The corresponding confidence interval on k itself is 0.89 6.52
&=--=
0.14
Conclusions
T* = instrument dial reading t 4 = value of t distribution for level of confidence and M - 2 degrees of freedom V = tangential velocity Greek Letters = level of confidence y = shearrate 6 k , 6, = half ranges in k and n 7,7* = shear stress, shear stress on bob w = bob angular velocity w* = bobrpm ~ i , = pairs of data points of bob shear and angular velocity i2 = sum as defined in (7) CY
This numerical treatment offers a method for reducing viscometer data obtained for a power-law fluid. It provides estimates and confidence intervals for the two necessary parameters which are nonsubjective, which is especially important in communicating rheological measurements. The general method presented here can be specialized to particular instruments by modifying the computational scheme so that it deals directly with the recorded d a t a torque (or scale factor) and rpm. This can readily be accomplished by appropriate substitution in eq 16. If all additional constants ~ , subsequent procedure are then grouped with k ( 2 / r ~ )the becomes clear. Nomenclature k,n = power law constants K = instrument spring constant L = bob effective length M = number of data points r = radial coordinate R = bobradius S, SI,S2, SB,T = sums as defined in eq 2-6
Literature Cited Back. A. L., Rubber Age, 84, 639 (1959). Beers, Y., "Introduction to the Theory of Enors", p 26, Addison-Wesley, Reading, Mass., 1957. Eubank, P. T., Fort, B. F., /SA Trans.,6, 298 (1967). Kreiger. J. M., Maron, S. H., J. Appl. Phys., 23, 147 (1952). McKennel, R.. Anal. Che?, 32, 1458 (1960). Miller, I., Freund, J. E., Probability and Statistics for Engineers", p 226, Prentice-Hall, Englewood Cliffs, N.J., 1965. Rosen, M. R., J. Colloid lnterface Sci., 36, 350 (1971). Rosen. M. R., J. Colloidlnferface Sci., 39,413 (1972). Scheve, J. L., Abraham, W. A,, Lancaster. B. B.. lnd. Eng. Chem., Fundam., 13, 150 (1974).
Received for review November 21,1974 Accepted February 16,1976
A Stirred Flow Microbalance Reactor for Catalyst Studies F. E. Massoth* and S. W. Cowley Depaltment of Mining, Metallurgical and Fuels Engineering, University of Utah, Salt Lake City, Utah 84 I12
A stirred flow microbalance reactor was constructed for simultaneously measuring catalyst weight changes and activities. It consists of a heated glass reactor in which the catalyst, suspended from a microbalance, is surrounded by a squirrel cage stirrer. Gas flow is up the stirrer shaft, into the bottom of the reactor volume, and out the reactor top. Catalyst weight changes are monitored continuously with a Cahn recording balance and catalyst conversions determined by gas chromatographic analysis of the reactor effluent stream. Gas mixing and gas-tocatalyst mass transfer efficiency tests demonstrated that the reactor performed as a constant stirred tank reactor. Consequently, direct catalytic reaction rate data are obtained. In addition, weight changes attending reaction under various steady-state conditions directly reflect amounts of equilibrium adsorption species present. An example of its use in a kinetic study of the hydrogenation of butene-1 over a molybdena-alumina catalyst is presented.
