3.64 16.7 3.12 1 353.2 46.5 23 2.09 13.6 3.83 2.42 1 298.2 11 2.10 12.9 3.88 2.41 1 298.2 11 2.11 13.0 4.12 2.43 1 303.2 11 2.18 12.9 2.50 1 323.2 5.01 11 2.52 2.22 11.7 5.61 11 1 343.2 2.25 8.9 5.90 2.47 1 363.2 11 2.27 4.4 6.05 2.37 1 383.2 11

Table IX. Literature References to Experimental Data in Tables 111-VI11 (1) Wilson, G. M. Infinite Dilution Activity Coefficients Estimation of One Binary Component from the Other. AIChE Symp. Ser. 1974,70,120. (2) Prauenitz, J. M. Private communication, 1990. (3) Tiegs, D., et al., Eds. Activity Coefficients at Infinite Dilution. Chemistry Data Series; Dechema: Frankfurt, 1986; VOl. IX, Part 1. (4) Thomas, E. R.;Eckert, C. A. Prediction of Limiting Activity Coefficients by a Modified Separation of Cohesive Energy Density Model and UNIFAC. Znd. Eng. Chem. Process Des. Dev. 1984,23, 194. (5) Tramp, D. M.; Eckert, C. A. Limiting Activity Coefficients from an Improved Differential Boiling Point Technique. J. Chem. Eng. Data 1990,35,156. (6)Pividal, K.A,; Sandler, S. I. Neighbor Effects on the Group Contribution Method Infinite Dilution Activity Coefficients of Binary Systems Containing Primary Amines and Alcohols. J. Chem. Eng. Data 1990,35,53. (7) Novotna, M., et al. Five Systems Containing the Bromide or the Chloride Group. Fluid Phase Equilib. 1986,27,373.

rep 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2

'For 24 systems AAPD on 7; is 19.0, maximum error 81.2. *References listed in Table IX.

strates that the correlation based on the modified scaledparticle theory satisfactorily predicts the effects of dispersion, inductive, and polar forces, except for polarnonpolar systems. Table VI summarizes results from 45 data sets for alcohol-nonpolar systems, and the average absolute error is about 26% in 7;. Table VI1 summarizes results from 21 data sets for alcohol-polar systems, and the average absolute error is about 28% in 7:. These results can be explained taking into account that an infinitely dilute alcohol will not behave in any way the same as a pure alcohol. To characterize these interactions correctly, it is necessary to apply some sort of "chemical"-type treatment

Table X. Summary of Deviations for the Calculation of y" from y" Wilson this work no. of data pointa class of AAPD max AAPD mas Wilson this work systems 14.0 14 18 6.4 13.0 2.3 nonpolarnonpolar 19.6 65.0 22.1 65.9 12 23 polar-nonpolar 17.2 35.0 11.1 64.9 6 12 p01ar- p01ar 47.3 543 26.0 158 32 45 nonpolaralcohol 15.4 46.0 27.6 88.0 13 21 polar-alcohol 25.6 70.0 19.0 81.0 15 24 watepalcohol 20.2 158 92 143 27.2 543 all systems

that accounts for the very specific hydrogen bonding that occurs in solution. Finally, Table VI11 summarizes results from 24 data sets for water-alcohol systems, and the average absolute error is about 19% in 7;. The results obtained for alcohols in nonaqueous solvents, in fact, are less satisfying than those of Lobien and Prausnitz (1982),who used the chemical theory to take into account association between alcohol molecules. The scaled-particletheory does not take account of this effect. A rough comparison of predicted activity coefficients with values predicted by the method proposed by Wilson (1974)is shown in Table X. Except for the class of alcohol-polar systems, our correlation gives better results. In the computation of the average deviations of the method of Wilson (1974),the maximum error of 543% was not taken into account.

Conclusions A new method is proposed for estimating the infinitedilution activity coefficient of one binary component starting from that of the other component. The method has been tested against 143 binary sets of data with satisfactory results. Comparison with other proposed methods shows that the modified scaled-particle theory can be used with confidence even when association occurs. In this case, however, the method proposed by Lobien and Prausnitz (1982)gives better results because they take account of association using chemical theory. Acknowledgment We are indebted to the Italian Minister0 dell'Universiti e della Ricerca Scientifica e Tecnologica for financial support. Registry No. Water, 7732-18-5;hydrogen sulfide, 7783-06-4; carbon disulfide, 75-15-0;carbon dioxide, 124-38-9; carbon tet-

Ind. Eng. Chem. Res. 1992, 31, 424-430

424

radoride, 5623-5; chloroform, 67-66-3; dichlommethane, 7509-2; methanol, 67-56-1; l,l,l-trichloroethane, 7 1 - 6 6 ethane, 74-844 ethanol, 6417-5; propylene, 115-07-1; acetone, 67-64-1; 1bromopropane, 106-94-5; propane, 74984 methyl acetate,79-209; n-propanol, 71-23-8; 2-propanol, 67-63-0; furan, 110-00-9;2-butanone, 78-93-3; ethyl acetate, 141-786; l-chlorobutane, 109-69-3; n-butanol, 71-36-3; sec-butanol, 78-92-2; n-pentane, 109-66-0; benzene, 71-43-2; phenol, 108-952; methylcyclopentane, 96-37-7; n-hexane, 11@54-3;n-peduorohexane, 35542-0; toluene, 108883; n-heptane, 142-82-5.

