Scavenger Kinetics in the Radiolysis of ... - ACS Publications

SCAVENGER KINETICS IN

THE

RADIOLYSIS OF CYCLOHEXANE SOLUTIONS

2233

Scavenger Kinetics in the Radiolysis of Cyclohexane Solutions. I. Pure Cyclohexane

by Inder Mani and Robert J. Hanrahan Department of Chemistry, University of Florida, Gainesville, Florida

(Received January 11, 1966)

A series of experiments has been done to study competitive reactions of H I and Iz with free radicals in ?-irradiated liquid cyclohexane. The experimental data consist of graphs of iodine concentration us. dose in experiments in which Iz,HI, or both are added to pure degassed cyclohexane before radiolysis. Rate equations, based on previously proposed mechanisms, have been set up and their integration has been done by numerical calculations using the second-order Runge-Kutta method on an IBM 709 computer. The theoretical curves so obtained fit the experimental curves well. A value for the ratio k H I / k I z for competitive scavenging of alkyl radicals by H I and Iz in cyclohexane has been obtained.

Introduction It is inherent in the concept of a free radical yield in radiation chemistry that radical scavengers should react by a process of “indirect action.” That is, radicals produced in the irradiated solvent are presumed to react with the solute, so that the G value for consumption of the scavenger should be independent of scavenger concentration. Iodine is one of the most reliable free radical scavengers used in studying the radiation chemistry of hydrocarbons, but its use is not entirely without complications. Although initial G values for iodine disappearance can be measured rather readily, some ambiguity is introduced by the fact that graphs of iodine concentration us. dose are not merely straight lines, indicative of a constant value for G( - Iz), but rather are always concave upward, indicating an apparent G value for iodine disappearance which decreases as the dose increasese2 A simple interpretation of this phenomenon is that hydrogen atoms, produced from radiolysis of the hydrocarbon solvent, react with iodine to form HI, which then enters into competition with IZfor the radicals present. Some years ago, this interpretation appeared untenable because H I could not be identified as a radiolysis product.’ The presence of HI in irradiated hydrocarboniodine solutions was later established by Meshitsuka and Burtonla but to date no attempt to explain quan-

titatively the curvature of the iodine-dose curves on the basis of H I has been published. A further advantage of an interpretation of H I 4 2 competition kinetics in hydrocarbon radiolysis is that it should be possible to apply such an analysis to systems in which H I rather than IZis added initially as a free radical scavenger. In such solutions, IZis produced during radiolysis, and again the competition between H I and IZoccurs. Another test of such a kinetic scheme is provided by solutions in which both H I and I2are added initially, so that the competition occurs from the beginning. This paper presents the results of a study of HI-12 competition kinetics in irradiated cyclohexane solutions. A somewhat similar kinetic situation was interpreted earlier by Hanrahan and Willard4; analytical integration was made possible by a simplifying assumption concerning the rate constant ratios. During the course of the present investigations, Schuler and Perner6 developed a method of treating several aspects (1) R. W. Fessenden and R. H. Schuler, J . Am. Chem. SOC.,79, 273 (1957). (2) B. M. Hughes and R. J. Hanrahan, J . Phys. Chem., 69, 2707 (1965). (3) G. Meshitsuka and M. Burton, Radiation Res., 10, 499 (1959). (4) R. J. Hanrahan and J. E. Willard, J . Am. Chem. Soc., 79, 2434 (1957). (5) D. Perner and R. H. Schuler, J . Phys. Chem., 70, 2224 (1966).

Volume YO, Number 7 July 1966

INDER MANIAND ROBERT J. HANRAHAN

2234

of the HI-I2 competition kinetics using an indirect analytical integration. In the work described here, numerical integration on an IBM 709 computer was employed. This was done largely to make possible direct extension of the method to the somewhat more complicated situations which occur in the radiolysis of cyclohexane-alkyl iodide solutions. Results on such systems will be described in future publications.