Introduction One of the more useful tools in kinetic investigation of catalytic reactions is the constant stirred tank reactor, as exemplified by the Carberry reactor (Carberry, 1964). The advantages of this type of reactor over the more conventional fixed-bed type are that rate data are directly obtained and better isothermal temperature control is achieved. Useful information on characterization of catalysts can be obtained by use of flow gravimetric techniques (Massoth, 1972).Among other things, this technique permits: (1)in situ pretreatment to a known level, (2) monitoring of amounts of a poison added to a catalyst, (3) following catalyst coking during reaction, and (4) determining changes in adsorbed species with reaction conditions. In order to combine the advantages of both techniques in the same reactor, a constant stirred, flow micro218
Ind. Eng. Chem., Fundam., Vol. 15, No. 3, 1976
balance reactor (SFMBR) was developed. With it, catalytic reaction rates and catalyst weight changes can be simultaneously followed. The only apparatus comparable to that described herein is that reported by Hsu and Kabel(1974), who used simultaneous gravimetric analysis with a static batch reactor. Their apparatus gives somewhat different information than ours in that reactant and product concentrations change with time whereas in our reactor steady-state concentrations are invariant in real time. Experimental Section The flow microbalance has been previously described (Massoth, 1972). To simulate a constant stirred tank reactor, the assembly was modified to incorporate a stirrer. Details are
9 f
e
I4
d
c
Figure 1. Flow microbalance assembly. a. Feed vessel and connections. b. Reactor top. Numbers are dimensions in mm. Code: (a) Teflon pivot; (b) iron magnet encased in glass; (c) feed gas inlet; (d) Teflon pin; (e) collar; (f) Teflon bushing for disconnect and shaft lower bearing; (g) O-ring seals; (h) disconnect; (i) glass spacer; (j) Teflon upper bearing; (k) glass rod; (1) temporary reactor outlet (later sealed off); (m)thermocouple well; (n) catalyst basket; ( 0 ) glass, squirrel-cage stirrer (4 fins); (p) hang-down wire; (q) gas non-back mixing tube; (r) disconnect with O-rings; and (s) reactor outlet tube.
given in Figure 1. The catalyst, contained in a fine mesh platinum basket (n), is suspended by thin quartz rods or wire (p) from a Cahn RG electrobalance (attached a t E-E, via a S joint). A squirrel cage fan (0)containing four blades surrounds the basket. This assembly is surrounded by a split-shell furnace, whose temperature is maintained constant by means of a proportional temperature controller. A thermocouple well (m) is located near the catalyst basket. The fan is attached through a central shaft, glass rod (k)to a bar magnet (b) located below the furnace. Removable Teflon bearings (f) and (j),located in the cold zone below the furnace, provide easy rotation and alignment of the shaft. Rotation is supplied by a horseshoe magnet attached to a laboratory stirrer. This arrangement provides relatively vibrationless operation. O-ring disconnects (Fischer-Porter) at (f) and (r) allow disassembly for charging catalyst. Initial tests were made to check the effectiveness of gas mixing in the reactor. For this purpose, a special temporary exit port (l),attached at the bottom of the reactor, was used. The upper piece was disconnected at (r) and the top exit of the reactor vessel was plugged off. Step changes, using pure Nz and air alternately, were introduced into the bottom inlet (c), and the temporary reactor outlet connected to a thermal conductivity cell. Tests were carried out at room temperature without catalyst. Analysis of the conductivity cell response with time to a step change was made employing a model consisting of two well-stirred reactors in series, corresponding to the feed volume compartment and the reactor. Volumes were measured by sequential filling with water. Following these tests, the temporary exit port (1) at the bottom of the reactor was permanently sealed off and the upper piece readded to the assembly. The bottom of the center tube (q) in the upper piece was plugged off, the exit to the reactor now passing out the side arm (s) of the upper piece. Similar gas mixing tests as above were then repeated. For testing the effectiveness of gas-to-catalyst mass transfer a relatively simple catalytic reaction was used, namely, hydrogenation of benzene. The catalyst, consisting of 60-65% nickel supported on activated alumina (Alpha Products) was sized to 20-40 mesh. Spectrophotometric grade benzene (Mallinckrodt) was contained in two bubblers, the first held a t room temperature and the second a t 8 O C. Ultrapure hy-
