Rate of Nitration of Benzene Vir. K. LEWIS AND T. J. SUEN, Massachusetts Institute of Technology, Cambridge, &lass.
P
R E S E K T knowledge of the kinetics of nitration of aromatic compounds using nitric acid, especially as mixed nitric and sulfuric acids, may be summarized as follows : Composition of the nitrating acid has an outstanding effect on both rate and extent of nitration. Slight dilution of the acid by mater may produce considerable inhibiting effect, and a t certain dilutions the reaction ceases entirely (6). This fact has not been completely explained, b u t qualitatively i t is generally believed t h a t the sulfuric acid removes water from a hydrated nitric acid, liberating anhydrous or so-called pseudo nitric acid which is responsible for the nitration (1, 5, 6, 10, 16, 17). However, from the mass action viewpoint the change in quality of the nitric acid caused by a little dilution can hardly account for the magnitude of change in the rate of nitration. It is agreed t h a t aromatic nitrations are irreversible (14).
Reaction rate data on liquid-phase nitration of benzene can be correlated with acid composition and temperature to determine equipment capacity as a function of operating conditions. Reaction occurs .in both aqueous and organic layers and is not localized at the interface. The rate is extraordinarily sensitive to composition of the acid but not composition of the organic phase. Except for acids in which reaction rate is very high, moderate emulsification is sufficient to keep each liquid saturated with the other, so that increase in agitation and dispersion has no further effect on rate.
The nitration of benzene into mononitrobenzene involves a free energy change under standard states in the neighborhood of -28,000 calories (6, 1 8 ) , an indication of substantially complete nitration a t equilibrium. Experimentally, hydrolysis of nitrobenzene in pure water (18) or in dilute sulfuric acid (19) a t temperatures above 100" C. is undetectable. Nitration reactions under all actual conditions are evidently not slowed up by approach to equilibrium but merely by retarded rate. Kitration of benzene derivatives in dilute homogeneous solutions in concentrated sulfuric acid follows the bimolecular reaction equation (11, 12, 23). Rate increases about threefold (12) for a 10" C. rise in temperature. Temperature has no great effect on the quality and character of the nitration products (4, 7, 15, 18, 24). The chemical mechanism of nitration most widely accepted is perhaps t h a t of Wieland's addition-elimination theory ( 2 ,S), but this mechanism is not based on kinetics and throws no light on it. Recently, however, other mechanisms have been
proposed, on the assumption t h a t more than one molecule of nitric acid is involved in nitration (6, 21); these still await general recognition. Almost no work has been done on the physical mechanism of heterogeneous nitration, although it has been conceived more or less as an interfacial reaction (8).
Heterogeneous Nitration of Benzene This investigation is a study of the effects of various independent variables on the nitration of benzene to mononitrobenzene. Although temperature is an important factor, i t was held constant in most of the runs. S o effort was made to vary total volume; results are reported as rate per unit volume of reacting liquid. This leaves four major variables: 1. The composition of the nitrating acid. Two independent variables are involved since the mixture is composed of nitric acid, sulfuric acid, and water. Organic material and acid decom osi tion products are also dissolved in the acid phase. The egects of these last variables are small under the conditions employed. 2 . The composition of the organic phase. This is dictated mainly by the ratio of unreacted benzene to the reaction product, nitrobenzene, but complicated by solution of small amounts of nitrating acid. 3. The relative volumes of the two liquid phases. 4. The character and degree of agitation.
Of these four variables, the composition of the nitrating acid has the greatest influence, so t h a t the effect of the last three can be determined only if acid composition is held constant. ( I t could be allowed for by computation were its effect known, but this can be determined only by experimental methods in which the other variables are held constant.) Most of the data in the literature are on batch nitrations, where acid composition is necessarily changing rapidly. Simultaneously, composition of the organic phase is also changing, due to conversion of benzene into nitrobenzene. Thus, study by batch technique of the general influence of composition is difficult. Hence, in this work continuous nitration was first employed, holding compositions constant. Continuous Nitration Runs Continuous nitration was achieved by introducing fortifying acid and pure benzene into the reaction mixture and u-ithdrawing the reaction products continuously. Devices were provided to maintain constant both composition and volume of each of the reacting phases and temperature of the nitrator. (Constancy of acid composition was followed by conductivity, measured between two electrodes placed in the acid circulating system.) Furthermore, efficient stirring gave good intermixture of the fresh feeds'. The significant relations of the continuous runs a t 25" C. are brought out in Figures 1 and 2. I n Figure 1 the independent variable was per cent conversion of the benzene, a e d in 2, the volume per cent of acid phase in the total reacting emulsion. The linear relation between rate and volume per cent of the phases in Figure 2, which holds over nearly 90 per 1 Details of a p p a r a t u s , method of operation, a n d results can be impplied to those interested by t h e D e p a r t m e n t of Chemical Engineering, hlasaaohus e t t s I n s t i t u t e of Technology.