Experimental Section Phillips “pure grade” cyclohexane was passed through silica gel before use. Examination of this material by infrared spectroscopy and flame ionization gas chromatography indicated that it contained about 1% of a mixture of branched-chain saturated hydrocarbons eluting before the parent on a silicone rubber column, but no detectable cyclohexene. Iodine and hydriodic acid were Baker Analyzed reagents. Hydrogen iodide was produced by dehydrating hydriodic acid. The hydriodic acid was frozen to liquid nitrogen temperature in a round-bottom flask and PzOSwas added on top of it. The frozen acid was then attached to the vacuum line and degassed. The hydriodic acid was allowed to melt and interact with P2OSJand the hydrogen iodide released was collected in another portion of the vacuum system. This collected hydrogen iodide was degassed and stored a t liquid nitrogen temperature until used. The amount of hydrogen iodide added to the samples was determined by gas measurements. Individual 4-ml samples were prepared volumetrically, dried with P2OS, degassed, transferred under vacuum to the irradiation vessels, and sealed off. The irradiation vessels were 13 X 100-mm test tubes with attached spectrophotometer cells. Irradiations were performed using a Coco y irradiator which has been described previously.6 The dose rate in the Fricke dosimeter [G(Fe3+) = 15.61 was found to be 0.554 X 1OI8 ev/ml min. For cyclohexane, the value of p(sample)/p(dosimeter) was 0.780 as obtained on the basis of electron density ratios. Iodine was analyzed spectrophotometrically using a Beckman DU spectrophotometer. The position of A,, and the extinction coefficient were used as given by Croft and Hanrahan.? Results Measurements of iodine concentration us. dose were made during the radiolysis of several cyclohexane solutions which initially contained concentrations of iodine varying from 0.3 X to 2.0 X lo-* M . The results of some of these experiments are shown by the circles in Figure 1.8 (The lines are theoretical; see below.) It can be seen that all of the curves are The Journal of Physical Chembtlyl

7 6

5

a*

-

\

1 4

9 i 3

B I

2

1 0

0

20

40

60 80 100 Radiolysia time, min.

120

140

160

Figure 1. Iodine consumption in the radiolysis of pure cyclohexane with added 1 1 as a function of radiation time. Circles are experimental; smooth curves are computed. Initial IZconcentrations, reading left t o right, are 0.31 X 10-3, 0.61 X 10-3, 1.16 X and 1.71 X M.

concave upward, with the solutions having higher initial iodine concentration showing the most curvature. However, the initial rat’e of iodine uptake in such experiments has been reported to be independent of initial iodine concentration over the range 5 X 10“ to 5 X M . g We have confirmed this observation for the range of concentration used in our experiments. We found an average initial rate of iodine uptake of 3.08 molecules/100 ev.’O When H I is added to a hydrocarbon prior to radiolysis, Iz is produced initially rather than consumed. Alkyl radicals abstract H atoms from HI, releasing iodine atoms which later form Iz. The results of several (6) R. J. Hanrahan, Intern. J . A p p l . Radiation Isotopes, 13, 254 (1962). (7) T. S. Croft and R. J. Hanrahan, J . Phys. Chem., 66,2188(1962).

(8) Radiation chemical yields are normally given as G values, defined as the number of molecules of a substance produced or consumed per 100 ev deposited in the system. In the present case, since concentration and time must be used as iteration parameters on a digital computer, it is necessary to use more convenient units. We have chosen to state concentrations as micromoles per P m l sample, and to use time in minutes, which is proportional to radiation dose. (9) R. H. Schuler, J . Phys. Chem., 62,37 (1958). (10) The value obtained for the initial G value of iodine uptake depends somewhat on the procedure used to interpret the concentration-dose graphs, since the graphs are nonlinear. It is especially disadvantageous to use directly the initial concentration-dose increments, since the first few points often show the most scatter. We have found most successful the procedure of calculating the net change of concentration (or optical density) from time zero to each successive radiolysis time t , graphing A(concentration)/t 2)s. t, and extrapolating this graph to zero time, which gives the desired initial rate.

SCAVENGER KIXETICS IN

THE


2235

7

6 a 6 d

;;;

$ 4

s, g-3 E

8 13”2 1

0 0

20

40

60 80 100 120 Radiolysis time, min.

