329
Ind. Eng. Chem. Fundam. 1983, 22, 329-335
(25.0 g) derived from the liquefaction of Illinois No. 6 coal was extracted with 1 N sodium hydroxide (3 X 100 mL). Drying over sodium sulfate, filtration, and removal of solvent by rotary evaporation yielded 2.46 g of phenolic extract. Gas chromatographic analysis (10% Carbowax 2OM, 10 f t x ' I 8in.) showed that this product consisted of 32.4% phenol, 46.0% cresol, 6.1% other phenols, and 15.5% residual solvent. Etherification of EDS Phenolics. The isolated EDS phenol (0.5846 g) was etherified with 7.40 g (132 mmol) of 2-methyl-2-butene and 0.092 g (0.38 mmol) of 40% sulfuric acid in methanol using 0.0621 g (0.338 mmol) of n-C13Hzsas an internal standard by reaction at 25 "C for 1 h and then at 0 "C for an additional 7 h. After neutralization with 0.12 g (1.19 mmol) of triethylamine the mixture was analyzed by gas chromatography (10% Carbowax, 20M, 10 f t X in.) and then concentrated to yield 0.67 g of alkylate. The GC analysis showed the alkylate to contain 38.1 mol % of unreacted phenolics, 57.3 mol % of ethers, and 4.5 mol % of carbon-alkylated products. The product mixture was then. taken up in ether, washed with 1N sodium hydroxide to remove unreacted phenolics, dried over sodium sulfate, filtered, and concentrated to yield 0.45 g of ether product. GC analysis confirmed this product to be a mixture of tert-amylphenyl ether and tert-amyltolyl ethers with small amounts of carbon-alkylation byproducts. In Situ Etherification of EDS Naphtha. EDS naphtha (0.15 g) was reacted with 1.85 g (26.4 m mol) of 2-methyl-2-butene and 0.0348 g (0.36 mmol) of 40% sulfuric acid in methanol for 4 h at 25 "C. After neutralization with triethylamine, analysis by gas chromatography (10% Carbowax 20M, 10 f t X in.) showed 41 mol % ether yield, 2-4 mol% ring-alkylated products, and 55-56% unreacted phenols. Analysis using an hexadecane external standard gave a mass balance of 92 % . Extraction of EDS Naphtha with Sulfuric Acid/ Methanol Mixtures. EDS naphtha was extracted with the desired quantity of sulfuric acid/methanol, the latter ranging from 10 to 80% sulfuric acid. After separation the organic layer was analyzed by gas chromatography (10%
Carbowax 20m, 10 ft X 1/8 in.) with n-C13H2sor n-C16H34 as an internal standard. Acknowledgment The authors are indebted to R. H. Schlosberg and J. G. Speight for their helpful suggestions for this work and critiques of this manuscript. The authors also acknowledge the contributions of T. Ashe, J. Brown, M. Melchior, R. Pancirov, and R. Rif for their parts in the experimental and analytical procedures. Registry No. 2-Methyl-2-butene, 513-35-9;p-cresol, 106-44-5; 2,4-dimethylphenol, 105-67-9;2-ethylphenol, 90-00-6; tert-amyl p-tolyl ether, 85709-98-4; 2-tert-amyl-4-methylphenol,34072-71-4; 2,6-di-tert-amyl-4-methylphenol, 56103-67-4; tert-amyl 2,4-dimethylphenyl ether, 85709-99-5; 2-tert-amyl-4,6-dimethylphenol, 85710-00-5; tert-amyl 2-ethylphenyl ether, 85710-01-6; 2-tert-
amy1-6-ethylphenol,85710-02-7; 2,4-di-tert-amyl-6-ethylphenol, 85719-48-8; 4-tert-amy1-6-ethylphenol,85710-03-8; sulfuric acid, 7664-93-9; methanol, 67-56-1.
