PULSE RADIOLYSIS OF AQUEOUS TETRANITROMETHANE
53
The Pulse Radiolysis of Aqueous Tetranitromethane.’ Rate Constants and the Extinction Coefficient of eaq-.
I.
11.
Oxygenated Solutions
by Joseph Rabani? William A. Mulac, and Max S. Matheson Department of Chemistry, Argonne National Laboratory, Argonne, Illinois
-
(Received April SO,1964)
~~
Aqueous solutions of tetranitromethane (TNM), both deaerated and oxygenated, have been investigated by the technique of pulsed radiolysis. This system enabled the direct determination of ee5780, the extinction coefficient of the hydrated electron) at 5780 8. as 10,600 ( flo$.’&) M-I cm.-’. e,5780 is essential for evaluating rate constants previously determined as Ic/e,57so. Also from e,5780 we calculate G, = 2.6 from values of G, X in the literature. A number of rate constants were determined, including k(e,,TNLI) = 4.6 X 1010M-l see.-’, k(H T N X ) = 5.5 X lo8 M-’ sec.-l, and Ic(e,,NF-) = 3.0 X 1O’O M-’ sec.-l, where WF- is the nitroform ion. Rate constants have also been measured for reaction of several organic radicals with TNM. In the presence of 02,k ( 0 2 TYJI) was measured as 1.9 X lo9 M-’ see.-’. Ic(H02 TNM) is less than as large. Measurement of the effective k as a function of pH gave pK = 4.45 f 0.25 for the 02-. dissociation, HOz H+
+
+
+
+
+
+
Introduction A direct determination of the extinction coefficient, eek, of the hydrated electron is important for two rea-
sons: (1)the rate constants, k,,of eaq- in reactions with other transients in pulse radiolysis are determined as k , / e e X ,so that e t X must be known before absolute rate constants can be calculated; (2) the product G, X eeX has been deterniined3s4and previously E,’ has been estimated from this product assuming G, from steady radiolysis scavenger work. On the other hand, G, can also be estimated from this product if e,’ is directly determined in pulse radiolysis experiments. Previous investigations of the steady radiolysis of tetranitromethane (TKBI) by Henglein and Jaspert6 and by Bielski and Allen6 suggested that this system could be used to determine E,’, Their work showed that the reducing species in ?-irradiated water will convert tetranitroniethane to nitroform. Kitroform is a moderately strong acid and ionizes in water to give C ( S 0 2 ) 3 -(hereafter referred to as NF-), yhich has a broad strong absorption peak at 3500 A. The extinction coefficient at the peak has been measuredS6b6
From these facts it appeared probable that, if the hydrated electron reacted rapidly and completely with tetranitromethane to give nitroform, the extinction coefficient of the hydrated electron could be rather directly determined by pulse irradiating aqueous T X M and then comparing the initial absorption of ea4- at 5780 A. with the final absorption of KF- a t 3660 8. In this paper the measureinent of eeb7So by the abovementioned method is described. The reactivity of ea,- and other species with T K l I has also been measured, both because the rate constants are of interest in themselves and because they are necessary to the (1) Based on work performed under t h e auspices of the U. S.Atomic Energy Commission. (2) Postdoctoral Fellow from the Hebrew University, Jerusalem, Israel. (3) (a) S. Gordon, E. J. H a r t , M .S.Matheson, J. Rahani. and J. K. Thomas, J . Am. Chem. SOC.,8 5 , 1375 (1963); (h) L. 11. Dorfman and I. A. T a u b , ibid., 8 5 , 2370 (1963). (4) J. P. Keene, Discussions Faraday Soc., 36, 304 (1963). (5) A. Henglein and J. Jaspert, Z . physik. Chem. (Frankfurt), 12, 324 (1957). (6) B. H. J. Bielski and A. 0. Allen, unpublished work.
Volume 69,Number 1
January 1966
J. RABANI,W. A. MULAC, AND M. S.MATHESON
54
-
determination of eeS7*, the experimental situation not being as siniple as implied above. Work in oxygenated solutions of aqueous T N M is also described. The radical-ion 02-reacts much more rapidly with TXnI than does HOz, so the pH dependence of reactivity yields the dissociation constant for HO2 G H + 0 2 - .