140

160

180

Figure 2. Iodine production in the radiolysis of pure cyclohexane with added H I as a function of radiation time. Circles are experimental; smooth curves are computed. Initial H I concentrations, reading downward, are 8.88 X 10-3, 4.10 X 10-3, 3.18 X 10-8, and 2.11 X M.

experiments of this type are shown in Figure 2. As the radiolysis proceeds, the I 2 produced enters into competition with H I for free radicals so that the net rate of iodine production decreases to zero (at the maximum of the curves) and then becomes negative; if the experiment is continued to a sufficiently high dose, all of the I2 and HI are finally consumed. It can be seen from Figure 2 that the iodine maximum and final “end points” of the experiments increase with initial H I concentration. However, the initial G value of iodine production is independent of initial H I concentration. Experiments with initial H I concentraM gave initial values tions from 2 X lou4t o 9 X of G(I2) ranging from 2.8 to 3.0 with no apparent dependence on initial HI concentration. A value of 2.96, based on several of the most reliable experiments, was used in the calculations described below. If it is true that production of H I is responsible for the curvature of I2 vs. dose plots with added 1 2 , then additives which prevent the back-reaction of H I should tend to linearize the curves. Additives which might be expected to react with HI and prevent its role as a radical scavenger include BaO and water; the latter has been used previously for this purpose by several worker^.^^^^ Results of the radiolysis of cyclohexane-iodine solutions with added BaO and with added H 2 0 are compared with experiments with only iodine added in Figure 3. It can be seen that experiments with BaC) or H 2 0 give iodine disappearance graphs starting with about 1.5 X 10-* M IZ which are much less curved than in the case of a similar experiment with only I2 added. (The experiments shown in

0

20 40 Radiolysis time, min.

60

Figure 3. Effect of added base in the radiolysis of pure cyclohexane with added I2 as a function of radiation time. Initial 1 2 concentrations were about 1.5 X M; 0, with no base; 4 , with added BaO; 0, with added HzO.

Figure 3 were done using about 20 pl of H2O added to 4 ml of cyclohexane-iodine solution,ll or about 1 g of BaO attached to the radiolysis cell through a fritted glass disk.)

Discussion Kinetic Analysis. Although a great variety of conflicting viewpoints have been expressed on the mechanism of cyclohexane radiolysis, essentially all investigators have agreed that cyclohexyl radicals are involved.12-10 The role of hydrogen atoms is far more obscure; at least one research group14prefers to talk of “precursors” which provide hydrogen atoms but which may or may not actually be hydrogen atoms. In an attempt to provide an internally consistent free-radical description which goes as far as possible toward in(11) L. J. Forrestal and W. H. Hamill, J . Am. Chem. Soc., 83, 1535 (1961). (12) Numerous papers have been published dealing with cyclohexane radiolysis. References 13-16 present several representative viewpoints, and give further references t o the literature. (13) R. H. Schuler, J. Phys. Chem., 61, 1472 (1957). (14) P. J. Dyne and W. M. Jenkinson, Can. J . Chem., 39, 2163 (1961); 38, 539 (1960). (15) E’. J. Dyne, J . Phys. Chem., 66, 767 (1962). (16) 9. K.H o and G . R. Freeman, ibid., 68, 2189 (1964).

Volume 70,Number 7 July 1966

2236


terpreting the present experimental results, we have adopted a simplified mechanism which assumes the presence of hydrogen atoms with an e$ective yield dependent on the total concentration of scavengers present. (At lower scavenger concentrations, it is assumed that the hydrogen atoms are replaced by a complementary yield of cyclohexyl radicals; see below.) At sufficiently high concentrations, both H I and I2 may become involved in electron capture or energy transfer p r o c e s s e ~ . ~ However, ~ ~ ~ ~ the highest concentration of scavenger which we have used is about M , and most of our experiments were done at millimolar scavenger concentrations. There is justificationla for assuming that HI and I2 behave predominantly as free radical scavengers at near millimolar concentration levels. Hence, for the present purposes we assume that the net result of primary processes is the production of hydrogen atoms and alkyl radicals, which then take part in competitive reactions under steady-state conditions. Reactions in Spurslg

and

+ ks[HII)

[R. 1 = A/(kr[Izl

(10)

Similarly, we set the thermal H-atom production rate equal to the rate of removal by reactions 6 and 7

D

+

k~[H.l[Iz] h [ H . ] [ H I ]

=

= [H-](ks[Iz] 4- k?[HI])

(11)

and

[Ha I = D/(ks [IzI

+

k7 [HI])

(12)

The rate of iodine production may be expressed as d[LI/dt = -(h/2)([121[R*I)

+

(ks/2) ( [HIJ [R * I> (k6/2N121[H.I) (h/2)([HII[H. 1)

+

(13)

+C-c~Hio-k H2 C-CBHIZ*

(2)

mole The factor of '/2 is introduced because only of iodine is consumed when a mole of radicals reacts with I2 (reactions 4 and 8). After substituting expressions for [ R . ] and [He] and rearranging, this becomes

C-C~H~Z* *c-C6K11 Ha Thermal Radical Reactions Re 1 2 +RI 1.