1095
.INDUSTRIAL AND ENGINEERING CHEMISTRY
1096
PERCENT COWERSKW OF BENZENE
FIGURE 1.
EFFECT OF PERCEST COSVERSIOS OF BENZESE AT 2.5’ C .
Acid compn , mole yo
Curve d
Curve B
Curve C
8.55 21.2s 70.17
9.32 21.35 69.33
2.49 27.19 70.32
41
41
. 6i
“08
HzSOa HzO
Vol. ‘Z of aqueous Dhase
cent of the range, is striking. I t s significance is accentuated by the fact t h a t it is undisturbed by inversion of phase. The explanation suggests itself t h a t under the conditions of these runs, each phase remains substantially saturated with the other, chemical reaction occurring in the body of each phase a t a total rate proportional to its volume, the rate per unit volume in each phase remaining constant because of the constancy of its composition. The rate characteristic of the organic phase would be the intercept on the rate axis a t the left of the diagram, 1.75 for curve A and 1.0 for B. The rates in the acid phases would be the corresponding intercepts t o the right of the diagram of the extrapolations of the straightline portions of A and B (9.05 and 10.1, respectively).
VOL. 32, NO. 8
The considerable reactivity within the organic phase, together with the f a r higher reaction rateindicated by the above analysis in the acid phase, offers a n explanation of the remarkable drop in rate a t the right of Figure 2, a t low ratios of organic phase to acid. If benzene is consumed-i. e., reacts rapidly in the acid-but has low solubility, its diffusion rate, by which alone it is distributed through the acid phase and its concentration there maintained, is low. If excess benzene is adequately distributed by emulsification and is present in sufficient amount, the acid phase can be kept substantially saturated n i t h hydrocarbon. As the amount of emulsified hydrocarbon is reduced, because of reduced interfacial area and increased effective thickness of the acid layer through which hydrocarbon must diffuse, diffusion can no longer keep the acid phase saturated with i t , and the rate will drop. Granting substantial uniformity of drop size (which iniplies uniformity of distribution of drop sizes and hence con>tant average drop size), the data of Figure 2 can be explained quantitatively on the assumption that a t the right of the diagram the rate of diffusion of benzene through the acid phase is the controlling factor. Consider unit volume of the reacting emulsion a t constant temperature, of which the yolume fraction, z, is organic phase. Acid composition i i constant except as benzene concentration in it is affected by variation in z. Assuming t h a t reaction occurs only within the body of the phases, v. here R R,, R,
= =
R = R , f R. total rate rates in each phase
Since organic composition is constant, rate per unit volume in this phase is also constant, or
Ro
=
ki~
Assume rate pw unit volume in the acid phase proportional to the average benzene concentration in it, y. Clearly, Ra
kty(l
- X)
To estimate diffusion of the hydrocarbon into the acid, visualize each emulsified droplet a t the center of a cube of surrounding acid of side 1. The number of droplets must be 2 - 3 , which in turn equals 3x/47rr3,where r is drop radius. Since J4 .I 2
&?
VOtUME PERCEHT OF AQUEOUS PHASE
e
=
.IO
Y
FIGURE2.
EFFECTOF VOLUMETRIC R.4TIO O F T W O PHASES b T ?\TITRATION TEMPERITURE OF 25O Acid compn., mole
c.
5;
Curve A Curve B
5
.08
0
5
.Ob
-8
P
.o 4
HNOz
8.55 2.50 HcYOa 21.24 27.15 Hz0 70.21 70.35 yo conversion of CaH6 64 64 Mixtures t o left of C are emulsions of acid in oil; to right of D , oil in acid; inversion of phase occurs between C and D .