drogen was first passed through a De-oxo and then 5A molecular sieves. The benzene-hydrogen feed gas was made by bubbling the hydrogen through the bubblers. A measured flow ratio of this stream was diverted to the reactor by means of a flow controller (Matheson),the rest being vented. In subsequent runs an auxilary stream of hydrogen was added to the benzenehydrogen mixture upstream to the flow controller, both streams being regulated by calibrated rotameters. The feed gases were introduced into the lower feed compartment at (c) and entered the reactor through the space surrounding the shaft. Reaction products, exiting from the top of the reactor, were mixed with an N2 purge coming down from the balance case through tube (9) (to prevent back-mixing of products into the balance), and passed out the side arm (s) to a gas chromatograph. Analysis was made by thermal conductivity, using an 8 ft X I/&in. stainless steel column containing 3% OV-17 on Gas Chrom Q held a t 35 OC. The benzene showed only one peak on the chromatograph, and reaction products showed only peaks for unreacted benzene and for cyclohexane. Any other products were less than 0.001 mole fraction (benzene feed basis). All runs were carried out at atmospheric pressure. Run conditions were varied by changing feed flow rate to the reactor, benzene partial pressure, and stirring speed. About 0.5-1 h was required to attain steady-state a t each run condition. The catalyst was pretreated in H2 a t 450 "C for 2 h prior to a run. In one series of runs, 100 mg of catalyst was used; in another 50 mg catalyst was mixed with 50 mg of quartz chips. Since the benzene hydrogenation reaction showed negligible weight changes a t different run conditions, another reaction was chosen to illustrate simultaneous weight changes and catalyst conversions. The test reaction employed was the hydrogenation of n-butene-1,using a 2 0 4 0 mesh size catalyst consisting of 8% Mo or 3% Ni plus 8% Mo impregnated on r-Al203. The butene was metered directly by a rotameter. Various compositions containing butene, Hs, NP, and H2S were separately metered to obtain various mixture compositions. These were then directed to the reactor via the flow controller as before. Analysis of reaction products was achieved by flame ionization gas chromatography. A 6 f t X lh-in. stainless steel column packed with n-octane on Porasil C (Durapak) held a t 50 "C was used. The catalyst was presulfided in a 9% H2S/H2 mixture at reaction temperature prior to the run. Results Gas Mixing Characteristics. In order for the reactor to perform as a constant stirred tank reactor, perfect back mixing must be achieved. Since the inlet feed vessel containing the magnet represents an appreciable volume, it was also considered as a perfect mixing vessel. The gases exiting from the feed vessel travel up the long but narrow space around the shaft before entering the bottom of the reactor. This segment was considered to be in plug flow. Thus, the inlet to the reactor is a t the same concentration as the feed vessel. Labelling the latter volume as VF, and the reactor volume as V R ,the following treatment applies if perfect mixing occurs in both volumes. Consider a step change in concentration of a tracer component (e.g., Nz to air, where 0 2 can be considered the tracer) from zero to co at the inlet of the feed compartment. Its concentration in the feed volume, C F at any time t will be given by
where F is the volume flow rate of the total stream. Equation Ind. Eng. Chem., Fundam., Vol. 15, No. 3, 1976
219
10,
I
I
1.0 I
I
I
I
I
I
I
I
I
.8 .6
1
\
/
Y
X
,4
2
,
I
0
,
/
2
1
I
1 3
3
0
7
1 can alternately be expressed in terms of fraction of tracer O(F,where CYF= CF/CO
Integration of eq 2 gives
- e-(F/VF)t
(3)
which is the time dependency for filling the feed volume with tracer for perfect mixing. Similarly, the rate of change of tracer in the reactor volume will be given by (4)
where CURis the time-dependent concentration of tracer in the reactor volume. For perfect mixing the reactor outlet concentration will be identical with that in the reactor. Measurements of the change in concentration of the reactor outlet with time with a step change in feed inlet (Nz to air, then air to Nz) were made at two flow rates and stirring speeds. In order to compare results with the theoretical equations, time zero was taken at the first evidence of change in concentration (breakthrough) a t the thermal conductivity detector. This eliminated tedious corrections for time delays due to flow (assumed plug flow) through the small connecting tubing and volume between the feed vessel and reactor. For convenience, a reduced flow parameter, TF, defined as TF =
(6)t
was used to correlate the results. The data obtained (Set 1)are shown in Figure 2, in terms of fractional change in reactor outlet vs. T F . The upper solid line is for LYF (perfect mixing in feed compartment, no mixing in reactor) and the lower curve for CUR(perfect mixing in both volumes). The open data points were obtained a t stirring speeds of 300 and 600 rpm (data were almost identical and averaged) and at flow rates of 44.9 and 84.5 cm3 (STP)/min. The agreement with the theoretical line for two perfectly mixed reactors is very good. The solid data points were obtained without stirring and show considerable deviation from the theoretical line. In fact, they lie between the two theoretical lines, indicating substantial incomplete mixing. This is most likely due to appreciable channeling of the flow be220
Ind. Eng. Chem., Fundam., Vol. 15, No. 3, 1976
3
T
Figure 2. Flow data set 1. Obtained without reactor top, using temporary reactor outlet. Upper curve, eq 3; lower curve, eq 5. VF = 203 cm3; VR = 120 cm3. 0,84.5 cm3/min,300 and 600 rpm; D, 44.9cm3/ min, 300 and 600 rpm; 0 , 84.5 cm3/min,no stirring.