(3)

d [Iz]/dt = - (A/2) (IC4 [I21 -

C-CgHlz -+ c-CeHlz* (la) C-CeHlz -+ (C-CgHlz' e-) +C-CeHlz* (lb)

+

+ R- + HI+RH H * + Iz+HI Ha + H I + H 2 I. + 1.

---,I2

+ + 1. + 1. + 1-

ks [HIl>/(k4 [I21 (4) (5) (6)

(7) (8)

The above reaction scheme can be treated by conventional kinetics. It is assumed that H atoms and alkyl radicals are produced according to zero-order kinetics by the radiation, and that IZand H I then compete for the radicals and H atoms according to eq 4 to 7. The rate constants for reactions 4 and 6 and for reactions 5 and 7 might be expected to be quite similar. The ratios k6/k4and Ic.r/ks should be even more similar; we have assumed these ratios to be equal, which greatly simplifies our calculations. The steady-state assumption is applied to the alkyl radical and H-atom concentrations. We shall let A be the rate of production of thermal alkyl radicals and D be the rate of production of thermal H atoms which escape from the spurs. Then we set the thermal alkyl production rate equal to the rate of removal by reactions 4 and 5

(D/2) (k6 [L] -

k7

+ ks [HII)

[HI l)/(k6 [Iz1 4-

After putting k6/k4 = h i k e = further, this can be expressed as d[Iz]/dt = (A

k7

[HI I)

(14)

and simplifying

+ 0)/2 -

+ D)[IzI/([LI + [ H I I ~ H I / ~(15) )

(A

Similarly, the rate of H I production can be expressed as d[HI]/dt = -kg[HI][R.]

+

h[Iz][H.] - h [ H I l [ H * l (16) After substitution for [R. 3 and [H. ] and simplification this becomes d[HI]/dt = - ( A (A

+ 0)+

+ 2D)[LI/([LI + [HIlkHI/kI,)

(17)

In order to obtain equations giving the 1 2 concentration as a function of time (and incidentally, also giving HI concentration as a function of time), it is necessary to solve eq 15 and 17, a pair of simultaneous, first(17) J. R. Nash and W. H. Hamill, J . Phye. C h m . , 66, 1097 (1962). (18) Asterisks represent electronically excited species.


THE


order, noclinear differential equations. A similar set of equations has recently been solved by Schuler and P e n ~ e r ,who ~ used an indirect analytical procedure. Their analysis applies to a kinetic scheme which is similar to ours except that no allowance is made for direct participation of hydrogen atoms. (It is assumed by them that hydrogen atoms attack the substrate and are converted to alkyl radicals; the question of the role of hydrogen atoms is discussed below.) Because we wished t.o treat not only the present case but also the similar, soniewhat more complicated kinetic scheme applicable to the radiolysis of hydrocarbon-alkyl iodide solutions, we chose to attack the problem using numerical integration. Slight modification of a published programlg for the second-order Runge-Kutta method of solving simultaneous differential equations proved applicable. Assignment oj Parameters. Before eq 15 and 17 can be solved by the computer, it is necessary to provide values for the quantities A and D (alkyl radical yield and hydrogen atom yield), and for the ratio of rate constants kHI/kI,. Some information is obtained from limiting forms of eq 15. When the concentration of H I greatly exceeds that of 1 2 , the equation reduces to the form

(dT)

=

(A

max

+ D)/2

and when the concentration of Iz greatly exceeds that of HI, one obtains

(“)

min

=

-(A

+ D)/2

(19)

