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Ind. Eng. Chem. Fundam. 1983, 22, 1-4
Excess Second Virial Coefficients for Nitromethane and Cyclohexane at 373.2 K and Nitroethane and Cyclohexane at 298.25, 323.16, and 348.38 K Kenneth N. Marsh"' and Harold P. D. Rogers' Department of Chemlcal Englneerlng, Universlty of Canterbury, Chrlstchurch, New Zealand
The excess second virial coefflcients of nitromethane and cyclohexane at 373.2 K and nitroethane and cyclohexane at 298.25, 323.16, and 348.38 K have been measured by use of a differential technique. The excess second virlal coefficients are large and posithre. The resutts for both pure nitromethane and the mixtures are satlsfactorlly predicted by the correlation proposed by Hayden and O'Connell.
Introduction A number of generalized correlation methods have been proposed for predicting the second virial coefficients of gases and gas mixtures (O'Connell and Prausnitz, 1967; Tsonopoulos, 1974; Hayden and O'Connell, 1975). While these correlations have been shown to give good predictions for nonpolar and slightly polar gases and gas mixtures they have not been fully tested on gases and gas mixtures involving fluids with a large dipole moment. The nitroalkanes are polar, having a large dipole moment of about 12 X 10-30C m (3.5 D) and in the gas phase they show little evidence of self-association. Measurements on these compounds and on their mixtures with nonpolar compounds should provide a stringent test for the correlations. The direct measurement of virial coefficients of polar gases, particularly at low pressures and at temperatures below their normal boiling point, is difficult because of the problems associated with adsorption. For mixtures, an alternative procedure is to measure the excess second virial coefficient since such measurements are not as sensitive to adsorption (Knobler, 1978). This paper presents the excess second virial coefficients for the binary mixtures nitromethane and cyclohexane at 373.2 K and nitroethane and cyclohexane at 298.25,323.16, and 348.38 K measured with a Delta P apparatus described previously (McElroy et al. 1980). The excess second virial coefficient, t, is defined by = B12 - Wll
+ B22)
(1)
where Blz is the mixture virial coefficient and Bll and Bz2 are the virial coefficients of the pure components. For measurements at pressures sufficiently low for virial terms higher than the second to be neglected, the excess second virial coefficient can be calculated from the pressure change Ap which occurs when volumes of two pure gases, initially at the same pressure, are mixed at constant total volume and temperature. E
= RTAp/b2(1 + A P / P ) ~ Y I Y Z ~ P(&I - Bz2)'/2RT + 2ptbiB11 + Y ~ & ) / R T (2)
where y1 and y2 are the mole fractions of component 1and 2. For the case where the gases occupy equal volumes then y1 = yz and a first approximation to eq 2 is Department of Chemistry, University of New England, Armidale, N.S.W., 2351, Australia.
t
-
2RTAp/p2
(3)
Equation 2 can be solved for a t iteratively using eq 3
to obtain an initial estimate of t. Convergence is generally rapid, two cycles being required for convergence to better than lo4 m3 mol-l. The conditions of all the experiments were such that the leading term of eq 2 dominated, with the second and third terms collectively contributing a maximum of two percent to the final value of t. The approximate estimate of the error in t is given by &/e
= [(SAp/Ap)2 + ( 6 T / q 2
+ 2 ( S p / ~ ) ~ ] (4) ~/~
The value of ( 6 A p l A p ) has the largest influence on the uncertainty in t.