aF = 1
2
1
Figure 3. Flow data set 2. Obtained with reactor top. Upper curve, eq 5; lower curve, eq 8. VT = 60 cm3.Data points same as in Figure 2.
tween the reactor inlet and the close proximity of the temporary outlet tube located a t the bottom of the reactor. In these tests the top of the reactor was plugged off. This temporary reactor outlet tube was then sealed off (permanently) near the reactor bottom for additional tests (Set 2). Now the gas flow exited at the top of the reactor, which included an additional top piece of volume VT before exiting from the apparatus. Results with this configuration revealed that mixing in the top piece had also to be considered. Assuming perfect mixing in the latter, the treatment was extended to three perfect-mixed reactors in series, yielding the following equations
(7)
where LYTis the concentration of tracer issuing from the apparatus. The data (Set 2) for the complete setup are shown in Figure 3. The upper solid curve is the theoretical curve for CIR (complete mixing in the feed and reactor volumes but plug flow in the top volume) and the lower curve for CYT(complete mixing in all three volumes). The data clearly show good agreement with the latter case. Surprisingly, good agreement was obtained even without stirring. (Data were practically identical with open circles in Figure 3). This would seem to indicate that the lack of fit obtained previously (Figure 2) without stirring was indeed due to channeling in the reactor and not to incomplete mixing in the feed vessel. The good fit with the complete assembly without stirring is probably due to the low flow rates employed, allowing ample time for molecular diffusion in each volume. Although these results show that stirring may not be required in this apparatus under the conditions tested to achieve perfect mixing, stirring is nonetheless deemed important to good contact between gas and solid catalyst phases. Indeed, Choudhary and Doraiswamy (1972) showed that stirring is essential to good mass transport to the catalyst in this type of reactor. In addition, stirring helped maintain a more isothermal environment in the reactor volume. Gas-to Catalyst Transfer. In order for the reactor to perform as a constant stirred tank reactor, gas-to-catalyst mass transfer must be rapid compared to reaction rates under study. The catalytic hydrogenation of benzene is a useful test reaction for this purpose since it follows closely a first-order
Table I. Effect of Stirring on Conversion"
Speed rPm
Temp,
CONV.
Conversion, mol fraction
OC
6- -I- - _ ' --I -
20
I
,
E
F
I S
l
o
-
-
A
B
d
84 0.54 100 86 0.60 200 86 0.60 300 85 0.60 400 85 0.59 a Catalyst, Ni/A1203; flow, 37.7 cm3/min; Charge, 99 mg; benzene. 0.039 atm. 0
dependency in benzene when hydrogen is in considerable excess. For a constant stirred reactor, the rate of reaction is given by (Carberry 1964)
W
where r B is the rate of conversion of benzene, F is the total flow into the reactor, X B O is the mole fraction of benzene in the feed stream, C is the conversion of benzene, and W is the catalyst weight. For a first-order reaction in benzene, the rate is also given by kPB
(11)
where k is the reaction rate constant and p~ is the partial pressure of benzene in the reactor. The following relationships also obtain P B = PBo
(1- C)
(12)
where PBO is the partial pressure of benzene in the feed stream and P is the total pressure in the reactor. Defining an activity parameter, Y , by
y=- C
1-c
C
D
R U N
Figure 4. Butene series 1.Run conditions given in Table I. Conversion is to n-butane.
