Ct = total molar concentration per unit volume of bed Dco-F~(coI( 5 ) = binary diffusivity in CO-Fe(C0)s mixture Deff = effective diffusivity of Fe(C0)5 in bed Eb = activation energy for deactivation constant, b E, = activation energy for overall reaction rate constant, krm
K , = equilibrium constant of carbonyl formation reaction, a F e ( C 0 )(51/ a C 0 5 = reaction rate constant defined by Equation 7, cm6/g-mol sec g k r m o = frequency factor fork,, k, = reaction rate constant in Equation 4 MFe = molecular weight of iron, 55.847 g/g-mol mFe = mass of reduced free iron per unit volume of bed mFe0 = initial mass of reduced free iron per unit volume of bed Npe = Peclet number, youo/Deff n = number of CO molecules adsorbed on nonreacting iron sites and involved in forming a molecule of Fe(C0)5 P = total pressure Pi = partial pressure of species i R = gasconstant r, = rate of carbonyl formation per unit surface area of free iron r , = rate of carbonyl formation per unit volume of bed S = conversion of free iron to iron pentacarbonyl, (mFeo - mFe)/mFe’ T = temperature t = time U = dimensionless velocity, u / u o uo = reference velocity, 0.272 cm/sec Xu = mole fraction of Fe(C0)5 Y = dimensionless distance from the distributor, y / y o
YH = reduced bed height, bed height/y, yo = reference distance, 7.28 cm y = axial distance along the bed from the distributor Greek Letters t = porosityofbed T = dimensionless time, t u o / y o T f = tortuosity factor
k,,
L i t e r a t u r e Cited Beebe, R. A , , Stevens, N . P., J. Amer. Chem. Soc., 62, 2134-40 (1940). Carlton, H. E., Goldberger, W. M., J . Metals, 17,611-15 (1965). Carlton, H. E., Oxley, J. H., Amer. Inst. Chem. Eng. J., 11, 79-84 (1965). Dufour-Berte, C., Pasero, E., Chim. Ind., 49, 347-54 (1967); CA, 67,24115a (1967). In Ital. Hayward, D. O., Trapnell, B. M . W., “Chemisorption,” pp 191-7, Butterworths, London, 1964. Hoogschagen, J., Ind. Eng. Chem., 47,906-13 (1955). Kim, C. S., Rhee, C. S., Li, Kun, Rothfus, R. R., Enuiron. Sci. l’ech., 7, 725 (1973). Kunii, D., Levenspiel, O., Ind. Eng. Chem. Process Des. Develop, 7, (4), 481-92 (1968). Lewis, R. M., Cookston, J. W., Coffer, L. W., Stephens, F. M., Jr., J. Metals, 10,419-24 (1958). Mond, L., Wallis, A . E.,J. Chem. Soc., 121,29-32 (1922). Okamura, T., Kozima, H., Masuda, Y . , Sei. Rep., Tohoku Uniu., A l , 319-25 (1949). Pichler, H., Walenda, H., Brennst-Chem., 21, 133-41 (1940); CA, 35,3207 (1941). In Ger. Stoffel, A,, Z. Anorg. Chem., 84, 56-76 (1914); CA, 8 (l), 639 (1914). In Ger. Wagener, S.,J . Phys. Chem., 61,267-71 (1957).
Received for review October 26, 1972. Accepted April 11, 1973. Work supported by the U.S. Department of the Interior.
Photolysis of NO, in Air as Measurement Method for Light Intensity Donald H. Stedman’ and Hiromi Niki Fuel Sciences Department, Ford Motor Co. Scientific Research Laboratories, P.O. Box 2053, Dearborn, Mich. 481 24
w We have investigated the photolysis of NO2 in air using a chemiluminescent O3/NO detector. The first 30 sec of photolysis provide a simple and rapid measurement of the light intensity k1. (NO2 hu NO 0 ) . The inhomogeneity of light intensity can also be measured. Both parameters are important in photochemical smog studies. This experiment also provides for a check on the 0 3 calibration by turning off the lights. Comparison of our k l and k d measurements confirms recent work which gives k l / k d = 0.64. According to the mechanism this gives the ratio of rate constants for 0 + NO2 M NO3 M to 0 NO2 NO 0 2 of 0.28 f 0.03.