Literature Cited Exxon Donor Solvent Coal Liquefaction Process Development Phase I I I A , Annual Technical Progress Report, Jan 1-Dec 31, 1976;D.O.E. No. Fe-
2353-9 (1977). Haggin, J. Chem. Eng. News Nov 30, 1981, 59, 32. Levas, P. E. Ann. Chim. 1938, 3 , 145. Natelson, S.J. Am. Chem. SOC. 1934, 56, 1583. Newman, M. S. "Steric Effects in Organic Chemistry"; Wiiey: New York,
1956. Niederi, J. E.; Natelson, S. J. Am. Chem. SOC. 1931, 53, 272. Olah, G. A. "Friedel-Crafts and Related Reactions", Vol. 11, "alkylation and Related Reactlons", Intersclence: New York, 1964. Schlosberg, R. H.; Scouten, C. G. U S . Patent 4256568,Mar 17, 1981. Singerman, 0. M. "Methyl Aryl Ethers from Coal Liquids as Gasoline Extenders"; SAE Technical Paper, Series SP-480,Society of Automotive Engineering: Warrendale, PA, 1981. Smith, R. A. J. Am. Chem. SOC. 1933. 55, 3718. Smith, R. A. J. Am. Chem. SOC. 1934, 5 6 , 717. Sowa, F. J.; Hlnton, H. D.; Nieuwland, J. A. J. Am. Chem. SOC. 1932, 5 4 ,
3194. Sowa, F. J.; Hinton, H. D.; Nieuwiand, J. A. J. Am. Chem. SOC. 1933, 55,
3402. Sprung, M. M.; Wallis, E. S. J. Am. Chem. SOC. 1934, 56, 1715. Stevens, D. R. J. Org. Chem. 1955, 20, 1232. Zavgorodny, S.V. J. Gen. Chem. USSR 1946, 16, 1495. Zavgorodny. S. V.; Fedoseev, K. J. Gen. Chem. USSR 1946, 76. 2006.
Received for review September 7, 1982 Revised manuscript received February 7, 1983 Accepted March 3, 1983
Absorption of Nitric Oxide in Nitric Acid and Water Giorglo Carta and Robert L. Pigford" Department of Chemical Englneerlng, University of Delaware, Newark, Delaware 1971 1
-
The rate of absorption and simultaneous reaction of nitric oxide in aqueous nitric acid solutions in concentrations up to 35 wt % has been measured experimentally in a string-of-spheres, falling-film laboratory absorber. Evidence was found that the overall reaction, 2N0 HNO, H20 3HN02, is catalyzed by the reaction product, HNO,, and takes place in the liquid film according to the sequence: HNO, HNO, N204 HO , (I) and 2N0 N204 2H20 = 4HN0, (11). The first step is relatively slow and rate determining; the second can be considered instantaneous. The penetration and the film theories for mass transfer wtth an autocatalytic reaction have therefore been developed and the solution of the penetratlontheory has been found to be in qualitative agreement with the experimental observations. Its comparison allowed an estimate of the forward rate constant for the decomposition of nitrous acid, reaction I. However, due to the autocatalytic nature of the reaction, the film theory significantly disagrees with the penetration theory outside some special cases.
+
+
Introduction Tail gases from plants for the manufacture of nitric acid constitute a source of atmospheric pollution of considerable importance. The presence of oxides of nitrogen in the
+
+
-+
+
atmosphere represents a serious hazard for the ecosystem, and control of these emissions appears to be an increasingly important need. Furthermore, the loss of nitrogen oxides obviously reduces the efficiency of the production plant
Q190-4313f83f1Q22-Q329$Q1.5QfQ 0 1983 American Chemical Society
330
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983
and causes some economic damage. In relation to a conventional ammonia-oxidation process for the manufacture of nitric acid, dilute nitric acid scrubbing is one of the ways of reducing the nitrogen oxides content of the tail gas. It has been proposed (Bolme and Horton, 1979) to contact the gas stream from the main absorption column, countercurrently with a 25-30 wt 70 solution of nitric acid in water. The solution will remove NO, oxidizing it and producing nitrous acid that will be entirely carried out by the liquid. The absorbent nitric acid solution will be regenerated in a stripping section where the scrubbed nitrogen oxides will be recovered. In view of this possibility and since NO is the principal form of NO, in the tail gas, the absorption and reaction of nitric oxide in nitric acid solutions acquire particular relevance. The Reactions of NO in Nitric Acid The early study of Lewis and Edgar (1911) showed that, when NO is bubbled through a volume of a dilute nitric acid solution, the rate of consumption of HN03 increases with time, reaches a maximum, and then decreases again as equilibrium is approached. Abel and Schmid (1928a,b,c) found that NO reacts in nitric acid solutions according to 2N0 + HN03 + H20 = 3HN02 (1) They suggested that the formation of HN02 occurs via the following mechanism HN02 + H+ + NO3- N204+ H 2 0 (2) 2N0 + N204 + 2H20 = 4HNO2 (3)
20
I I
-1
0
01
02 ; .W .