+
Experimental The pulse radiolysis apparatus developed by Matheson and Dorfman' has been described elsewhere.* I n thLs work we used a modified apparatus and procedure9 further modified by incorporating a multiple reflection cell based on the principle described by White.l0 This cell enabled the use of long optical paths of up to 80 cnl. with an actual cell length of only 4 cm. I n the present work this was important since low concentrations of transients could be used, thus minimizing the fraction of esq- which reacted with itself and with other transients rather than with TNAI. This minimizing of second-order reactions increased the precision of deterniination of both e1.5780 and of the pseudo-first-order rat e constants measured. 'The multiple reflection arrangement is shown in Fig. 1. The reaction cell C, which has a 2-cm. internal diameter and a 4-ciii. internal length, sits in thin V supports of Lucite in a Lucite box as indicated. The cell is fitted with two capillary 5/20 ground jointsfor use in the usual syringe technique of filling and draining. Xot shown is a vertical rod and support for the syringe. The spherical mirrors l\I1,AI,, and 1 1 2 ' of the multiple reflection system are made of high purity silica (to minimize radiation discoloration and luminescence) 2 mm. thick, with both front and rear surfaces ground to the same center of curvature. The mirrors (silver is best for wave lengths longer than 4000 8. and aluminum for general use) are deposited on the back surfaces and can be renewed as necessary. The analyzing light beam enters the unsilvered upper left-hand corner of the front mirror 111arid exits through the unsilvered upper righthand corner. 112 and hlz', the halves of a single spherical mirror, pivot about pins P (only one shown) to vary the number of light traversals of the cell in the manner described by White.lo A separate screw assembly S (only one shown) for each half controls the rotation of M 2 and Mz'. To miniinize the reflection losses a t the windows of the cell C , the Lucite box was filled with distilled wa,Ler. The cell C essentially touches the front (silica) surfaces of the niirrors so as to reduce the amount of irradiated water in the light path exterior to the cell. This water is aerated so that the strong eaq- absorption in the visible region is converted to weak 0 2 - absorption The J o u r n a l of Physical Chemistry
Figure 1. Multiple reflection cell assembly.
in the ultraviolet region. Pulse radiolysis experiments with deaerated 0.0001 M sulfuric acid in C showed that no absorption exterior to the cell was produced in our experiments. In this design AI1 must be drawn back in an O-ring sealed sleeve in order to insert the cell with a twisting motion. To seal the cell at the split mirror end, a plastic film (Saran wrap) was passed over O-ring O2 and under O-ring O1. The Saran wrap is close to (0.5 mm.) but does not touch the mirror, since silver in particular adheres poorly to silica. ;\Iz and 112'were protected froni the water by a thin spray coat of clear acrylic paint (Krylon). Although not exposed to water, the front mirror >I1 was also sprayed with Krylon except in the unsilvered corners. It was the susceptibility of the mirrors to corrosion that necessitated that the mirrors be deposited on the rear silica surfaces. The electron beam entered axially into the cell C as Bhown and was uniform across the entering face of the cell as checked by the discoloration produced in niicroscope slides. Tetranitromethane (a toxic and explosive compound)ll froni K and K Laboratories, Janiaica, K.Y., was shaken 10 or 11 times with fresh volumes of distilled water, using a water to T S l I volunie ratio of (7) M. S. Matheson and L. M . Dorfman. J . Chem. Phys., 32, 1870 (1960). (8) L. M .Dorfman, I. A. T a u b , and R. E. Buhler, i b i d . . 36, 3051 (1962).
(9) S. Gordon, E. J. Hart, M. S. Matheson, J. Rabani, and J. K. Thomas, Discussions Faraday Soc., 36, 193 (1963). (10) J. U. White, J . O p t . SOC.Am., 32, 285 (1942). (11) N . I. Sax, "Dangerous Properties of Industrial Materials," 2nd Ed., Reinhold Publishing Corp., New York, N.Y . . 1963, p . 1236.