Experimental Section Materials. Koch-Light Puriss grade cyclohexane with a specified purity (determined by GLC) of greater than 99.0 mol % was used without further purification for the measurements at 348.38 K and for one of the measurements at 323.16 K. The cyclohexane used for the remainder of the measurements was May and Baker laboratory grade material distilled on a Teflon spinning-band distillation column at atmospheric pressure, the retained fractions being stored over sodium wire. Analysis by GLC indicated that the purity was greater than 99.9 mol %. The nitromethane (Matheson, Coleman and Bell specified purity greater than 98 mol '70)was distilled on a thirtyplate Oldershaw column at 13 kPa. The retained middle fractions were stored in a well-stoppered flask to minimize moisture contamination. The purity, as determined by GLC, was greater than 99.8 mol %. The nitroethane (Matheson, Coleman and Bell) was purified in a similar manner and had a purity of greater than 99.9 mol %. Apparatus. A detailed description of the apparatus and the procedure for operation has been published (McElroy et al., 1980). The apparatus is shown schematically in Figure 1. The volume of each of the three stainless steel containers was about 6 L. After evacuation to better than 0.05 Pa, V I , V3, and V5 were closed and an excess of cyclohexane was distilled into vessel MIX 2. Valve V2 was closed and the line was evacuated. Valve V1 was then opened and either nitromethane or nitroethane was distilled into the vessels MIX 1 and REF. When the gases reached thermal equilibrium, valve V6 and tap T2 were opened and dry nitrogen was admitted through T1 until the differential pressure gauge (an M. K. S. Baratron) registered approximately zero differentially pressure. The
0196-4313/83/1022-0001$01.50/00 1983 American Chemical Society
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Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983
Table I. Excess Second Virial Coefficients for the Mixture Nitroethane + Cyclohexane and Nitromethane + Cyclohexane
~
vac
-
I
1
~
T/K
J
I man
I
1
Figure 1. Schematic diagram of the mixture virial coefficient apparatus.
final adjustment to zero differential pressure was obtained by altering the volume of the ballast valve (BJ. The nitrogen pressure was read from the mercury manometer with a Precision Tool and Instrument cathetometer readable to 0.001 cm. However, vibration in the manometer and the presence of thermal gradients in the manometer case reduced the accuracy of the loading pressure to -10.01 kPa. The nitrogen was removed by evacuation and then V6 was closed. Valve V5 was then opened and cyclohexane was bled through V2 until there was a zero differential pressure across the gauge. The adjustment was done in small increments as the pressure difference approached zero because it was necessary to wait for thermal equilibration after the cooling which occurs because of the adiabatic expansion. The true gauge zero was then obtained by opening V3 and slowly closing V4. Valve V5 was closed and the components were mixed by freezing both components into vessel MIX 1. Valve V3 was then closed and the re-entrant well of MIX 1was warmed to the bath temperature and the mixed gas was then expanding into the total volume by opening V3. Valve V5 was opened after a short period and the difference in pressure between the mixture vessels and the reference vessel was determined from the reading of the differential gauge after attainment of thermal equilibrium. A final check on the zero of the differential gauge could be obtained by opening V4 at the completion of the experiment. The effect of premature mixing caused by opening V3 to obtain the gauge zero, and the amount of gas trapped beyond V5, and therefore unmixed, were taken to have a negligible effect on the measurement. The oil bath temperature was maintained to fO.O1 K at 323.16,348.38, and 373.15 K and to f0.02 K at 298.2 K. Measurements were made at 2 or 3 pressures at each temperature. Temperatures were measured with a Rosemount platinum resistance thermometer (Serial number 409) and Rosemount precision comparator bridge (model VLF 51A). The precision in the differential pressure measurements ranged from 0.3 to 3 % . Adsorption Correction. Shannon (1976) has given an expression for a correction due to adsorption A€ = V(n1
+ n2)[(n2”- n2/)/n2 + (n,” - nl’)/nll/(2nln2) ( 5 )
where the adsorbed quantities of each component before
p/Pa
Ap/Pa
E(uncor)/ €(cor)/ cm3 cm3 mol-’ mol-’
298.28 298.21 323.16 323.17 348.39 348.38 348.38
Nitroethane + Cyclohexane 1619 0.83 1561 1699 0.87 1484 4633 4.44 1100 6380 9.08 1182 7530 8.85 894 9314 13.04 859 16041 37.74 831