Titration in the organic phase was confirnied by completely segregating it from contact with mixed acid and following further disappearance of nitric acid in the organic layer by analysis; the results are shown in Figure 3. T h a t such reaction can occur is easily understood in view of the considerable quantities of nitric acid dissolved in the organic phase. Thus, in run A the organic layer contained about 13 mole per cent nitric acid, 2.6 times the nitric acid of run B .
92 0
TIME AFTER SEPARATION FROM THE AQUEOUS PHASE -HWRS
FIGURE 3.
h-ITRATION IN THE ORGANIC PH.4SE
83 per cent nitrated; priginally saturated with acids, containing 56.4 weight per cent nitric acid, 26.78 per cent sulfurlc acid, and 17.77 per cent water.
the average value of r seems substantially independent of L, 1 is inversely proportional to QZ The rate of diffusion of benzene into its corresponding cube of acid should be propor. tional to the effective values of concentration difference, cross section of path, and reciprocal of diffusing distance.
IIVDUSTRIAL AND ENGINEERING CHEMISTRY
AUGUST, 1940
T h e first will be assumed to be .c0 - X , where z0is the benzene concentration in the acid phase a t the interface itself, a value which, on the accepted concepts of diffusion in such cases, should be constant or nearly so. The effective cross section of path is probably best approximated by the geometric mean of the areas of droplet and surrounding cube of acid (ZZ), b u t since surface of the droplet is constant, this makes it proportional to 1. The average distance of diffusion is also presumably nearly proportional to 1. Benzene diffusing into *= 10 x 2
2
8
i
b
2 3 0
s-
g 2 c" -
0
0
-
I X
20 :VOL
60
.40
40
LW
FRACTION OF AQUCWS PHASE
R
(104)
1097 =
x
(1 + 737 - _ _ ~ 70z+1 5
2)
-
Since this equation was developed on the assumption of diff usion in the acid phase as the controlling factor in emulsioncontaining little organic phase, it allows for the influence on rate of variation in proportion of the phases throughout the range; one must conclude, therefore, t h a t there is no evidence of selective nitration a t the interface, but the chemical reactions occur within the body of the two phases. I n Figure 1 the flatness of the curves in the middle of the range is impressive. I n A and B a high percentage of the total reaction probably occurs in the organic phase because there is more of it and it; nitric acid content is inc-eased hy high concentration in the acid layer. Presumably this is the reason for the relative flatness of ,4 and B. High conversion means high nitric acid solubility in the organic layer, which holds up conversion rate in that layer a t the right of the diagram; this behavior is important when t h a t layer accounts for a considerable part of t h e whole conversion. However, this cannot be the major factor. Perhaps as conversion increases, solubility of benzene in the acid phase also increases, going along with some nitrobenzene.
FIGURE4. CONTINUOUS SITRATION AT 25" C. WITH 2.50 MOLE PER CEKT SITRIC ACID, 27.15 SULFURIC ACID,ASD 70.35 WATER, TO 64 PERCEST CONVERSION (Constant total volume and variable volumetric ratio of the phases)
the acid must equal t h a t reacting in it, and total benzene thus diffusing is t h a t per drop times the number of drops. Algebraic combination of these relations gives
where k , depends on the proportionality constants of the relations and ka depends on these constants and on the solubility zo. This equation should check the experimental results if its assumptions are substantially dependable. Figure 4 reproduces the experimental points of curve B of Figure 2, b u t the curve drawn through them is calculated from the equation:
-
H2SO4
'HpSO4
(Ma X)
FIGURE 6. RATEOF KITRATIOS OF BESZESE, IS MOLESPER LITEROF THE ACIDPHASE PER HOUR
FICCRE5.
INSTANT.4XEOUS
35"
RATE O F NITRATIOS
c.
AT
Rate refers to one mole of nitric mid at the starting point of the batoh reaction. Dotted lines are data from continuous nitrations.