03
Ob 05 weight fraction
06
07
Figure 1. Correlation of experimental equilibrium data of Theobald (1968).
-
Reaction 2 was assumed to be the slow and rate-determining step. Reaction 3, which is probably itself the result of a series of elementary steps, is known to be relatively fast. Neglecting the reverse of reactions 2 and 3 during the initial stages of nitrous acid formation, a pseudo-steadystate assumption for the intermediate NO yields the rate expression
(4) or
r = k1[HNO2] kl, as well as k, is a function of the nitric acid concentration and of the ionic environment in general. Indications on the equilibrium of reaction 1can be obtained from some experimental data given by Theobald (1968), who measured the equilibrium in the system NO, NOz,HN02,HN03, H20. We have correlated Theobald's data in terms of the two independent reactions 3N02 + H 2 0 = 2HN03 + NO NO + NO2 + H2O = 2HN02 defining the empirical equilibrium constants K3 = W H N O ~ ~ P N O / P N O ~ ~ K2 = WHN0,2/(PNO)(PNO*) The results are given in Figures 1and 2. Combining K , and K2, K1, the equilibrium constant for the reaction in which we are especially interested and defined as
K1 =
WHNO$PN02/WHN0,3
is given by In K1 = 10.359 - 3.078 WHNO~
(5)
at 25 "C. Theobalds data show that the weight percentage
\
-6l 0
'
'
'
'
0'
02
03
OL
Ww,
wQl*t
* ' O C
05
06
I 07
frUCtIOn
Figure 2. Correlation of experimental equilibrium data of Theobald (1968).
of nitric acid can be as great as 35 wt ?& while permitting the NO oxidation to proceed in the Bolme-Horton absorber. Mass Transfer with an Autocatalytic Reaction. Penetration Theory Equations In order to simplify the mathematical problem and for interpreting laboratory data, the following additional assumptions are made in addition to those standard for the penetration theory for gas absorption with chemical reaction (Astarita, 1965). The concentration of nitric acid is assumed to be constant everywhere in the liquid film because it is present in large excess. Thus, kl of eq 5 can be treated as a constant. As a consequence, only the slow and fast reaction regimes need to be considered here. Reaction 3 is assumed to be at equilibrium in the bulk of the liquid and the concentration of Nz04very small and approximately equal to zero throughout the film and in the bulk of the liquid. Furthermore, it is assumed that the process is not equilibrium limited. Let A refer to NO and E to HNOz local concentrations. The overall reaction can simply be written as
kl
3E (6) The two following coupled partial differential equations and boundary conditions represent the absorption process 2A
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983 331
D , -a2E =-ay2
1.0
3klEH(A)
>0
. a a
y = 0: A = Ai, dE/dy = 0 for t > 0 a:
1
I
at
t = 0 A = 0, E = Eofor y y =
,
A = 0, aE/ay = o
0
where the step function H(A) is defined by H(A) = 1 when A > 0
H(A) = 0 when A = 0 The step function, introduced in analogy to the approach of Astarita and Marrucci (1963) for a zero-order reaction, accounts for the fact that no reaction occurs outside a layer of liquid near the interface where A is greater than zero. Introduction of the following dimensionless variables reduces to two the number of independent parameters. a = A/Ai
e = E/E,
z = (kl/DA)1/2y
05
0
1.0
=@
I
1.5
Figure 3. Dimensionless concentration profiles of A at different times of exposure. I
I
0
I
1
6 = klt
R = Eo/Ai [ = DA/DE The resulting dimensionless form of the differential equations and boundary conditions is
>0 a = 1, de/& = 0 for 0 > 0
6 = 0: a = 0, e = 1 for z z = 0:
z =
OD:
u = 0,ae/az = o
The enhancement factor can be calculated from either of the two equations
2
3
L
5
e:qt
Figure 4. Time dependence of the dimensionless flux of A at the interface at different values of R = Eo/Ai.