FXBO C
rB =-
rB =
0
(14)
combinations of eq 10-14 yields
k = - FY
PW
The constancy of k over a series of runs of varying flow rates, benzene partial pressures, and catalyst weights will attest to the effectiveness of mass transfer. Table I presents the results on the effect of stirring on benzene conversion. For stirring speeds above 100 rpm, conversion is essentially unaffected. Without stirring however, conversion and temperature were lower. The effect of changing process variables is shown in Table
11. Different flow rates and catalyst gave different conversion responses but calculated k values were essentially unchanged. A slightly lower value of k was obtained a t the highest flow rate with the smaller catalyst charge but not with the larger charge. I t is possible that under the former conditions we are close to the boundary where perfect gas-to-catalyst contact no longer holds. The results of these tests demonstrate that the reaction, under the conditions employed, is unaffected by mass transfer effects. Therefore, the reactor can be safely assumed to be operating in a constant stirred tank reactor mode. In these runs, the catalyst picked up about 1.5mg of weight (99 mg of charge) before line-out was achieved. After that, weight changes over the entire series of runs were negligible. Catalyst Tests. In order to test the response of the apparatus in a catalytic reaction which would give both conversion and weight changes under steady-state conditions, the hydrogenation of butene-1 to butane was studied over a molybdena-alumina catalyst. Under the reaction conditions employed double-bond isomerization to cis- and trans- butene-2 was rapid compared to hydrogenation to butane. Conversion here is confined to hydrogenation and is defined by moles of butane formed/moles of butene-1 in feed. Because of our interest in the reactivity of the sulfided state of this catalyst (Massoth, 1975) and the reported retardation in butene hydrogenation by HzS (Desikan and Amberg, 1964) a series of runs at varying compositions of butene, Hz, HzS, and Nz was made. Run conditions are given in Table 111. Figure 4 presents the results obtained in terms of conversion and weight changes at the steady-state condition for each run. Run F duplicated the conditions of Run A to check repro-
Table 11. Effect of Process Variables on.Rate Constant"
Catalyst wt, mg
Benzene pressure, atm
Flow rate, cm3/min
Conversion, mole fraction
99.1
0.0390
18.8
0.0195
75.4 37.7 37.7
0.0390
37.7
0.759 0.427 0.614 0.610 0.763 0.431 0.379 0.754 0.427
18.8
49.1
18.8
75.4 37.7
k
X
cm3/min g atm 7.0 6.7 7.1 7.0 7.2 6.8 7.4 5.96 6.7 Av 7.0 =k 0.2
" Catalyst, Ni/A1203; speed, 300 rpm; temperature, 85 O C total pressure, 0.85 atm. Run omitted. Ind. Eng. Chem., Fundam., Vol. 15, No. 3, 1976
221
Table 111. Butene Hydrogenation Conditions Series 1 Catalyst Charge, mg Pretreatment H2S/H2 Temp, O C Time, h Reaction Temp, "C Time, h
Series 2
8%MOly-AlzOs
200
3% Ni, 8%Moly-AlzOa 200
1/10 345
1/10 400
2
2
345
400 lh-1 h to steady state at each run condition
Run feed comDositions. mole fraction Feeda
C
B
A
Butene-1 0.05 H2 0.92 H2S 0.03 Balance is Nz.
0.025 0.93 0.045
D
0.025 0.63 0.015
0.05 0.29 0.03
E 0.025 0.60 0.045
F
A
0.05 0.92 0.03
0.03 0.94 0.03
30m c 20
CONV.
I
I
4
I O
MG.
