T h e reaction kinetics were found in the following way. We assume the amount of CO which is oxidized to be proportional to AT, and define the fractional conversion to be hT/AT,,,. At a given temperature, the fractional conversion is independent of CO concentration, indicating a first-order reaction. For a given CO level, the conversion was not affected by changes in the 0 2 partial pressure for 02-to-CO ratios of 1.3 to 3.5, the stoichiometric ratio being 0.5. The reaction is thus independent of the 0 2 concentration within the specifications mentioned above. T o determine the activation energy, the natural logawas plotted us. 1/T. From rithm of A T m a x / ( A T m a x the slope of the linear portion (20-70% conversion or 180220") a n activation energy of 17 kcal/mol was calculated. These results agree quite well with those obtained by Hertl and Farrauto (1973) using a more conventional catalytic reactor.
An
Summary The DSC test is a convenient way to evaluate the catalytic oxidative performance of materials and to determine their response to certain treatments. We have found t h a t some information about reaction kinetics can be gotten from DSC data. Although detailed agreement between
DSC results and those of more sophisticated experiments is not always found, there is good correlation of general performance trends. In general, samples which showed poor DSC response did not perform well on either bench or engine tests. Acknowledgments Some of the experiments discussed in this paper were done following suggestions of Dr. Larry E. Campbell. Mr. Norman A. Woodward performed some of the measurements. The authors are grateful for their assistance. We would also like to thank the anonymous reviewers who suggested improvements to the original manuscript. L i t e r a t u r e Cited Altshulier, A. P., Cohen, I. R . , Ana/. Chem.. 32,802 (1960). Hertl. W.. Farrauto, R. J., J. Cafai., 29, 352 (1973). Locke, C. E., Rase, H.F., lnd. Eng. Chem., 52, 515 (1960). Papadatos, K., Shelstad. K. A,, J. Catai.. 28, 116 (1973). Shelef, M., Dalla Betta, R. A,, Larson, J. A,, Otto, K., Yao, H. C., presented at the 74th National Meeting of the AIChE. New Orleans. La., March 11-15, 1973.
Received for reuieu: April 19, 1973 Accepted July 9, 1973
Correlation and Prediction of Excess Thermodynamic Functions of Strongly Nonideal Liquid Mixtures lsamu Nagata" and Toshiro Yamada Deparfment of Chemical Engineering, Kanazawa University. Kanazawa, 920, Japan
Excess enthalpy of mixing data are obtained for the ethanol-cyclohexane system at 35 and 45" and for the ethanol-methylcyclohexane system at 25, 35, and 45". The Wilson equation whose energy parameter differences are given by a quadratic function of temperature can be very useful for the prediction of binary excess heat capacity data. Good predicted results are shown for five binary alcohol-hydrocarbon systems using the parameters obtained from the excess Gibbs free energy and heat of mixing data over a moderate temperature range. This technique is easily extended to multicomponent systems. The ternary prediction of these three thermodynamic functions is presented for the ethanol-cyclohexane-nheptane mixtures over a 20-60" range.