+
+
+
+
-
+
+
-
+
The primary process in photochemical smog reactions is the photodissociation of NOz, and the rate of this reaction is a critical parameter for understanding the mechanism *To whom correspondence should be addressed. Present address. Chemistry Department, University of Michigan, Ann Arbor, Mich. 48104.
of smog formation. The relevant reactions have been reviewed recently (Schuck and Stephens, 1970).
+ + + - + + - + + - + + - + + + - + +
NO2 hv NO 0 0 0, M 0, M NO 0, NO* 0, SO? 0, KO3 o2 0 NO, NO O2 0 NO, M NO, M NO, NO:, NZOj KO NO, 2N0, 0 NO M NO, M 2NO 0, 2N0,
+ + + + +
---
+
(1) (2)
(3) (4) (5) (6) (7) ( 8) (9) (10)
The photolysis of NO2 in N2 is commonly used for measuring the light intensity in a photochemical smog chamber. The method consists of filling a photochemical reactor with a low concentration of NO2 in an inert gas (usually Nz) and monitoring the decay of NO2 as a function of Volume 7, Number 8, August 1973
735
irradiation time (Tuesday, 1961). In the absence of 02, the mechanism is generally considered to be as above with the omission of Reactions 2, 3, and 4. With the further simplifying assumption that in the initial stages [NO] 5 x [O,]. These runs d[NO],’dt d[O?]dt cornwere repeated for the condition [NO21 > [NO] = [03], and initial. k l (direct). k l (pstat). puter f i t . [NOr]o. initial. min m1n-l min~’ in this case [NO] and [os] showed an equal gradient with pprnrnin-‘ p p m m i n - ’ ppm radius. An experiment in the presence of hydrocarbon for 0.13 0.14 1.3 0.14 1.3 0.9 which [NO21 > [O,] > 10 x [NO] showed the gradient 0.13 0.14 5.4 0.14 3.7 5.2 only in the [NO] and no detectable gradient in [O,]. Thus 0.13 0.14 10.8 0.14 8.0 11.7 the light intensity gradient manifests itself in the concen-
I
c I
-/-
Volume 7, Number 8, A u g u s t 1 9 7 3 737
tration of whichever is the species in the lowest concentration. It is difficult to model kinetics quantitatively in systems in which the light intensity and the concentrations of minority species are inhomogeneous. Therefore it is desirable to ensure as even a distribution of light intensity as possible. For this purpose, the externally illuminated vessel described earlier was used. The light intensity was mapped in the same way, using the photostationary ozone concentration. In this case the radial decrease in light intensity was from 0.21 min-l a t the edge to 0.17 min-l a t the center. The vertical differences were less than 0.03 min-l from 13 cm above the base plate to the top of the jar (75 cm). As expected, the light intensity decreased to 0.1 min-l a t the base plate. The average light intensity was 0.19 min-l and 93% of the gas in the vessel experienced a light intensity between 0.17 and 0.21 min-I. To determine experimentally the relationship between k d and k l , (Equation l),we determined k d in the externally illuminated bell jar. Some experiments performed a t 1 ppm NO2 tended to be nonreproducible and to give 10-20 ppb [O,] in the first 15 sec of photolysis. This effect, which may be due to 0 2 impurity discussed earlier, was overcome by using 10-15 ppm of NO2. The initial NO, and NO readings were made, then [NO] was monitored for 5 min while the vessel was irradiated. Since [NO,] was constant, then [NO21 could be read from the [NO] curve by subtraction. First-order decay of [NO21 over this period was observed. The values of k d obtained in the externally
Table II. Comparison of Measures of Light Intensities ki and k d k l , min-’
0.195 0.19 0.185 0.18 0.187 0.187 0.17 0.15
kd.
min-’
k~[MI!ks (from Equation l )
kilkd 0.65 0.65 0.66 0.60 0.67 0.64 0.63 0.65
0.30 0.29 0.28 0.30 0.28 0.29 0.27 0.23
0.30 0.30 0.32 0.20 0.34 0.28 0.26 0.30
Average 0.29 f 0.03 (20)
Schuck and Stephens (1970) Troe (1969) Ford and Endow (1957)
0.33 f 0.08 0.27 f 0.03 1.9
illuminated system are compared in Table I1 with direct estimates of 121 from the photolysis of NO2 in air mentioned previously. In the internally irradiated system (see Figure 2 ) , kd was measured with the NO probe a t 10.6, 4.9, and 2.7 cm from the lamp. The values obtained were 0.110, 0.113, and 0.113 min-I, respectively. The reasons why k d determination does not detect the light intensity gradient are discussed later.