A
B
C
D
E
F
R U N
Figure 5. Butene series 2. Run conditions given in Table I. Conversion is to n-butane: 0,initial data; 0 , data after coking.
ducibility of the catalyst during the series. A decrease in catalyst conversion was noted between the initial and final run, indicating a loss in catalyst activity. The weight changes showed a concomitant weight increase between initial and final runs. We may surmise that the loss in catalyst activity was most likely due to coke formation during the series. In fact, the weight change plot shows a significant discontinuity a t Run D, indicating that this run was responsible for the irreversible coking. Inspection of the run conditions for Run D shows that it contained a high concentration of butene and the lowest concentration of Hz. When the catalyst was exposed to only a butene-Nz stream in a separate test, rapid and irreversible coking was obtained. It appears, therefore, that under the reaction conditions of Run D, sufficient hydrogen was not present to prevent catalyst coking. The use of the SFMBR here not only demonstrated that activity loss was related to catalyst coking, but also permitted determining the specific run that was responsible. A second series was run with a companion catalyst, in which the conditions that gave coking in the previous series were avoided. The run conditions of this series are given in Table I11 and the results in Figure 5. It can be seen that the catalyst activity remained stable during this series as evidenced by a return to the initial conversion a t the end of the series and a 222
Ind. Eng. Chem., Fundam., Vol. 15, No. 3, 1976
B 0.015 0.94 0.045
C
0.015 0.64 0.015
D
0.015 0.61 0.045
E
F
0.03 0.91 0.06
0.03 0.94 0.03
lack of discontinuity in the weight changes. (The weight change in Run A appeared to be low compared to Run F, probably due to initial slow approach to an equilibrium state.) To ascertain if coking affected catalyst activity, a butene-NZ stream was passed over the catalyst until about 12 mg of weight had been added. The series was then repeated with the results shown in Figure 5. A drastic decrease in conversion was obtained, demonstrating that coking did indeed affect catalyst activity. A slight gain in activity was noted in this case as evidenced by the increased conversion in Run F vs. Run A, which was also reflected in a weight loss over the period. Apparently, some of the more volatile portion of the coke slowly desorbed during the series, accounting for the slight increase in catalyst activity. It should be noted that the trends in conversion and weight changes generally followed those of the initial series. Returning to an examination of the initial responses due to the particular run conditions, the following conclusions can be made. (1) Conversion and weight changes appeared to be independent or at most weakly dependent on butene concentration. For pseudo-first-order reactivity in butene, conversion will remain the same, especially at low conversions. Satterfield and Roberts (1968) found butene hydrogenation to be first order in butene with weak butene inhibition. Weight response for changes in butene concentration is not obvious from Figure 5 due to the masking influence of H2S (see (2) below), but appear not to affect the weight much. Butene is probably weakly adsorbed. (2) The effect of H2S on conversion and weight change is marked. Conversion decreased with increase in H2S concentration and corresponding increases in weight were observed (Runs C vs. D and F vs. E). Clearly more H2S was adsorbed a t the higher concentrations and this competed for butene adsorption sites, resulting in a lowering in conversion, in agreement with Desikan and Amberg (1964). It should be noted that this is due to a reversible retarding phenomenon and not to a permanent poisoning of the catalyst as evidenced by the reversible weight changes obtained. (3) In addition to the strong H2S retarding effect, an Hz concentration effect is also noted. For example, conversion decreased and weight increased a t lower H2 concentration (Runs B vs. D). The conversion loss can be explained on the basis that reactivity is proportional to H2 concentration. The weight change response is another matter. Apparently, higher partial pressures of H2 (weight of adsorbed Hz is ignored here