The subscripts max and min are used because the first case refers to the initial, maximum value of the rate of production of II with added HI, whereas the second refers to the initial rate of consumption of IZwith added Iz,which is a minimum in the algebraic sense. From eq 18 and 19 it is clear that the initial rate of iodine production with added H I and the initial rate of iodine consumption with added Iz should be identical. The values which we obtained, 2.96 and 3.08, respectively, can be considered the same within experimental error. An average of the two values was used in establishing a value of the quantity ( A D), the total yield of alkyl radicals and hydrogen atoms. The value of the hydrogen atom yield D cannot be established directly from our experimental results. Some evidence on its value is given by the experiments of Meshitsuka and Burton8 in which the initial value of the yield of H I in cyclohexane with Iz found to be 2.1 molecules/lOO ev. This can be taken

+

20

0

2237


so

100

Figure 4. Role of H-atom yield as an adjustable parameter: IZ consumption in the radiolysis of pure cyclohexane with added IZ (1.16 X 10-8 M ) as a function of radiation time. H-atom production rates, reading left to right, are 0.0, 0.01, 0.02, 0.03, 0.04, and 0.05 pmoles/4 ml min. Corresponding G values are 0.0, 0.35, 0.7, 1.05, 1.4, and 1.74,respectively. Circles are experimental; smooth curves are computed.

as an upper limit ‘for the hydrogen atom yield, applicable in solutions with scavenger concentrations of about 2 X M or greater. At sufficiently low scavenger concentrations (of the order of the scavengable hydrogen atom yield is effectively zero, because the hydrogen atoms react with the hydrocarbon substrate to form Hz and are replaced by a correspondingyield of alkyl radicals H*

+ C-CsHiz

---+

Hz 4- C-CsHn

(20)

At higher concentrations, iodine and other good scavengers can compete with this reaction. Using iodine, the reduction in the corresponding hydrogen yield occurs mainly in the concentration range from to M.13 It has been reported that a concentration of 3 X M iodine decreases the hydrogen by 50% of the ultimately observed red~cti0n.l~Hence, for our purposes, the effective G value of scavengeable hydrogen atoms should vary from zero a t M IZ or HI to a maximum of about 2 a t ca. 2 X M scavenger. Since sufficiently detailed data were not available, the hydrogen atom yields in the present study were obtained by using the D factor in eq 15 and 17 as an adjustable parameter for curve fitting. The alkyl radical yield A was obtained by difference, since the sum ( A D ) is calculable. The calculated effect of varying the hydrogen yield on a typical experiment on the radiation-induced uptake of IZ is shown in Figure 4. It can be seen that increasing G(H.)

+

(19) J. M. McCormick and M. G. Salvadori, “Numerical Methods in Fortran,” Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964, pp 253-255.

Volume 70,Number 7 July 1966

2238


I

2.0

* 2

5 t

1.6

8 1.2

M

a

9 0.8 0 3

0.4 0 0

20

40


100

Figure 5. Role of H-atom yield as an adjustable parameter: IZproduction in the radiolysis of pure cyclohexane with M) as a function of radiation t,ime. added HI (2.11 X H-atom production rates, reading left to right, are 0.0, 0.01, 0.02, 0.03, and 0.04 pmoles/4 ml min. Corresponding G values are 0.0, 0.35, 0.70, 1.05, and 1.4, respectively. Circles are experimental; smooth curvm are computed.

20

0

120


80

Figure 6. Role of kar/krz as an adjustable parameter: It consumption in the radiolysis of pure cyclohexane with M ) as a function of radiation added I2 (1.16 X time. Ratios of k a ~ / k reading ~ ~ , left to right, are 0.0, 0.3, 0.6, 0.9, 1.5, 2.0, and m .

I increases the end point of the experiment, the dose for complete removal of Iz. In Figure 5 it can be seen that increasing G(H.) causes a similar increase in end point for experiments with added HI. (In Figures 4 and 5 the ratio kHCHr/kI, was taken as 0.71, which is the value giving the best fit of experimental data.) Although there is experimental evidence suggesting that kHI/k12in nonpolar solvents is of the order of unity,4 there were insufficient data to assign an accurate value for our experiments. Accordingly, the ratio kH1/kIn was also treated as an adjustable parameter in the calculations. Figure 6 shows that changing this ratio modifies the curvature of a graph of Iz concentration vs. radiolysis time, but does not affect the end point unless the ratio is essentially zero. In that case, the products at the end point would include HI as well as alkyl iodides. As long as kH&, is finite, then all of the iodine in the chemical intermediate HI as well as that present as Iz must ultimately appear as alkyl iodides. It can be seen that the end point of the experiment is the same for all finite values of kHI/kIz, but the curvature increases as kHI/kIadecreases. (This is perhaps opposite to what a casual consideration of the kinetics might lead one to expect.) It will be seen that the initial slope is the same in all cases (except k~I/kI= , ) and approaches that for which kHI/k12 = 0. The computed effect of varying kHI/kI* for an experiment with added H I is shown in Figure ?. Again, variation of kHI/kII does not affect the end point. As kEI/kI, increases, the maximum iodine concentration achieved in the experiment becomes greater, and the radiolysis time corresponding to the maximum The Journal of Physical Chemistry