Film Theory Equations The previous assumptions still holding, steady state diffusion and reaction in a film of finite thickness, 6, is assumed here. The pertinent equations and boundary conditions are
n‘
e
1 2
3
10 20 50
4
ion
1
0
1
2
3
y = 0: A = Aj, dE/dy = 0 y = h : A=O,E=Ex EA and X (Sa), the distance from the interface at which A becomes equal to zero, are determined by the two additional requirements that
:Ey L
z
5
6
7
Figure 5. Dimensionless concentration profiles of E at different times of exposure.
Solution of the Equations An exact analytic solution to eq 8a and 8b could not be found. A numerical solution was obtained by a completely implicit, finite-difference method. The calculated concentration profiles of A, depicted in Figure 3 for specific values of R and 5, show that the depth of penetration of A into the liquid film initially increases because of rapid diffusion from the interface. Because of the autocatalytic reaction the depth then reaches a maximum after which it decreases with time. Conversely, the instantaneous flux
332 Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983 XKXa
two '0
100 u1
0
10
w1
om
13
0'
'SO
R:E./P,
Figure 8. Effect of the ratio of the initial concentration of E to the interfacial concentration of A. 1
3
6
4
6
:
8
10
k,:
The solution of the film theory, eq 9-11, in the special case of equal diffusion coefficients is
Figure 6. Time dependence of the dimensionless concentration of E at the interface ( R = Eo/Ai).
R = -3
1 2 1 - sec ( a h ) + ah tan ( a h ) 3 1 - a h tan ( a h ) a h tan ( a h ) = 1 - sec (ah) + ah tan ( a h )
+
5
(13) (14)
where a = (3k1/D)'I2 Film and penetration theories are compared in Figure 9. The substitution of 6 = (rDt/4)'I2 has been made. The graph shows that the two theories agree only in limited regions in the prediction of the enhancement factor. They agree for small values of 8 when the reaction is not important at all and I is approximately equal to 1; they also agree for large values of R , and sufficiently small values of 8, when the situation is close to that of a zero-order reaction for the bulk conditions and the autocatalytic effect is not important. Outside these cases considerable disagreement occurs. The difference is due to the intrinsically transient behavior of the autocatalytic absorption. As a consequence, close agreement could not be expected a priori by replacing the film thickness 6 with the group (rDt/4)'l2. Figure 9 shows that, depending on the conditions, the film theory can overpredict the value of the enhancement factor by as much as an order of magnitude and more. Experimental Section A string-of-spheres, laminar-film absorber was used in this study. A cross section is shown in Figure 10. The absorbent liquid was evenly distributed over the top sphere (3.75 cm diameter) and taken off by means of a constant level device which set the liquid level inside the absorber. The sphere column was enclosed in a Lucite cylinder. A constant-leveldevice provided a nonfluctuating liquid flow. Gases were supplied by high-pressure cylinders and metered through rotameters or soap-film meters. Other details of the experimental techniques are given by Carta (1982). The hydrodynamics of the flow over the wetted sphere and the degree of mixing at the junction between adjacent spheres were characterized by absorbing C 0 2 in distilled water. Absorption rates from an atmosphere of watersaturated C 0 2were measured volumetrically by means of a soap-fib meter. The results are given in Figure 11. The solid lines represent the theoretical predictions of Davidson and Cullen (1957, 1959) under the two extreme assumptions of complete mixing and no mixing at the junction, as indicated. Known values of solubility and diffusivity
, I 3'
0 : k,!