Introduction Recently several investigations have been carried out to fit the excess enthalpy of mixing as well as the excess Gibbs free energy for completely miscible liquid mixtures using the Wilson equation. Orye (1965) and Hanks, et al. (1971), used the simplified assumption t h a t the energy parameter differences (AL, - A L L ) were independent of temperature. However, in order t o obtain the simultaneous good representation of both excess data for a great number of nonideal systems whose heat of mixing values are more than about 120 cal/mol, it is found that the Wilson parameters should be assumed to change with temperature as pointed out by Ratkcovics (1970), Ratkovics and Rehim (1970), Duran and Kaliaguine (1971). Kaliaguine and Ramalho (1972), Trinh, Ramalho, and Kaliaguine (1972), Nagata and Yamada (1972), and U'olfbauer (1972). Kaliaguine and others adopted the A[, form as the
Wilson parameters. On the contrary, other investigators used the energy parameter differences (AL, - A L L ) .Ratkovics, Rehim, Nagata, and Yamada assumed that the energy parameter differences varied with temperature linearly. Wolfbauer used the energy parameter differences and their derivatives with respect to temperature in curve fitting. Nagata, et al. (1973a,c), further demonstrated t h a t the assumption of a quadratic function of temperature for the energy parameter differences is suitable for the simultaneous correlation of excess Gibbs free energy ( g " ) and heat of mixing ( h b : ) data over a moderate temperature range and that it is also successful for the prediction of excess heat capacities Ic,E) for binary alcohol-hydrocarbon and hydrocarbon-hydrocarbon mixtures, showing the superiority of the Wilson equation over the nonrandom two liquid (Renon and Prausnitz, 1968) and Heil (Heil and Prausnitz, 1966) equations. In other words, this Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
47
Table 1. Physical Constants of Compounds Compound Cyclohexane Ethanol Rlethylcyclohexane
BP, "C
Density (25')
80 8
0 7739
80 725' 78 3 78 29' 100 9 100 934a
Refractive index n Z 5 ~
1 1 1 1 1 1
0 773891 0 7852 0 78504" 0 7652 0 76506a
42355 42354a 35944 35941" 42052 4205@
Riddick and Bunger 11970). Table 11. Experimental Heat of Mixing D a t a for the Ethanol(l)-Cyclohexane(2)System at 35 and 45"
35
45O
_____-___.
h' , cal 'mol
XI
XI
0,1099 0.1976 0.2947 0.3951 0.4940 0.5364 0 5898 0,6900 0 7940 0.8958
118.28 142.35 162,14 172,59 182.53 172.63 163,74 128.06 69.67
0.0985 0.1528 0.2098 0,2919 0.4552 0.5477 0.6114 0.7547 0.8999
_--
h' , callmol
162.47 192.18 213.72 214.17 212.02 204.11 190.97 170.23 130.66 79.77
MOLE FRACTION ETHANOL
Figure 1. Heats of mixing for the ethanol-methylcyclohexane system: calculated (--); experimental ( A ) 25', this work; ( O i 35", this work; ( H i 35', Brown, et ai.(19563; ( 0 )45', this work.
Table 111. Experimental Heat of Mixing Data for the Ethanol~l)--Methylcyclohexanei2) System at 25,35,and 45"
25
means that our proposed form for the Wilson parameters leads to the successful correlation of three independent thermodynamic quantities @, hE, and cI,E in consistent way. T h e complexity of the analytical expression for .illin Wilson's equation permitted Kaliaguine and others the use of .til's and their first derivatives with respect to temperature in the simultaneous fit of p" and hE d a t a . Which form is valid as the LVilson parameters should be checked by comparing experimental c I , E data with calculated results derived from the Wilson equation with proposed parameter form. As a matter of fact the simultaneous fitting of g E and h" and t h e subsequent prediction of c , , ~is actually a test of simultaneous representation of t h e &'s, of their first derivatives ( 6 - i l J / d T )and , of their second derivatives (P.i /a P ) ,respectively. The objective of the present investigation is *toshow the capability of Kaliaguine and coworkers' method and the present author's approach concerning the Wilson parameters for the prediction of c!," d a t a for binary alcohol-hydrocarbon solutions and to predict the three excess thermodynamic functions of the ethanol-cvclohexane-nheptane system over a moderate temperature range from binary parameters.
x1 hi., ca1:mol
0.1046 0.1980 0.2983 0,3479 0.4995 0.5450 0.6966 0,7985 0,8487 0,8905 0.8940
45
35 O
________ x,
111.12 124.99 134.15 135.98 135.80 135.51 121.60 97.61 85.24 63.58 62.81
hl:,
0,1043 0,1546 0.1986 0.3113 0,3929 0.4939 0.5431 0,5924 0,6920 0,7923 0.8886 0.8895
cal