2.5

d ; -

2.0

8, 1.5 d 2

8

1.0

d 0.5

0 0

20

40


100

120

Figure 7. Role of k ~ r / k as r ~ an adjustable parameter: I2 production in the radiolysis of pure cyclohexane with added HI (2.11 X 10-3 M) as a function of radiation time. Ratios of kHI/kIz, reading downward, are 2.0, 1.5, 0.9, 0.6, and 0.3.

increases. (Again, a superficial examination of the kinetics could easily give the opposite prediction.) Comparison with Experiment. Since varying the Hatom yield affects the end point but the ratio kHI/kI* does not, it is quite easy to adjust both of these quantities to give the best fit of the experimental data. The results of such efforts are shown by the smooth curves in Figures 1 and 2; the circles represent experimental data. Since the radiolysis temperature (25 f 2') was constant for all experiments and the solvent was essentially pure cyclohexane, the ratio kHI/kII should be the same in all cases. In fact, it mas found that kHI/k12 = 0.71 gave a good fit in all cases. (Schuler and Perner find a ratio of 0.83 in n-de~ane.~) Because of the competition between solvent cyclohexane and added scavenger for H atoms, the D factor is expected to be dependent on initial scavenger con-


THE


centration. Since the scavenger concentration during each experiment decreases as the experiment progresses, it is possible to account for scavenging of hydrogen atoms only semiquantitatively. However, the alkyl iodides produced during radiolysis are also good hydrogen atom scavengers” so the change in total scavenger concentration is never more than a factor of 2.20 The effective hydrogen atom yields used in the calculations for Figure 1 for the various values of initial iodine concentration are as follows: 0.31 X 10-3 M , G(H.) = 0.70; 0.61 x 10-3 M , G(H.) = 0.80; 1.16 X M, G(Ha) = 1.40; 1.71 X M, G(H+) = 1.43. For the experiments in Figure 2, the H-atom yields which correspond to various initial hydrogen iodide concentrations are as follows: 2.11 X 10-3 M , G(H.) = 1.40; 3.18 x 10-3 M , G(H.) = 1.46; 4.10 X 10-3 M , G(H-) = 1.57; 8.88 X M, G(H.) = 1.74. It will be noted that a greater concentration of H I than of I2 is required to achieve a given value of G(H.), implying that I 2 is a somewhat better hydrogen atom scavenger than HI. Consideration of Figures 4-7 allows comparison of the present kinetic analysis with that of Perner and S ~ h u l e r . ~Starting with essentially the same mechanism as used by us, they present a simplified kinetic scheme for experiments with added HI. Their equations can be integrated analytically, although indirectly. Their analysis allows variation of the parameter kHI/k12 (actually used in the form of the reciprocal by them) but does not provide for direct allowance for the reaction of H atoms with I2 producing additional HI. However, this effect is clearly evident in their results as shown by deviations in experimental data compared with predictions of their kinetic scheme, and is SO interpreted by them. Their analysis would give a curve identical with that for D = 0 in Figure 5. Since the error in ignoring the H-atom effect is rather large for concentrations as great as 2 X 10-3 M (corresponding to Figure 5 ) , they worked mainly at much lower H I concentrations. For experiments with added 1 2 , the approximation that G(H.) = 0 gives merely a straight line (Figures 4 and 6), so Perner and Schuler did not treat this case. However, they did note the curvature of experimental I2 vs. dose graphs, and interpret this effect as we do. Their analysis of the effect of varying k E I / k r , is qualitatively similar to ours; the resulting graphs differ slightly because of our allowance for the hydrogen atom yield (Figure 7). Two types of scavenging experiments, with 12 or H I added initially, have been discussed above. Another possibility is to conduct experiments in which both H I and 1 2 have been added initially. As a further test of the kinetic scheme, we performed a series of

2239

7 6

a5 $3 a

1 2 1 0

0

40

80

120 160 200 240 Radiolysis time, min.