The relatively small effect of conversion on rate shown in Figure 1 is important in t h a t it discloses a helpful technique for a n exploratory study of the effect of acid composition as a n independent variable. Although continuous nitration alone makes it possible to study the effect of changing one variable a t a time, the method is time consuming. However, a batch nitration can be so conducted that only acid composition and per cent conversion of hydrocarbon to its nitration product change significantly during the run. Thus, the only change in volume of organic phase is t h a t due to difference in molal volume of nitrobenzene and benzene and to solubility effects, such as solution of acids in the organic layer. Moreover, except for acids dissolving in the organic phase, the mole fraction of sulfuric acid remains constant, since each mole of nitric acid reacting is replaced by one of water. By following the course of a batch reaction by analysis, one can get the rate a t each intermediate point condition from the slope of the curve of nitric acid consumed us. time. Since in the middle range, conversion has only a minor effect on rate, the changes in rate actually measured are due mainly to
IKDUSTRIAL AND ENGiINEERIKG CHEMISTRY
1098
I0
.70 10
20
FIGURE 7.
30
40 50 60 70 UOC PERCENT Of HMO, IN VAPOR
80
90
.I2
CONSTAXTS FOR INTERPOLATING VAPOR COMPOSITION DATA
changes in acid composition. The whole relevant range of mixed acid composition is readily covered by a, limited number of batch runs, each with a properly selected initial composition of mixed acid. [Batch nitrations of this type were used on benzene by Hetherington and Masson (6),but they did not study reaction rates, determining rather the conditions a t which reaction ceases. They found that this point depends mainly on relative concentrations of nitric acid, sulfuric acid, and water in the acid phase. At sufficiently high ratios of sulfuric acid to water the nitric acid may be substantially all consumed. ]
VOL. 32, NO. 8
controlling the acid supplied and in estimating attainable reaction rates in commercial operation is obvious. Attention should be called to the general parallelism between the constant-rate curves of this figure and those of Figure 5 . Study of the diagram clarifies the advantages of continuous nitration in avoiding temporarily high reaction rates with corresponding excessive temperatures and side reactions. The general effect of acid composition in the ranqe investigated is best seen from the curves of constant rate of Figure 5. At 25 per cent nitric acid, a reduction of this acid of only 3 per cent, at constant sulfuric acid (nearly equivalent to a batch nitration), reduces the rate to one tenth its initial value. At the bottom of the diagram the lower rate curves may be displaced somewhat to the right, because the points determining them in this region correspond to conversions so high that neglecting the effect of conversion is probably not justifiable. For comparison, two dotted constant-rate curves from the continuous runs are shown, which correspond to a tenfold change in rate. (The rates are expressed on an entirely different basis, and the relatively narrow range covered by the continuous runs is obvious, despite a much more extensive experimental program.) Complete correlation is not to be expected, in view of the unavoidable differences in nitrator construction and stirring in the two sets of runs. The parallelism is satisfactory. I n attempting to determine the cause of the extraordinary sensitivity of nitration rate to changes in acid composition, it is necessary first to allow for variations in the nitric acid activity in the mixed acid. Unfortunately, the data in the literature (26) do not cover the temperature range in question, so that it was necessary to determine it experimentally. The method employed was to measure vapor pressure and vapor composition us. liquid composition of mixed acids.
Batch Nitrations Definite amounts of mixed acid and benzene were allowed to react at constant temperature and stirring rate, the course of the reaction was followed from point to point by chemical analysis, and the quantities of nitric acid and of benzene converted a t any time were calculated. From these data two curves were plotted for each run-time against fractional conversion of benzene to nitrobenzene and against mole per cent nitric acid in the mixed acid. The slope of the first times the quantity of benzene initially taken is the rate of nitration. The second curve determines the concentration of the mixed acid layer. This second curve was based upon complete analysis of the acid layer, and was used solely for purposes of interpolation in coordinating slopes with acid composition (benzene conversion being stoichiometrically related to acid composition). A similar curve might have been employed for sulfuric acid, but the change in this was too small to require such a procedure. From these two sets of curves a triangular plot correlating nitration rate as a function of acid composition was drawn (Figure 5). Because of the complexity of the factors involved, choice of a method of correlation of reaction rate data free from objection is difficult. An alternative is presented in Figure 6. Here the rates indicated on each curve are expressed as gram moles of nitrobenzene synthesized per hour for each liter of reacting acid phase, of the composition corresponding to the point in question on the diagram. Figure 6 is constructed for 35' C., and for reasons already explained, assumes good agitation, adequate quantity of the organic phase, and low percentage conversion of the bemene in this phase (below about 80 per cent). Multiplication of the rates indicated for each constant-rate curve by the factor 0.0623 converts them into pound moles of nitric acid disappearing or nitrobenzene synthesized per hour for each cubic foot of acid phase present in the reaction zone. The utility of a diagram of this sort in
"01
A
H,S04 (MOL 7)
H2S04
OF VAPOROVER MIXEDACIDS FIGURE 8. COMPOSITION
35"
c.