2145 1954 1206 1211 947 893 839
313.15 373.15 373.15
Nitromethane t Cyclohexane 9927 11.08 691 21315 88.74 116 30806 115.5 7 34
729 721 738
mixing (n;) and after mixing (n?) can be calculated from the BET expression (Emmett and Brunauer, 1937) ni = [ A m S C i ( ~ i / ~ i o ) l1/1 - ~ i / ~ i 0 1 [+1 (Ci- 1 ) ~ i / ~ i 0 l (6)
where A, is the monolayer capacity in amount of substance per unit area, S is the surface area available for adsorption, Ci is a constant for the interaction between the adsobate and the substrate, pi is the pressure, and piois the pure component saturation vapor pressure. For cyclohexane, A , and C are taken as 4.5 X lo+ mol m-2and 100, respectively (Shannon, 1976; McElroy, 1980). The surface area available for adsorption was taken as the geometric surface area of the cylinden, 0.24 m2but because of the known nature of stainless steel surfaces this is regarded as an underestimate. The monolayer capacity for nitroethane and nitromethane was estimated (Gregg and King, 1967) from A , = 1/ [ L f ( M / L d ) 2 / 3 ]
(7)
where d is the density, f is a packing factor, and L is the Avogadro constant. Using the calculated liquid density at 323 K and assuming a packing factor of 12 for the bulk liquid, A , for nitroethane and nitromethane were calculated to be 6.1 X lo4 and 7.1 X lo* mol m-2, respectively. However, the adsorption behavior of polar molecules on polar substrates is poorly understood and consequently there is some doubt regarding the reliability of the value of A,. The parameter C was taken as 1000 for the nitroalkanes to reflect strong adsorption as inferred from the comparitively slow rate with which they were evacuated from the stainless steel cylinders. However, the adsorption isotherm is not greatly affected by the choice of the various parameters as indicated by the following calculations. With C at 100 for nitroethane and calculated values of €(cor) are approximately 1.5% lower at 298 K and less than 0.5% lower at the remaining temperatures. Values of C larger than 1000 lead to the/ same value of €(cor)as that obtained with C = 1000. The main error in the adsorption correction is the uncertainty of the true surface area of the vessels. Results and Analysis The experimental results together with the corrections due to adsorption are given in Table I. In order to determine the mixture virial coefficient BIZthe virial coefficient of the pure components as well as the excess mixture virial coefficient must be known. The second virial coefficients for cyclohexane and nitromethane have been critically compiled by Dymond and Smith (1980). Since
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983 3
Table 111. Calculated and Experimental Second Virial Coefficients 298.15 323.15 348.15 373.15
f
1
I
1'
300
I
I
320
1 340
I
I
1
360
T/K
B,, (calcd)/cm3mol-'
Cyclohexane -1725 -1355 -1095
B,, (calcd)/cm3 mol-'
Nitroe thane -5140 -3235 -2210
Nitroethane t Cyclohexane E(exptl)/cm3 mol-' 2050 1208 c(calcd)/cm3mol-' 2356 1404
890 923
Figure 2. Comparison between the Prausnitz and O'Connell correlation (---) and the O'Connell and Hayden correlation (-'-) for nitromethane and the experimental results (-).
Nitromethane B,, (exptl)/cm3mol-' -2900 -2060 -1510
Table 11. Parameters Used for Calculating the Pure Second Virial and Mixture Second Virial Coefficients
E
cyclohexane nitromethane nitroethane
553.2 588.15 557.15
40.2 62.3 52.0
308 173 215
2.90 2.31 2.90
0 3.44 3.65
E
0 1.60 1.60
there are no measurements on nitroethane it was necessary to estimate a value by a correlation procedure. Three empirical correlations for the prediction of second virial coefficients were investigated (O'Connell and Prausnitz, 1967; Tsonopoulos, 1974; Hayden and O'Connell, 1975). The suitability of the various correlating procedures was gauged from the ability of the particular procedure to predict the experimental second virial coefficient of nitromethane. The correlation of O'Connell and Prausnitz (1967), using the parameters recommended for nitromethane, gave a poor prediction of the second virial coefficient as shown in Figure 2. The Tsonopoulos extension of the treatment of O'Connell and Prausnitz requires parameters derived from experimental data on representative members in each class of compound. There are insufficient measurements on the nitroalkanes to calculate the various parameters and estimates using the available parameters gives poor agreement with the experimental results. The correlation proposed by Hayden and O'Connell (1975) is a predictive method based on a consideration of intermolecular