280

320

Figure 8. Iodine production in the radiolysis of pure cyclohexane, with both HI and Ip added, as a function of radiation time. Circles are experimental; smooth curves are computed using G(H*) = 1.5 and ~ H I / ~=I 0.71. ~ HI concentrations, reading left to right, are 1.08 X lo+, 1.91 X 2.43 X and 3.43 X M. IZ concentration is 1.53 X M in all cases.

experiments all starting with an initial iodine concentration of 1.53 X Af, but using various amounts of added HI. The resulting experimental points and corresponding theoretical curves are shown in Figure 8. As in the previous cases, the value taken for ICHI/k~, was 0.71. On the basis of the work described above, the range of values of G(H.) expected for combined H I and 1 2 concentrations in the experiments shown in Figure 8 was 1.40 to 1.60. For convenience, G(H.) = 1.50 was used for all of the calculations illustrated. (Preparation of a series of solutions with the same initial iodine concentration was facilitated by the use of a vacuum line buret.21 In view of the various assumptions made, the agreement between the predicted curves and experimental points in Figures 1, 2, and 8 seems quite satisfactory. Further, the values of the parameters (rate constant ratio and hydrogen atom yields) which give the best fit of the data appear to be reasonable.22v23For the (20) Perner and Schules have pointed out similarities in over-all stoichiometry which suggest that the “effective H atom yield,” approximation is less drastic than it may appear. (21) R. J. Hanrahan, S. Chem. Educ., 41, 623 (1964). (22) Our rate constant ratios should be fairly accurate because they depend on the maxima rather than the tails of the graphs. It haa recently become possible to compare our hydrogen atom yields with data obtained by Schuler and PernerzS on photolysis of TI in 1zhexane. Using a nominal maximum G value for hydrogen atoms of 2.0 and their rate constant ratio for reaction of T atoms with TI v8. hexane, a graph can be constructed showing a prediction of effective H-atom yield us. scavenger concentration, covering the range of about 10-4 to 10-1 M scavenger. Our effective hydrogen atom

Volume YO, Number 7 July 1966

2240

most part, the deviations which occur are most pronounced toward the end of the experiments. This is just the condition where the ambiguity concerning scavenging of H atoms by alkyl iodides is most significant. An additional source of error likely to become important at large doses is the reaction of H I and IZ with cyclohexene, which is known to be a product of the radiolysis. However, such reactions would remove scavengers from solution and shorten the end point of the experiments; this effect would be opposite to the trend of the data. Reaction of hydrogen atoms with cyclohexene can probably be ignored because HI, 1 2 , and cyclohexyl iodide are all better H-atom scavengers,11,23,24 and at least one of them is always present in greater concentration than cyclohexene. Results of the radiolysis of pure cyclohexane's-16 provide evidence that the reaction of cyclohexyl radicals with cyelohexene is not significant. It might be possible to include in the kinetic analysis quantitative corrections for reactions involving cyclo-

The Journal of Physical Chemistry

INDER MANIAND ROBERTJ. HANRAHAN

hexene and alkyl iodide products. However, the kinetic scheme is already moderately complicated and these further refinements would probably obscure its value as an aid in obtaining an insight into the behavior of a kinetic system of this type. Acknowledgment. This work was supported by Atomic Energy Commission Contract No. AT-(40-1) 3106 and by the University of Florida Nuclear Science Program. Services of the IBM 709 computer were provided by the University of Florida Computing Center. Some of the data presented here were obtained by Mr. William C. Blasky of this laboratory. yields parallel this graph quite systematically, but are about a factor of 2 higher in the low concentration region. (R. H. Schuler, private communication.) There may be some uncertainties involved in comparing the two systems. However, due to the approximations involved in our use of an “effective” hydrogen atom yield, our values would not be expected to be more accurate than about *50%. (23) D. Perner and R. H. Schuler, J . Phys. Chem., 70, 317 (1966). (24) T. J. Hardwick, ibid., 66, 291, 2246 (1962).

Scavenger Kinetics in the Radiolysis of ... - ACS Publications

Recommend Documents