Literature Cited Boublik, T.; Fried, V.; Hala, E. The Vapor Pressures of Pure Substances, 2nd ed.; Elsevier: Amsterdam, 19W, pp 65-67. Brandani, V.;Di Giacomo, G.; Mucciante, V. A Group Contribution Method for Correlating and Predicting the Second Virial Coefficient of Hydrocarbons, Including Second V i Croea-Coefficients. Chem. Biochem. Eng. Q. 1987,1, 109. Bruin, S.; Prauanitz, J. M. OneParameter Equation for Excess Gibb Energy of Strongly Nonideal Liquid Mixtures. Znd. Eng. Chem. Process Des. Dev.1971, 10, 562. Choliiski, J.; Szafranski,A.; Wyrzykowska-Stankiewicz,D. Computer Aided Second Virial Coefficient Data for Organic Zndividual Compounds and Binary System. PWN-Polish Scientific Publishers: Warszawa, 1986. Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures. Clarendon Presa: Oxford, 1980. Geller, E. B.; Battino, R.; Wilhelm, E. The Solubility of Gases in Liquids. 9. Solubility of He, Ne, Ar, Kr, Nz, Oz, CO, COz, CHI,

CF, and SFein some Dimethyl-Cyclohexane at 298 to 313 K. J. Chem. Thermodyn. 1976,4197. Hirschfelder, J. 0.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954. Lobien, G. M.; Prausnitz, J. M. Correlation for the Ratio of Limiting Activity Coefficiente for Binary Liquid Mixtures. Fluid Phase Equilib. 1982,8, 149. Moelwyn-Hughes, E. A. Physical Chemistry, 2nd ed.; Pergamon Press: Elmsford, NY,1961. Pierotti, R.A. A Wed Particle Theory of Aqueous and Nonaqueous Solutions. Chem. Rev. 1976, 76, 717. Prausnitz, J. M.; Grens, E. A.; Anderson,T. F.; Eckert, C. A.; Hsieh, R.; OConnell, J. P. Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria; Prentice-Hak Englewood Cliffs, NJ, 1980. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. Riddick, J. A; Bunger, W. B. Technique8 of Chemistry; Weesberger, A., Ed.; Organic Solvents, Vol. 11, 3rd ed.; Wiley-Interscience: New York, 1970. Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17, 236. Taeeioa, D. SinglaPammeter Equation for Isothermal Vapor-Liquid Equilibrium Correlations. AIChE J. 1971, 17, 1367. Wilson,G. M. Infiiite Dilution Activity Coefficiente Estimation of One Binary Component from the Other. AIChE symp. Ser. 1974, 70, 120. Received for review May 13, 1991 Revised manuscript received Auguet 22,1991 Accepted September 5,1991

Chemistry of a Single-Step Phosphate/Paint System Chhiu-Tsu Lin,* Ping Lin, and Meen-Woon Hsiao Department of Chemistry, Northern Illinois University, DeKalb, Illinois 60115-2862

Dean A. Meldrum and Frank L. Martin Finishes Unlimited, Znc., Wheeler Road, P.O. Box 69, Sugar Grove, Illinois 60554

A single-step phosphatelpaint system comprised of polyester-melamine enamels and H3P04was successfully formulated. The system stability, compatibility, and thermal curing behavior as well as chemical mechanism were investigated using the experimental techniques and theoretical modelings. When the unicoat system is applied on a “qpanel, the experimental results indicate that H3P04tends to diffuse to and react with the metal surface, providing a corrosion protective barrier to the substrate and simultaneously making available the proper functionality to form chemical bondings with polymer resins. Electrochemical impedance spectroscopy was employed to measure the resistive properties for the single-step phosphate/paint system. The data show that the unicoat film is a quasi-nonporous coating that has a good quality of the adhesion layer to the substrate and which also has a good corrosion-protective barrier-type property.

Introduction The surface treatment of steel prior to the application of a mating or adhesive is a conventional industrial practice to improve the adheaion and inhibit corrosion (Hare, 1978). The phosphate conversion coating consists of a nonconductive layer of crystals/amorphous that insulatethe metal from any subsequently applied film and provides a topography with enhanced “tooth”for holding the film (Hall, 1978). The quality of finish required by an industrial product determines the degree to which the pretreatment and phosphatizing are carried out in the multistep process. The metal surface is normally cleaned by several possible pretreatment steps, phosphated, sealed, dried, and then painted.

* To whom correspondence should be addressed.

The development of a single-step phosphate/paint system technique by incorporating a polymeric resin, cross-linker, and H3P04has never been reported. The simplicity involved in the application of a single-step phosphate/paint over present multistep methods will make this product attractive to many manufacturers of metal products. The success of a single-step phosphate/paint system will increase the quality of finish coatings without the capital and operating expenses of a separate phosphate line. The present state of the art in the principal pretreatment or metal conditioner of the maintenance painting industry is the WP-1Wash Primer (Hare, 1978)or onepack etch primer (Waldie et al., 1984). These primers contains no cross-linker in the formulations. However, this unique material is a two-pack phosphate/vinyl butyl resin system or a single package of poly(viny1 butyral) resin/

0888-5885/92/2631-042~~~3.00 f 0 0 1992 American Chemical Society