AT
VAPOR-LIQUID EQUILIBRIA OF MIXEDACIDS. Mixed acids of various compositions were distilled in an Othmer apparatus (13) under vacuum. By pressure adjustment, temperature was held constant a t 35' C. The vapor distillate was condensed in a cooling bath of solid carbon dioxide in alcohol (-20 t o -30" C,). To avoid bumping, a faint but continuous stream of air from a capillary tube was passed through the liquid. The pressure was read from a mercury manometer, and correction was made for pressure drop due t o vapor friction by noting the height of the liquid column in the side tub-
AUGUST, 1940
INDUSTRIAL AND ENG INEERIKG CHEAIISTRY
ing ( I S ) . After steady conditions were attained, both the liquid and the vapor condensate were analyzed, the former for nitric and sulfuric acid contents, and the latter for nitric acid. The vapor condensates were free of sulfuric acid. The technique gave accurate data on vapor-liquid compositions a t equilibrium, but the precision of the pressure readings was not very high. Interpolation of the experimental data on vapor composition was facilitated by developing the empirical equation,
1099 HNOs
concentration of HzO in liquid, weight yo concentration of HNO, in liquid, weight % 100-H-AV= concentration of H,S04 in liquid, weight 7, a, b, m = constants, which, however, are functions of concentration of HNOBin vapor, as indicated in Figure 7
where H AL’
=
=
The precision of the equation can be judged from the last two columns of Table I. Except for the last three points, agreement between calculated and experimental values is probably within experimental accuracy. Figure 8, a graphical representation of the equation, shows that the Iast three points lie in a range where water content of the liquid is very sensitive to small changes in the nitric acid content. The values in Figure 8 are close to those given in the literature (9) for a total pressure of 760 mm. For interpolating the somewhat less dependable data on total pressure, curves were drawn with the total pressures as ordinates and weight per cent of nitric acid in the liquid as abscissa, maintaining sulfuric acid as a parameter. (In carrying out the measurements, sulfuric acid concentration in the liquid under equilibrium conditions was actually kept constant in each series.)
TABLEI. DATAON Total Pressure
Mm. Hg 14.5 14.5 14.5 14.5 16.0 16.3 13.5 13.5 11 5 12.8 13.7
9:0 11 2 10.0 3 3 2 2
* The
Exptl. Vapor Compn. Mole Yo
HNOa
49.49 40.43 49.05 35.04 26,04 18.30 37.62 54.05 27.05 21.40 13.96 48.10 36 72 19.68 63.66 68.1 57 5 28.6 60.9
10
20 H,SO,
30 (MOL ‘L)
-
40
H2s04
HNO,
VAPOR COMPOsITION OVER M I X E D ACIDS
Exptl.
N
a*
b*
1-m*
H Exptl.
Calcd.
I?