Figure 7. Enhancement factor for absorption of A.
of A at the interface, starting at infinity, reaches a minimum after which it increases again (Figure 4). A few concentration profiles of e ( z ) are shown in Figure 5. Figure 6 is a plot of the dimensionless concentration of E at the interface as a function of 8, the time of exposure, for different values of R. It shows that e, grows exponentially only in a range of small values of 8, if the layer of liquid saturated with A (where the reaction takes place) is relatively deep. For larger values of R, the relative increase of the concentration of E becomes smaller for the same &interval and much longer times are required to obtain a significant accumulation of E near the interface. In Figures 7 and 8 the enhancement factor calculated according to the penetration theory is shown for different values of R and 8. Figure 8 shows the effect of different R values. It may be seen that for each time 8 and a sufficiently large value of R, the curves converge to the asymptotes for a fast, pseudo-zero-order reaction. The relative increase of E at the interface becomes negligible and ei is approximately equal to 1. The asymptote for a fast zero-order reaction is given by Astarita and Marrucci (1963) and in our nomenclature can be expressed as I = (TRO)''~.The enhancement factor appears to be relatively insensitive to the value of R and, for sufficiently high values of 8, I becomes substantially independent of R in a wide range.
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983 333
0.001
0.01
0.1
10
1
100
R k,t=Re
Figure 9. Comparison of estimates of the enhancement factor by use of film and penetration theories. Gas outlet
,
B
-
m
0 ,
6
,
-
i 5 2
e
1
0
P 3 0 0
0 "
2
1
0 Q,, Water
f l o w rate
(cm3/sec1
Figure 11. C02 absorption in water: T = 20 "C; P = 1 atm. Figure 10. Laboratory gas absorber.
were used in the calculations. A fairly good agreement is shown by the one-sphere data at water flow rates below about 1.8 cm3/s. The assumption of complete liquid mixing at the junction seems also to be adequate in the whole range investigated, as shown by the five-sphere data. The deviations from the theoretical predictions start, in fact, at approximately the same flow rate for a single sphere and for a string of five. These deviations are attributed to the rippling of the liquid film that took place at the higher flow rates. As revealed by visual experiments of smoke injection, the gas phase in the absorption chamber was well-mixed at the gas and liquid flow rates used. An average gas-film mass transfer coefficient was estimated from experimental absorption rates of ammonia in water from a dilute nitrogen stream. After correcting for the different diffusion coefficients of ammonia and nitric oxide in nitrogen by means of the relationship kg,NO/kg,NHs
=
(DNO/DNH,)2'3
the resulting mass transfer coefficient for NO was estimated as kg = 1.50 X mol/(cm2)(s)(atm). The water
flow rate was kept constant in these runs at the value of 1.6 cm3/s. Absorption rates of NO in nitric acid solutions were obtained either by chemical analysis of the exit liquid or volumetrically, by means of a soap-film meter. The results of the two different measurements in the same conditions agreed within 10% with the stoichiometry of reaction 1. The HN02 contents of the exit liquid was determined by standard oxidimetric techniques (Stubblefield, 1944). Since relatively high partial pressures of NO were used and appreciable changes did not occur, the gas phase was analyzed only for its NO2 contents by means of infrared spectroscopy. NOz was found to be virtually absent in any run. The results are given in Figure 12. The diluent gas was nitrogen and the absorbent solutions were prepared by diluting 70% AR grade nitric acid with distilled water. They contained an initial small amount of nitrous acid. Only its order of magnitude could be estimated, about M. The nitric acid concentration did not vary appreciably during the absorption. The average partial pressure of NO at the interface, piNo,was calculated from the experimental data by using the estimated gas-phase mass transfer resistance. The correction never exceeded 10% of the NO
334
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983
Table I. Absorption of NO in Nitric Acid. Summary of Absorption Rate Measurementsa
9,
10.0 20.0 25.0 30.0 32.5 35.0 a
T
=
0.086 0.100 0.083 0.022 0.001 0.001
0' 0 2 0 3 0 4 05 06 0 7 08 0 9
P&
10
1.0 1.0 1.0 1.0 0.3 0.3
k,,s 0.013 0.33 2.45 6.60 13.2 26.0
25 "C; Q = 1.6 cm3/s;5 spheres.