Discussion Experiments such as those shown in Figure 1 were conducted with the aim of demonstrating that an analysis of [NO] and [ 0 3 ] in the first 30 sec of photolysis of NO2 can lead to a direct measurement of the light intensity, and of understanding the details of the reactions in the NO2 photolysis system. The rapid initial buildup of equal concentrations of NO and O3 is predicted by just reactions 1-3 in the mechanism. The slower increase of [NO] and decrease of [ 0 3 ] will be discussed elsewhere. Ripperton and Lillian (1971) also carried out the photolysis of 10 ppm NO2 in air as a base line experiment for a photochemical smog study. They observed rapid increase of NO and O3,.as expected but then [03]increases slowly, and [NO] decreases. This contrasts with the behavior we observe between 1 and 10 ppm NO2 shown in Figure 1. However, it should be pointed out that even in the present system, prolonged photolysis finally leads to a decrease in [NO] and increase in [03], ascribed to organic impurity. Ripperton and Lillian also suggest that their observations may be indicative of an organic impurity. The results suggest that our system may be somewhat less contaminated. In the previous unpublished work, the first 30 sec of reaction were shown to be adequately calculated by a chemical kinetics computer program [Sharp and Daby (1971) adapted a chemical kinetics program (deTar, 1967)] using the rate constants and mechanism in Table 111. The only important rate constants in obtaining this agreement are k~ and the measured value of k 3 . This provides a method of estimating k l by the computed fit to the first 30 sec of data. Figure 1 shows the computed fit in the first 30 sec for three photolyses run concurrently; the computed best fit in each case is to k.l = 0.140 min-l with uncertainty of 3~0.006.This compares well with the direct measurements in Table I taken from the initial slopes of d[NO]/dt and d[&]/dt. The photostationary state determination of k l (pstat) from Equation 13 is slightly slower because of a correction (averaging 5%) for the data in Table I for the removal of [03]by the NO2 O3 reaction. This method of determining kl is useful for photochemical smog studies, because
+
Table I l l . Detailed Mechanism for Photolysis of NO2 in Air No 1
Rate constant, ppm-’min-’
Reaction NO2 f h ~ +N O f 0 0 f 0 2 f M-03 f M NO f 0 3 NO2 0 2 NO2 0 3 N O 3 -I-O2 0 NO2 NO f 0 2
2 3 4 5 6
0 f NO2 f M
7
NO2 f NO3
+ +
-
+
+
+
+
-
+
NO
+M
N205
c
a 9 10
* 738
NO f NO3 2N02 0 f NO f M + N O 2 f M 2N0 f 0 2 2N02
-
Units min-’. Expressed as a bimolecular rate constant In 1 atm of air
Environmental Science & Technology
0.15 20 25.5 9.5 x 1 0 - 2 6.5 x 103 2.0 K 103 4.5 x 103 14 3.2 x 104 2.5 x 103 2.8 x 1 0 - 4
Rate constant, crn3 molecule-’ sec-l 1.37 x 10-14 1.73 x 10-14 6.5 x 10-17 4.4 x 10-12 1.36 X 3.06 X 1 0 - l 2 2.2 x I O - ” 1.7 X 1 0 - l 2 1.9 x 10-19
Ref
This worka (Stuhl and Niki, 1 9 7 1 ) b This work This work Clyneand Cruse (1971) This workb (Zafonte, 1970) ibid. a ibid. /bid.