30.10 32.33 30.02 33.67 36.38 39.37 33.17 30,95 37.49 39.21 42.31 33,3s 35.66 39.71 30.32 24.27 28.16 30.01 25.45
30,04 32.40 30.04 33.92 36.60 39.04 33.14 30.84 37.60 39.08 41.70 33.20 3 5 72 3 9 . 60 30.12 24.40 27.3 29.6 27.4
Wt. % 69.90
A_..I. 7 fi7
67.96 66.13 63.62 60.63 66.83 50.80 44.52 42.75 40.60 30.57 28.21 24.24 33.46 8.66 3.34 1.09 4.35 values of a, b, a n d 1-m
2 5 . 5 0 . 1 7 8 0.880 27.2 0 . 1 6 s 0.867 2 5 . 6 0.177 0.881 26.3 0.163 0.890 2 9 . 9 0.154 0 . 8 9 4 31.3 0.146 0.897 27 S 0 . 1 6 5 0 . 8 8 9 24 6 0 . 1 8 2 0 . 8 7 6 2 9 . 7 0 155 0 . 8 9 4 3 0 . 7 0 149 0 . 8 9 6 3 2 . 2 0 141 0 . 8 9 7 2 5 . 6 0 . 1 7 6 0.882 2 7 . 9 0 165 0 . 8 8 9 31 1 0 . 1 4 8 0 . 8 9 6 22.6 0.193 0.863 1 7 . 6 0 222 0 . 8 1 3 2 3 . 9 0 186 0 . 8 7 2 29.4 0.157 0 , 8 9 3 23.2 0.190 0.867 are read from Figure 7.
By use of these curves with those of the vapor composition, partial pressure of both nitric acid and water were calculated against liquid composition, and are plotted on Figure 9. I n Figure 9 constant-rate lines as functions of mixed acid composition are plotted on the same diagrams with lines corresponding to constant values of composition of the vapor, partial pressure of nitric acid in the vapor, and partial pressure of water in the vapor. Although no direct correlation appears to exist between rate and partial pressure in either case, there is striking parallelism between rate and vapor composition. Keeping in mind t h a t only the nitric acid and water have detectable volatility, this is equivalent to saying t h a t the rate is a function of the ratio of PENO, and PH,O. Furthermore, the curves of the upper triangle of Figure 9 make i t clear t h a t a twofold increase in the ratio of nitric acid to water in
HNOi
FIGURE 9.
COMPOSITION O F VAPOR ( t o p ) , P A R T I A L PRESSURE NITRICACID (center), AKD PARTIAL PRESSURE OF WATER (bottom) OVER M I X E D ACIDS A T 35’ c. AS COMP.4RED WITH RATE OF NITRATION OF
INDUSTRIAL AND ENGINEERING CHEMISTRY
1100
the vapor makes more than a tenfold difference in reaction rate. EFFECTOF TEMPERATURE. A few batch runs were made to study the effect of temperature on the rate of nitration. T h e experimental technique employed was the same as that described in the preceding section. Identical initial reaction mixtures were nitrated a t different temperatures, and the instantaneous rates of reaction, as measured from the slopes of the conversion curves, were compared a t identical acid compositions. The results (Figure 10) show that for a 20' rise in temperature, the rate increases four t o fivefold. I n other words, i t doubles for a rise in temperature of approximately 10" C., which indicates that the rate of nitration is controlled b y chemical reaction rate rather than by rate of diffusion between the phases (20).
VOL. 32, NO. 8
significant factor is the relative motion of one liquid phase past the other a t the interface. This is to be expected, inasmuch as diffusion from one phase into the other would be determined almost entirely thereby. These data fully confirm the conclusions based on the data of the continuous runs as t o the part played by diffusion. There is no indication of restriction of interaction to the interface.
Summary Continuous liquid-phase nitration of benzene under conditions controlled t o maintain constancy of the operating variables has been used t o study independently the effects of those variables on the rate of the chemical reaction. The following generalizations can be drawn as t o the reaction kinetics of nitration of benzene t o mononitrobenzene with mixed acids a t concentrations which avoid localized overheating: 1 . The nitration reaction goes on in both phases. By emulsification each phase can be kept saturated with the other. Under these conditions, other things being equal, the rate in each phase is constant, that in the acid phase being several fold the rate in the organic phase. Total rate of nitration per unit of total volume is linear in the volume fraction of the phases. If the interfacial surface of contact between the phases is limited in amount, as by reducing the amount of benzene emulsified in the acid or by avoiding emulsification, reaction rate drops rapidly because diffusion is no longer sufficient to keep each phase saturated with the reacting component from the other phase. This reduction in reaction rate conforms quantitatively to the assumption that diffusion has now become the controlling factor. KO indication of localization of reaction a t the interface is found.