135
0
mol/s x 105 0.49 1.60 2.87 6.0 4.50 6.20
1
11
~ a t m ~
Figure 12. Absorption of NO in nitric acid: T = 25 "C, QL = 1.6 cm3/s; Qg= 50 cm3/s, 5 spheres. Lines are calculated according to the penetration theory numerical solution.
0
2
1
Q l,
Figure 13. Absorption of NO in nitric acid. Effect of liquid flow rate: 7' = 25 O C ; P = 1 atm; 5 spheres. Lines are calculated according to the penetration theory numerical solution.
bulk partial pressure and was almost negligible in most cases. Figure 13 shows the effect of the liquid flow rate on the rate of absorption. As a consequence of the decreased time of exposure and of the larger dilution at the junction between adjacent spheres, increase of the liquid flow rate causes a decrease of the absorption rate of NO. The absorption rate was found to increase with the initial HNOz concentration. When only the nitric acid solutions and nitrogen were fed to the absorber, NOz, stripped from the liquid was present in the gas phase. Its characteristic brown color could be visually observed. The brown color completely disappeared, however, when nitric oxide was admitted to the absorption chamber. The solid lines of Figures 12 and 13 were calculated according to the numerical solution of the penetration theory. The average time of exposure was estimated according to t=-
4DA XkLo2
kLo was calculated using the expressions given by Davidson and Cullen for the physical absorption on a wetted sphere. For each value of R, the enhancement factor, I , could thus be calculated for the jth sphere and the value of R for the subsequent sphere obtained from
2
3
-
[HN031
3
d q u d flow rote (cm3/sec)
1
5 (mole/ I
6
'
8
,
Figure 14. Pseudo-first-orderrate constant for reaction 2: T = 25 OC.
Equation 15 was derived from the mass balance assuming that the depth of penetration was small and that complete liquid mixing occurred at the junction between adjacent spheres. A value of M was assumed for the initial HNOz concentration. However, as previously pointed out, the model is rather insensitive to the initial value of R. Various other physical constants had to be estimated where experimental values were not available. The solubility of unreacted NO in nitric acid solutions was estimated from the solubility in water using the method of Van Krevelen and Hoftijzer (1968). The ratio of the diffusion coefficients of NO and HNOz was estimated to be equal to 2 in every condition, independent of the nitric acid concentration. The numerical solution was extended to this particular case. Finally, the pseudo-first-order rate constant for the decomposition of HN02, k l , was estimated for the various nitric acid solutions by fitting the penetration model to experimental observations. Table I shows the data used for this purpose and lists the values of kl found. The results of these studies are given in Figure 14,where they are compared with the values given by Schmid and Bahr (1964) and Schmid and Krichel (1964). Schmid and Bahr considered only low temperatures or dilute solutions. Schmid and Krichel used an approximate mathematical procedure to obtain kl from electrochemicalmeasurements. The remarkably strong dependence of kl on the nitric acid concentration is not totally surprising due to the ionic character of the reactions involved. Schmid and Bahr observed a similar effect also when an inert electrolyte was added to the nitric acid solutions. The effect was attrib-
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983 335
,
1 ,
,
,
,
,
,
,
,
/
d
-
0 / 0
Nomenclature
/
-
01
I
3
-
-
O/
-
/
-
.-. \
-
/
N
0
/ 1
001
0 This work
A A
A
SchmdLBahr
0 Equilibrium data
t
i
"""/
0
1
2
3
4
5
.