This w o r k b
the fluorescent lamps commonly used do not have a constant output with time, and thus measurement of kl before each experiment helps to fix this important input parameter. Such measurements are possible since the actual determination takes only 30 sec of irradiation time, and the gases used (air and NO*) are readily available in photochemical smog studies. Our experimental values for the ratio k l / k d are shown in Table 11. In terms of the mechanism leading to Equation 12, k6[M]/k5 = (2 k l / k d - l ) .Our values of k ~ [ M ] / k , are compared with the previous data in Table 11. These results confirm the data of Schuck and Stephens and Troe, and indicate that the results of Ford and Endow may be in error. The best value of k6[M]/k5 a t atmospheric pressure in air is 0.28 f 0.03. Figure 2 shows that the k l determination can measure inhomogeneous distribution of light intensity throughout the reactor. The agreement with the photometric curve is reasonable considering that the photometer does not measure a three-dimensional average. The measurements also show that under photostationary conditions the light intensity gradient appears entirely in the concentration of whichever of NO or O3 is the minor species. This arises because the minor species has the shortest chemical lifetime. For [&] in Figure 2, the lifetime was -8 sec owing to reaction with 0.3 ppm NO, and the mixing processes are not fast enough to compete. This effect of intensity gradient appearing in the minor species, and, incidentally, also in [O], should be considered in formulating kinetic models. Our technique of measuring k l provides a simple method whereby such inhomogeneity may be directly checked. The procedure was described in detail for the externally illuminated vessel. Measurement of kd, which takes a time interval of 5 min, does not show the light intensity gradient comparable to the order of Figure 2. When the data of Figure 2 were averaged graphically, a mass mean k1 of 0.074 gives k d = 0.113 min-l, which is in agreement with the values of 0.110, 0.113, and 0.113 min-I measured across the vessel. The fact that k d does not vary suggests that mixing is sufficiently fast t o remove the effect of the light intensity
gradient over a period ‘of a few minutes. T o check this possibility, a simplified model of 1-cm-radius cylindrical cells in an r - l light intensity gradient, connected by a thermal diffusion constant of 0.2 cm2 sec-l, was integrated numerically. The results were satisfactory, since the computed kd values differed by only 3% across the vessel, and the computed direct k l values from the first 5 sec of illumination were within 5% of the true values. Acknowledgment The authors acknowledge helpful discussions with members of the Fuel Sciences Department, particularly E. E. Daby. Literature Cited
e.,
Altshuller, A. Bufalini, J. J., Enuiron. Sci. Technol., 5 , 39 (1971). Breitenbach, L. P., Shelef, M., J. Air Pollut. Control Ass., 23, 128 (1973). 67, 2869 Clyne, M. A. A., Cruse, H. W., Trans. Faraday SOC., (1971). DeTar, D. F., J . Chem. Educ., 44, 193 (1967). Dimitriades, B., Enuiron. Sci. Technol., 6, 253 (1971). Fontijn, A,, Sabadell, A. J., Ronco, R. J., Anal. Chem., 42, 575 (1970). Ford, H. W., Endow, N., J. Chem. Phys., 27, 1156, 1277 (1957). Leighton, P. A,, “The Photochemistry of Air Pollution,” Academic Press, New York, N.Y., 1961. Ripperton, L. A,, Lillian D., J. Air Pollut. Control Ass., 21, 269 (1971). Sham. T. E.. Dabv. E. E.. Scientific Lab ReDort 71-111. Ford Motor Co., Dearborn, Mich. 1971. Stedman, D. H., Daby, E. E., Stuhl, F., Kiki, H., J Air Pollut. Control Ass., 22, 260(1972). Stephens, E. R., Hanst, P. L., Doerr, R. C., Scott, W. F., Ind. Eng. Chem., 48,1498 (1956). Schuck, E. A,, Stephens, E . R., Aduan. Enuiron. Sei., 1, 73 (1970). Stuhl, F., Niki, H . , J . Chem. Phys., 55, 3943 (1971). Tuesday, C. S., “The atmospheric photooxidation of trans-2-butene and nitric oxide” in “Chemical Reactions in the Lower and Upper Atmosphere,” Interscience, New York, N.Y. (1961). Troe, J. Van, Ber. Bunsenges. Phys. Chem., 73,906 (1969). Zafonte, L., Project Clean Air, 4, Task Force No. 7, Sec. 4, Univ. of California (1970). Received for reuieu, October30, 1972. Accepted May 1, 1973.
Volume 7, Number 8,August 1973
739