CONCENTRATIO(I OF HNO,
IN AWfOOS
PHASE -MOL PERCENT
FIGURE 10. EFFECTOF TEMPERATURE FIGURE11. EFFECT OF RATE OF STIRRISG .IT CONSTAST I X T E R F A C I A L AREA
Nitration of 1 mole of benzene with mixed acid containing initiaily 1 mole of nitric acid; concentration of sulfuric acid in t h e aqueous phase, 2 1 . 6 mole per cent.
R E A C T I O N RATEAT C o i i s ~ a i iIXTERFACIAL ~ AREA. The technique of batch nitration was also used t o study the influence of interfacial surface between the liquid phases and t o check conclusions drawn from the results of the continuous runs as t o the part played by diffusion in the reaction mechanism. Definite volumes of mixed acid and benzene were introduced into a 2-liter wide-mouthed bottle, fitted with two stirrers, one in the acid and the other in the organic layer. Each stirrer was adjusted a t a constant distance from the interface. T h e stirrers rotated in opposite directions, and speed was controlled so t h a t no emulsification developed, although the interface was always somewhat disturbed by waves. Temperature was held a t 25' C. by immersion in a water bath. Samples of each phase were removed from time to time and analyzed. At constant total liquid volume, increase in the acid phase increases reaction rate, despite constancy of interfacial area. However, unlike the runs in which emulsification occurred, the rate is not approximately proportional to the volume of the acid phase but rises less rapidly. Under the experimental conditions of these runs the distance through which hydrocarbon must diffuse t o get into the middle of the acid phase is approximately proportional t o the quantity of t h a t phase, so t h a t as the amount of the phase is increased, the concentration of hydrocarbon in i t goes down and results in a reduction in nitration rate per unit volume of acid despite a n increase in nitration rate as a whole. Moreover, the rates realized are of a lower order of magnitude than if the phases are emulsified, even under comparable concentration conditions. Reaction rate a t constant interface is influenced by the rate of stirring in both phases, but Figure 11 indicates that the
Interfacial area, 95 sq. c m . ; temperature of nitration, 25.0' C.; volume of aqueous phase, 400 ml.; volume of organic phase, 800 ml. --Composition, Mole 7'-C u r v e A Curve B Curve C 3 31 HSOI 3 45 3 17 27 80 27 74 HzSOn 27 80
HzO
88 75
68 89
69 09
R PM. OF STIRRING OF BOTH STIRRERS)
2. Rate of reaction is extremely sensitive to the composition of the acid phase. Over a considerable range of composition, a variation of only 3 mole per cent in nitric acid content can make a tenfold variation in rate of nitration. The variation in isothermal rate of nitration with composition of the nitrating acid correlates with the mole fraction of none of the components in the liquid. ( I t is true that the variation in water content along a constant-rate curve is not large, but because an increase of less than 5 per cent of the total water present can reduce the rate to one tenth its original value, the assumption that rate depends
primarily on water content seems untenable.) Kitration rate parallels the partial pressure of neither the nitric acid nor the water in the mixture, but there is a decided parallelism with the ratio of the partial pressure of the nitric acid to that of the water. This suggests that the driving force of the reaction may be proportional to the activity of the nitric acid in the mixture, but that there is an inhibiting action which, in turn, is proportional to the activity of the water. 3. Rate of nitration is relatively insensitive to the composition of the organic phase-i. e., t o the percentage conversion of benzene to nitrobenzene-so long as the conversion is not above 8090 per cent. I t may be that a high percentage of nitrobenzene in the organic phase increases solubility of acid in that phase sufficiently t o counterbalance the decreased concentration of hydrocarbon. 4. Rate of nitration doubles, other things being equal, for a temperature rise of about 10" C.