forces developed within the framework of the dynamics of pair collisions. The authors claim it to be a versatile predictive procedure and to be the only correlation suitable for mixtures involving large nonpolar molecules with polar molecules. This correlation gave very good predictions of the second virial coefficients of both cyclohexane and nitromethane using the parameters given by Fredenslund et al. (1977). The parameters required by the Hayden and O'Connell method are the critical pressure P,, the critical temperature T,,the dipole moment p , the mean radius of gyration R d , an association parameter 7 and a solvation parameter. In this work the association and solvation parameters were taken as adjustable parameters. The radius of gyration can be calculated (Reid and Sherwood, 1958; Fredenslund et al., 1977), but it was treated as adjustable for cyclohexane. The solvation parameter was taken as zero. The fit to cyclohexane was further improved over the temperature range of interest by adjusting R d from 3.56 to 2.90 A while the fit to nitromethane was improved by adjustment of 7 from 1.66 to 1.60. The parameters used are tabulated in Table 11. For nitroethane the only effective adjustable parameter is 7. As this parameter is linked with the polar nature of the molecule and since the dipole
Nitromethane t Cyclohexane (exptI)/cm3mol-' (calcd)/cm3mol-'
730 629
moment of the two nitroalkanes are similar it was assigned a value of 1.60. The excess mixture virial coefficients were calculated directly from the equations given by Fredenslund et al. (1977) without using any further adjustable parameters and the results for the two mixtures are give in Table 111. Discussion The values of the excess mixture second virial coefficient determined with a Delta P apparatus for mixtures involving highly polar substances particularly at low temperatures are sensitive to adsorption but not to the same extent as would be observed in a conventional p,u,T experiment. The estimated maximum uncertainities in the values o f t are 150 cm3mol-l at 298 K, 60 cm3mol-' at 323 K, and 50 cm3 mol-' at 348 and 373 K. Taking these uncertainities into account the agreement between the experimental results and the values predicted by the Hayden and O'Connell method is satisfactory when one considers that no adjustable parameters have been used. The O'Connell and Prausnitz correlation gave the wrong value for the second virial coefficient of nitromethane, and the values of t for the two mixtures were considerably different from the experimental values. It is possible to bring the values calculated from the Hayden and OConnell approach into agreement with the experimental results at all temperatures by a small adjustment of the association parameter from 1.60, the value given for nitromethane, to 1.45. One would expect a decrease in this association parameter as the size of the hydrocarbon residual increases. It is concluded that the Hayden and O'Connell correlation for the calculation of the mixture second virial coefficient is reasonable for mixtures of nitroalkanes with cyclohexane, Acknowledgment The authors are grateful to Professor A. Williamson for his hospitality during a stay at the University of Canterbury, Christchurch, New Zealand. K.N. Marsh thanks the University of New England for leave and H. Rogers was a recipient of a Commonwealth Postgraduate Scholarship. Registry No. Cyclohexane, 110-82-7; nitromethane, 75-52-5; nitroethane, 79-24-3.
Literature Cited Dymond, J. H.; Smith, E. B. "The Virlai Coefficients of Pure Gases and Mixtures", Oxford Unlversity Press: Oxford, 1980; pp 34, 162. Emmett, P. H.; Brunauer, S. J. J . Am. Chem. SOC. 1937, 59, 1953. Fredenslund, A.; Gmehiing, J.; Rasmussen, P. "Vapour-Liquid Equilibrium Using UNIFAC, A Group Contribution Method";Elsevier: Amsterdam, 1977; Chapter 2. Gregg, S. J.; King, K. S. W. "Adsorption Surface Area and Porosity"; Academic Press: London, 1967; p 67.
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Ind. Eng. Chem. Fundam. 1983, 22, 4-6
Hayden, J. G.; O'Connell, J. P. Ind. Eng. Chem. Process Des. Dev. 1975, 74, 20s. Knobler, C. M. I n "Chemical Thermodynamics", McGlashan, M. L., Ed.; The Chemical Society: London, 1978; Vol. 2, Chapter 7. McElroy, P. J.; Shannon, T. W.: Williamson, A. G. J. Chem. Thermodyn. 1980, 72, 37 1. O'Connell, J. M.: Rausnitz, J. M. Ind. Eng. Chem. Process Des. Dev. 1967, 6 , 245.
Reid, R. C.; Sherwood, T. K. "The Properties of Liquids and Gases"; McGrawHill: New York, 1958: p 21. Shannon, T. W. Ph.D. Thesis, University of Canterbury, New Zealand, 1976. Tsonopoulos. C. AIChE J. 1074, 2 0 , 263.