HN02 at the interface has an important beneficial effect. It is its rate of decomposition that determines the rate of absorption of nitric oxide in nitric acid solutions.
w t % The accumulation of
6
7
8
LW3I, ( m o l d 1 1
Figure 15. R a t e constant f o r reaction 2: T = 25 "C.
uted to the influence of the neutral salt on the activity coefficients of the reactive species. Figure 15 shows the effect of the nitric acid concentration on the value of k, the rate constant defined by eq 4. On the same graph a square dot represents the value of k at infinite dilution. This value was estimated by combining the rate constant for the reverse of reaction 2, the hydration of N204,as determined by Wendel and Pigford (1958),and the equilibrium constant for that reaction. The electrode potential measurements of Pick (1920) were used to estimate the equilibrium constant. Conclusions The mathematical modeling of this particular case of gas absorption with chemical reaction, zero order with respect to the absorbing gas and pseudo-first order with respect to the reaction product, presents remarkable differences from the usual chemi-absorption problems. It is believed that the qualitative indications of the solutions of the penetration and film theories should not be restricted to the special kinetics considered here. In particular, the possible considerable disagreement of the two theories in the prediction of the enhancement factor should be considered whenever autocatalytic kinetics is encountered. The penetration theory explains qualitatively the experimental observations of absorption rates of NO in nitric acid solutions. The model, however, does not account for the equilibrium limitations, important in other conditions. Extension of the model in this sense should be recommended for design purposes. From our experimental observations the appropriateness of the proposed reaction mechanism emerges. Considerable enhancement of the absorption rate can be achieved with nitric acid solutions in concentration of about 25-30
a = A/Ai A = NO concentration, mol/cm3 D = diffusion coefficient, cm2/s e = E/Eo E = HN02 concentration, mol/cm3 H = solubility, mol/(cm3 atm) H ( A ) = unit step function I = enhancement factor, = k%/kLo k = reaction rate constant, L /(mol2 s) kl = reaction rate constant, s-l k, = gas-side mass transfer coefficient, mol/(cm2 s atm) kL = liquid-side mass transfer coefficient, cm/s kLo = mass transfer coefficient for physical absorption, cm/s P = pressure, atm QL = liquid flow rate, cm3/s R = Eo/Ai t = contact time, s W = weight fraction y = depth in the liquid film, cm Z = (k1/DA)'l2y Greek Symbols a = (3kl/D)ilz 6 = film thickness, cm
5 = DA/DE
8 kit X = depth of penetration (film theory), cm 4 = rate of absorption, mol/s
Subscripts
i = interfacial 0 = initial or bulk conditions A = NO E = HNO2 Registry No. NO, 10102-43-9; HN03, 7697-37-2; H N 0 2 , 7782-77-6.
Literature Cited Abel, E.; SchmM, H. 2.fhys. Chem. 1928a, 132, 56, 64. Abel, E.; SchmM. H. Z . Phys. Chem. 1928b, 734, 279. Abel, E.; Schmid, H. 2.fhys. Chem. 1928c, 136, 153, 419. Astarlta, G. "Mass Transfer with Chemlcal Reaction"; Elsevier: Amsterdam; 1965. Astarlta, G.; Marruccl, G. Ind. Eng. Chem. Fundam. 1963, 2 , 4. Bolme, D. W.; Horton, A. Chem. Eng. Rogr. 1979. 75, 95. Carta, G. M.Ch.E. Thesis, University of Delaware, Newark, DE, 1982. Davldson. J. F.; Cullen, E. J. Trans. Inst. Chem. Eng. 1957, 35, 51. DavMson, J. F.; Cullen, E. J. Tfans. Inst. Chem. Eng. 1959, 37, 122. Lewis, G. N.; Edgar, A. J. Am. Chem. SOC. 1911, 33, 293. Pick, H. 2.E/ektrochem. 1920, 26, 182. SchmM, G.; Bahr, G. 2.fhys. Chem. 1964. 68, 8. Krlchel, 0.2.€/&rochem. 1964, 6 8 , 677. SchmM, 0.; StubblefieM, F. M. Anal. Chem. 1944, 76, 368. Theobaid, H. Chem. Ing. Tech. 1968, 15, 40. Van Krevelen, D. W.; Hoftijzer. P. J. R e d . Tfav. Chim. 1966, 67, 563. Wendel, M. M.; Pigford, R. L. AIChEJ. 1958, 4 , 294.
Received for review M a r c h 26, 1982 Revised manuscript received April 21, 1983 Accepted April 29, 1983
