Stuart M. Koop and Paul J. Ogren Central College pella, Iowa 50219
H02 Kinetics in Simple Systems An introductory problem in computer simulation
Our physical chemistry laboratory work in kinetics consists of two experimental prohlems introducing standard approaches followed by one or two problems which illustrate areas of current interest in chemistry. As an example of the latter, we describe here a particular exercise in computer kinetic simulation which has given students important benefits such as: (1)an appreciation for the use of the computer in analyzing the hehavior of complex reaction systems; (2) confidence in program construction; and (3) experience with examples of fast reactions and a common experimental approach to their study which many small laboratories, ours included, cannot provide directly. The problem chosen is a fairly simple yet realistic one from the recent literature dealing with the perhydroxyl radical, Hop,' an important intermediate in flame chemistry and in atmospheric photochemi~try.~J Although the complexity of the reaction system is sufficient to convince students that simulation is necessary, the relative simplicity permits one to readily understand the effects of changing a given rate constant, and avoids the tedium of including Blmost endless terms in each rate equation. When the exercise is completed, students have great satisfaction in comparing their results with those in the literature. The Reaction System
The system we chose to simulate involved the flash photolysis of H z 0 vapor in the presence of a small amount of 0 2 and an atmosphere of Hz or Ar at 25'C.I Typical conditions were 3% H20,2% 02, and 1 atm total pressure. Reactions following the flash led to formation and decay of HO2, the perhydroxyl radical. The original objectives of the literature work were to determine r,. for the HOn radical and the rates of H02 reaction. Leaving the latter objectives aside for the moment, we note that the flash produced -1 /AMeach of H and OH radicals in the literature study. These radicals then participate in the following reaction scheme4
MICROSECONOS b
H O ~ H + O H (productiongoverned by flash time profile) OH
-
+ H,
H,O HOr
+ O2 + H,H + 0, + ArH
+ O? + H,O-
H
HO, OH
-
+HO~
+ HO,
HOP + Ar HO, H20
+
k = 4.0 X lo6 M-'s-' k, = L7 X 10" M-'s-'
ks = 5.9 x 109 M-'s-' k, =L4 X 10"K2s-'
+
~ $ 0 O, ~ ks = 5.7 x 10'
+ OH -H,O OH + OH + Ar-H,Oi
+ H,O-H,02
(1) (2)
(3)
(4)
S-'
(5)
S-'
(6)
+0
k, = 1.6 X log K' s-'
(7)
+ Ar
k, = 5.4 X 10' M-'s-'
(8)
+ H20
kg =LO X 10"M-2 s-'
(9)
+
H ~ O O,
OH
OH +OH
+H
+ H,
h, = 12. x 10" M'
In He, OH is rapidly converted to H by eqn. (1). H then quickly forms HOz by eqns. (2)-(4) and the long term kinetics are dominated by the simple second-order decay of HO2 by eqn. (5). In Ar, OH is not converted to H, and HO2 is then removed by the rapid reaction (6). Choice of different hulk gases thus leads t o completely different kinetic behavior, as shown in the figure. 128 /
Journal of Chemical Educatbn
Computer simulation of HO? kinetics. (a) He + 3 % HzO + 2 % 0 2 . Total pressure 1 atm, 0.96 pM H and O H produced by flash.(b) Ar + 3% H.0 + 2 % 0 2 . Total pressure 1 atm. 0.96 gM H and O H produced by flash. In the original study of a Hp system, maximum HOz ahsorption was observed near 205 nm. Optical densities of the HOz band a t the peak of the flash were determined by extrapolation of simple second-order plots of the absorption hand disappearance. This information was used with measurements of Hz02 final product yields and the assumption that HOz reacted only by eqn. (5) t o determine both ks and em,. for H02. Simulation was required in the study to see if these evaluation procedures would give valid results, particularly since significant reaction occurs on the same time scale as the flash.' Although we do not ask students to apply their simulations in this way, it is clear to them that this is one of several possible applications of their efforts. The Simulation In our course, students are asked to determine H, OH, and H0z concentrations as a function of time during the first 25 /ASof reaction (after this time only one or two reaction species remain in significant concentrations, and the kinetics are simpler). Initially they are to assume that the