Received for review July 2, Accepted August 24,
1981 1982
Global Rates of Reaction in Trickle-Bed Reactors: Effects of Gas and Liquid Flow Rates Mordechay Herskowltz' and Shelomo Mosserl Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel
Global rates of reaction were measured in a batch-recycle trickle-bed reactor. The hydrogenation of a-methylstyrene to cumene on a Pd/A1,03 catalyst at atmospheric pressure and 40 O C was employed. The liquid and gas flow rates were varied over a wide range in the gas-continuous flow regime. The effect of gas and liquid rates on the rate of reaction is Significant. Calculations of the wetting efficiency were performed with intrinsic kinetic parameters measured in a stirred tank and the Goto and Smith correlation for the liquid-solid mass transfer. The results indicate that the wetting efficiency depends strongly on the liquid rate at high gas rates, and it is almost independent of liquid rate at low gas rates.
Trickle-bed reactors have been the subject of numerous experimental studies during the past decade. Recent studies (Morita and Smith, 1978; Herskowitz et al., 1979; Mata and Smith, 1981) have indicated that in the gascontinuous flow regime the liquid flow rate may have a significant effect on the global rate of reaction, especially at low liquid flow rate. The effect is twofold. Increasing the liquid flow rate enhances both the rate of liquid-solid mass transfer and the wetting efficiency of the catalyst particles (defined as the fraction of the particle external surface covered by flowing liquid). The wetting efficiency f, is less than unity at liquid Reynolds numbers less than about 20. It has been reported in a number of studies (Herskowitz, 1978) that f decreases with decreasing liquid flow rate, but no reliable correlation off as a function of the liquid flow rate and other operating parameters has yet been proposed. If the particle is not completely covered by flowing liquid (f < l),gaseous reactants may be transferred from the gas to the particle surface through a very thin layer of stagnant liquid (called the gas-covered surface or the dry surface). The resistance to mass transfer on the gas-covered surface may be significantly lower than on the liquid-covered surface. This would enhance the global rate of reaction. As a result, the global rate of reaction may increase with decreasing liquid flow rate, even though the liquid-solid mass transfer rate decreases. Herskowitz et al. (1979) and Mata and Smith (1981) have measured global rates of reaction that decreased with increasing liquid flow rate, reached a minimum, and then increased with further increase in liquid flow rate. Clearly, this behavior is expected if the liquid-solid mass transfer resistance is important over the range of liquid flow rates. The effect of the gas flow rate on the global rate of reaction has also been investigated. Morita and Smith (1978) and Herskowitz et al. (1979) found this effect to be insignificant. However, the experiments were performed at relatively high liquid flow rates. Furthermore, the ac-
tivity of the catalyst was not high so that the effect of the gas flow rate would be expected to be insignificant. The objective of this work was to determine the effect of the gas and liquid flow rate on the global rate of reaction. The hydrogenation of a-methylstyrene on a Pd/ A1203catalyst was selected for this work. The reaction is first order in hydrogen, with cumene as the only product. At ambient temperature and atmospheric pressure a relatively active Pd/A120, catalyst could yield high intrinsic rates of reaction, so that the interphase mass transfer resistances would be important. The intrinsic kinetics was measured in a batch reactor for the liquid. Trickle-bed runs were performed in a batch-recycle reactor.
Experimental Section The stirred tank reactor consisted of a 1-Ljacketed resin flask manufactured by Sovirel. A four-bladed turbine impeller powered by a variable-speed motor provided thorough agitation. The reactor operation was semibatch with the hydrogen being introduced through a dispersion tube and leaving through a condenser. The dispersion tube was located just below the impeller to improve the gasliquid mass transfer. The condenser was maintained at 0 "C so that liquid loss could be avoided. In the batch-recycle system the liquid was pumped from a reservoir (where the liquid was saturated with hydrogen) to the reactor, flowed concurrently with the gas (hydrogen), and then was separated from the gas and returned to the reservoir. A schematic diagram of the apparatus is shown in Figure 1. The liquid was fed to the reactor by a variable speed peristaltic pump (Heidolph). Fluctuations in the pump discharge were dampened with a surge tank. The distributor consisted of five 0.09-cm i.d., 1.1cm long capillary tubes (stainless steel) for the liquid and eight 0.05-cmholes for the gas, placed uniformly as shown in Figure 2. Several runs were performed with a similar distributor made of twelve tubes.
0196-4313/83/1022-0004$01.50/00 1983 American Chemical Society