AUGUST, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
Literature Cited (1) Farmer, R . C . , J. SOC.C h e m . I n d . . 50,751‘ (1931). (2) Gilman, H . , “Organic Chemistry. an Advanced Treatise”, Val. 11, p. 111, New York, John Wiley & Sons, 1938. (3) Grignard, V.,“Trait6 de chimie organique”, Vol. IV, p. 232, Paris, hlasson et Cie., 1936. (4) Groggins. P. H . , “Unit Processes in Organic Synthesis”, p . 23, New E-ork, McGraw-Hill Book Co., 1935. (5) Hantssch. A , , Ber., 50, 1422 (1917), 58, 612, 941 (1925). 60, 1933 (1927): Z.Elektrochem., 24,201 (1918). 29,221 (1923),30, 194 (1924), 31,167 (1925); 2 . p h y s i k . C h e m . , 134,406 (1928). (6) Hetherington, J. A , , and Masson. I . , J . Chem. Soc.. 1933,105. ( 7 ) Holleman, -1.F . , “Die direkte Einfuhrung Ton Puhstituenten in den Bensolkern”, pp. 71, 97, Leipeig, Verlag von Teit und Camp., 1910. Sal-age. W., and Van Malle. D. J . , C h e m . 12 .\let. ( 8 , Hough, -1., Eng., 23,666 (1920). ( 9 ) International Critical Tables, 1-01. 111, p. 307, S e i v York, McGraw-Hill Book Co., 1928. ( 1 0 ) Kullgren. C . , Z . ges. Schiess- Sprengstoflw., 3 , 146 (1908). (11) Lauer, K., and Oda, R.,J . prakt. Chem., 144, 176; 146,61 (1936).
1101
(12) Martinsen, H . , Z . p h y s i k . Chem., 50, 385 (1904): 59,605 (1907). (13) Othmer. D. F . , ISD. EEG.CHEM.,20,743 (1928). (14) Parks, G . S., and Huffman, H . M.,“Free Energies of Some Organic Compounds”, A . C. S. Monograph 60, p. 221, Xew York, Chemical Catalog Co., 1932. (15) Pounder, F . E., and Masson, 1..J. C‘hem. SOC.,1934,1352. (16) Saposchnikow. A . W., 2. p h y s i k . C h e m . , 49, 697 (1904), 51, 609 (19051, 53, 225 (1905); Z. ges. Schiess- Spreng&o$w., 4, 441, 462 (1909). (17) Schaeffer, K . , Z. anorg. allgem. Chem., 97, 285; 98, 70, 77 (1916). (15) Bpindler, P . . B e r . , 16, 1252 (1883); Ann., 224, 283 (1884). (19) Suen. T . J . , M a s s . Inst. Tech., 9 c . D . thesis, 1937. (20) Taylor, H . S.,“Treatise on Physical Chemistry”, 2nd ed., Vol. 11, p. 1026, Kew York. D. Van Nostrand Co., 1930. (21) Tronov, B. V. et al., J . Russ. Phys. Chem. SOC.,62, 2267 (1930); Ckrabz. Khem. Zhirr.. 7 , No. 1, Sci. pt. 55 (1932). (22) Walker, W.H . , Lewis, W. K., and McAdams. W. H., “Principles of Chemical Engineering”, 2nd e d . , p. 128, New Tork, MrGraw-Hill Book Co.. 1927. (23) Wibaut, J . P . . Rec. trav. chim., 34,241 (1915); 54,409 (1935). (24) Wyler. O., Hela. C‘him. .4cta. 15, 23, 591, 956 (1932).
MULTICOMPONENT RECTIFICATION Minimum Reflux Ratio’ E. R. GILLILAND Massachusetts Institute of Technology, Cambridge, Mass.
.4pprosimate equations are derived for the estimation of the minimum reflux ratio for multicomponent mixtures, and these equations can be used to calculate upper and lower limits for the true minimum reflux
F
OR a given separation by rectification, the minimum number of theoretical plates a t total reflux and the minimum reflux ratio corresponding to an infinite number of plates render valuable aid to the designer, by defining the limits within which his calculations must be confined to give an operabIe design. Satisfactory methods for the calculation of both of these factors have been developed for binary mixtures. However, for the case of multicomponent mixtures, the problem is more complev than for binary mixtures, and only for the case of the minimum number of theoretical plates a t total reflux have suitable methods been developed ( I ) . Several methods for predicting the minimum reflux ratio for multicomponent mixtures have been published; of these, t h a t of Underwood (6) has been the most widely used by other investigators. Underwood’s equation is:
This equation was derived on the basis of assumptions which were equivalent to assuming t h a t for the condition of minimum reflux the concentrations of the key components mere the same on the feed plate as in the feed. Such a n assumption i, true for binary mixtures of normal volatility but is seldom triie for multicomponent mixture