flash produces a total of 0.96 each of H and OH. T h e problem requires several simple programming considerations 1) It is convenient, although not necessary, to obtain results in micromolar and microsecond units. It is thus useful to convert the rate constant values to these units. These units are used throughout the remaining discussion of this paper. 2) 1" a given time interval DT, species may be formed by the flash and formed or removed by chemical reaction. A normalized flash term, FLASH = .1444*T*VEXP(-.16*T**2), was used to closely describe the experimental time profile of the flash. .... . .-.~. -
3) A simple expression for a change in a reactant such as H may nbw be written, e.g. DH = DT*(UMSFLASH Kl*OH*H2 K2A*H*02*H2 - K2BaH*02*AR - K2C*H*02*H20) where Hz, Ar, 02, and H20 are the fixed initial coneentrations of these gases in the system, UM is the total aM eoncentration of H and OH produced by the flash (e.g. 0.96 aM), and H, OH, end FLASH are determined by the time T of the simulation. Such an expression, although representing a rather unsophisticated numerical approach: is an obvious rearrangement of the expression for dHldt including eqns. (1)-(4), and a production term due to the flssh. Having seen this, students can then readily proceed with the other necessary equations. 4) Using the above illustration, one can start at time zero with H = 0, calculate DH, and thus form H = H DH at the end of time T DT far successive iterations. One serious pitfall in the above procedure is that H may become negative in the numerical calculations, with interesting results in later iterations. This may he prevented by a cheek which resets negativeconcentration values tozero prior to the next iteration.
+
-
+
+
DT mieht loeicallv - . be chosen to he 0.01 to 0.1 us: . . comparison o? these extremes is often of interest. Values of the desired variables are then listed a t convenient times for hand plotting, or stored for a computer plot. Results of such plots are illustrated in the figure. Given the above guidelines, students with a minimal exposure to programming can proceed t o satisfactory results, and even thosewith no background have been able to proceed with a small amount of additional help. Although this problem has been programmed in other languages, our typical student programs in Fortran IV require a deck of
around 30 cards, with an execution time on our IBM 1130 (8K) system of ahout 2 min. Students interested in further work may choose to examine the effects of additional reactions (see footnote 1, for example), different amounts of H and OH produced by the flash, or changes in some of the rate constants. There is a wide variation in the literature values of rate constants for many of these reactions, and the latter exercise can be particularly informative in the case of eqns. (5) or (6) in demonstrating how choice of one extreme or another can drastically affect system kinetics."' Such a demonstration shows why there is continued interest in obtaining good rate information on many important fast reactions by a variety of experimental techniques. Concluding Remarks Three programs have been developed for use in this simulation. Written in Fortran IV for our IBM 1130 with a CALCOMP 560R olotter. thev can he easilv modified to adapt to other machine configurations. The first program is a subroutine which sets un and labels the axes and lots the concentration data for each species. The second program is a mainline program similar to a student-prepared program. The third program is a more sophisticated mainline program allowing easy student alteration of reaction conditions and rate constants. Program source listings and decks are available upon request.
.
-
'Hoehsnadel, C. J., Ghormley, J. A,, and Ogren, P. J., J. Ckem.
.-..
Phvs.. SR. 442fi. 1972. ~,~ -
'L1oyd.A. C..Int. J. Chem Kiner.. 6,169(1974). 'Chesirk, J. I'.,.]. CHEM. Kl)IIC., 49,722 11972,. 4Soureesof rate constants are given in Ref. ( I ) . 5De Tar, D. F., J. CHEM. EDUC., 44.191 (1967). 1.8 X lo9. and 2.2 X 109M-'sCL for ks and 6Valuesof 6.5 X an estimated value of 6 X 109M-'s-' for ke are listed in the recent survey of Ref. (2). 7An additional interesting modification is suggested by recent work reporting a significant dependence of ks on Hz0 concentration. (Hamilton, E. J., J Ckern.Phyhys., 63,3682 (1975).
Volume 53. Number 2,February 1976 / 129