because of its low molecular weight) a t the same partial pressure of HzS, suppress H2S adsorption, implying a t least a partial competition for adsorption sites. It is beyond the scope of the present report to discuss these runs in more detail. A complete kinetic analysis of this and other data will be published a t a later date. Suffice it to say that the ability to measure catalyst reaction rates and weight changes simultaneously under reaction conditions greatly extends the scope of basic catalyst reaction mechanism studies. Acknowledgments This article is based partly on work conducted by one of the authors (F.E.M.) while employed at Gulf Research and Development Company, Pittsburgh, Pennsylvania, and partly on ERDA Contract E (49-18)-2006and the State of Utah. Special thanks are due to Dr. C. L. Kibby for help in the design and Mr. Silba for fabrication of themicrobalance reactor. Nomenclature c = concentration of tracer C = conversion F = flow rate of gas at inlet to feed vessel k = reaction rate constant p~ = partial pressure of benzene in reactor
PBO
= partial pressure of benzene in feed
P = total pressure rg = rate of benzene reaction t = time V = volume
AVij = defined b y e q 9 W = weight of catalyst x B O = mole fraction of benzene in feed stream Y = activity parameter defined by eq 14 a = fractional value of tracer T = dimension less time given by eq 6
Subscripts F = feed vessel R = reactor T = top piece assembly Literature Cited Carberry, J. J., Ind. Eng. Chem., 56 (ll), 39(1964). Choudhary, V. R., Doraiswamy, L. K., Ind. Eng. Chem., Process Des. Dev., 11,
420 (1972). Desikan, P., Amberg, C. H., Can. J. Chem., 42,843 (1964). Hsu, S.M., Kabel, R. L., J. Catal., 33, 74 (1974). Massoth, F. E., Chem. Techno/.,285 (1972). Massoth, F. E., J. Catal., 36, 164 (1975).
Received for reuiew July 7, 1975 Accepted March 29,1976
C O M M UNICAT 1 0NS
On the Choice of Acentric Factor
An empirical equation relating the reduced vapor pressure, the reduced temperature, and the acentric factor in the region of the coexistence of liquid and vapor phases (Pr ranging from 0.001 to 0.040) has been obtained and found to fit the vapor pressure data for numerous nonpolar and polar organic liquids accurately.
Pitzer et al. (1955)have suggested the theorem of corresponding states in the following form:
where PI, V,, and T , are the reduced vapor pressure, reduced volume, and reduced temperature, respectively. w is called the acentric factor defined by w = -log P, - 1.000 where P , is the value of reduced vapor pressure a t the reduced temperature T , = 0.700.The acentric factor takes into account the deviations of the intermolecular potential from that of a simple fluid as well as the contributions of interactions between the various parts of the complex molecules. These workers have found that the compressibility factor a t various reduced temperatures is a function of w in the case of nonpolar molecules Ar, Xe, N P ,COS,CHI, CZH6, C3H8, n-C4Hlo, C(CH&, and n-C7H16, and slightly polar H2S molecules. Since the class of substances which conforms to the theory is that designated as normal liquids (Hildebrand and Scott, 1950),one would be interested to know to what extent the more complex or highly
polar molecules such as saturated and unsaturated aliphatic hydrocarbons, alkylbenzenes, alicyclics, esters, ketones, ethers, halobenzenes, and haloalkanes would obey the same equation of state. We have calculated the values of w, log PI,and T,-l for a large number of substances shown in Figure 1, by making use of vapor pressure data reported by Jordan (1954),Timmermans (1950),and Fried and Schneier (1968),and the critical constant data reported by Kudchadker et al. (1968), and Weast (1971).The plots of log P, vs. T,-l yield smooth curves for each of the substances. For fixed values of log PI equal to -3.0, -2.6, -2.2, -1.8, and -1.4, the plots of the values of T,-l vs. w also yield smooth curves, showing that at a fixed value of P,, Tr-l is a function of w alone. The temperature-vapor pressure data for the various substances along the saturation curve are found to fit the following equation: 2A log P, = -B
+ [B2- 4A(T,-'
- C)]'"
(2)
where A = 0.0094- 0.0144d, B = 0.4506 - 0.4371 w + 0.2127 w2, and C = 0.9827 f 0.0736 w - 0.0210 w2. Values of the conInd. Eng. Chem., Fundam., Vol. 15, No. 3, 1976 223