PULSE
RADIOLYSIS OF A4QUEOUS TETRANITROMETHANE
about 50 each time. Then the T K M was added to a dilute aqueous bicarbonate solution (volume ratio about 1: 20). In a closed Pyrex system the TNRI was fractionally distilled by bubbling a stream of nitrogen through the mixture, the gas stream then passing through a drying tube containing calcium chloride and finally through a trap surrounded by liquid nitrogen where the TSSI was condensed. A stock solution was prepared, usually a t a concentration of about 0.2 nil. of T X l I in 1 1. of water. Triply distilled water was used to prepare all solutions. Generally, freshly distilled T S l I was used for each day’s experiments, except in a few cases where the distilled TSSI was stored for up to 2 weeks in the dark at -20’. Stock solutions were prepared only a few hours before use (maximum 7 hr.) and were niaintained at ice temperature. Suitable volunies of stock solution were diluted with room temperature water less than 1 hr. before the resulting dilute solution was irradiated. In experiments where relatively high concentrations of TXAl were used, the amounts of cold stock solution used gave diluted solutions significantly below room (or irradiation) teinperature (23’ unless otherwise stated). For these experiments the stock solution was stored at room teniperature before use. Solutions could be kept at 0’ for periods up to 1 week with little decomposition, as indicated by the following data. Optical density changes measured with a Becknian DU spectrophotoineter showed that in a 2.8 X 10-5 M T S l I solution, 2.5 x M KF- was found after 36 hr. room temperature storage, and in a 1.6 X lop3M TXRI solution, 4 x lo-’ M XF- was found after 19 hr. For experiments on the reaction of eaq- with T K M and on the determination of ceX, care was taken that the initial coriceritrations of SF- and SO3- were so low that these species did not react appreciably with eaq- in the presence of TSAI. Since the reaction of eaq- with TSAI is very fast, this experimental requirement was easily met. However, when radicals less reactive toward TSAI were studied, such as the HOz02-combination in equilibrium in acid solution, it was not obvious a pricri that the T K N hydrolysis products, KF- and SOa-, would not compete with the TXSI for the radicals, even though [TYMM] >> [SF-] [ S O 3 - ] . However, our results, as will be seen later, indicate that such a competition could be of only minor Importance. In early experiments using the optical arrangement previously d e ~ c r i b e dthe , ~ diluted T S N solutions were deaerated by shaking with argon gas in a syringe (see Fig. 1 of ref. 9 for the type of syringe) and then expelling the gas. This procedure was repeated four times for air-free solutions. For oxygenated solutions,
+
55
a similar procedure of shaking with oxygen was repeated twice. Unfortunately, T N M is volatile and subsequent analysis showed that -6Yo of the TXM was lost with each shaking for M TKSI and somewhat snialler percentages were lost for iiiore dilute solutions. Controlled procedures were adopted and 6 to 4%, depending on TKM concentration, was subtracted for each shaking with gas, either oxygen or argon. Analysis indicated f5y0 error in TSM concentration was introduced by this procedure and correction. In later experiments using the niultiple reflection cell in which was determined and the rate constants for T N M and H TSRl were measured, this eascorrection was avoided. I n this latter case the stock solution was deaerated in a syringe and a portion of the contents subsequently analyzed. Dilutions were made with deaerated water or dilute acid by direct transfer from syringe to syringe, using microsyringes where necessary for accuracy.l2 Analyses for T S l I were made by using hydrazine sulfate to reduce it to nitroform, the nitroforni being estimated spectrophotometrically, Exposure of the solutions to air was minimized as much as possible before and during the reduction to avoid lomes by evaporation. The potassium salt of nitroforni, BC(S02)3 (also exp l ~ s i v e ) ,was ’ ~ prepared by mixing about 3 nil. of T S l I with 70 nil. of concentrated cold KOH and then shaking the mixture until the TXRI had reacted (-30 niin.). Yellow crystals of KC(N02), precipitated during the reaction and were separated froin the solution by decantation. The crystals were washed twice with cold distilled water and then washed with absolute ethyl alcohol and finally with diethyl ether. A sample of the crystals was weighed to make a solution of known concentration. From this solution the E N F - ~ ~ O O was measured as 14,600 1 V - I ciii.-l (log (loI ) = ECZ) a t 25O, using either a Beckman DU or Cary Model 14 spectrophotometer. This agrees satisfactorily with the value obtained by Allen arid Bielsk? of 14,800. Because a mercury arc was used in our experiments, it was desirable to follow KF- concentrations by the absorption a t 3660 -1. Further, since a high-pressure mercury arc with broadened emission lines was used, since the aperture in front of the monitoring photomultiplier in the spectrograph passed a 44-a. band, and since the extinction coefficient of S F - decreases -197, from - ~ determined ~ ~ ~ 3638 to 3682 8.,the effective E ~ F was
+
+
(12) E. J. Hart, S. Gordon, and J. K. Thomas, J . Phus. Chem.. 68, 1271 (1964). (13) I. Heilbron and H. M.Bunbury, Ed., “Dictionary of Organic Compounds.” Val. 111, Oxford University Press, New York, N. Y . , 1946, p. 878.
Volume 69, Number 1
January 1966
J. RABANI,W. A. MULAC,.4ND M. 8. A~ATHESON
56
directly with the experimental setup used in the pulse for [e,,-] in eq. 2 , one can then integrate eq. 2 and by radiolysis experiments, that is the same lamp, optical substituting appropriate optical densities and extinctrain, and spectrograph. This was done by preparing tion coefficients in the integrated equations obtain six known concentrations (1.4 to 12 p M ) of NF- (from eq. 4 and 5 . the potassium salt) and coniparing the optical densities of a reaction cell containing these solutions with the optical density of the same reaction cell containing pure water. The optical densities were obtained by photographing photoiiiultiplier signals on the oscilloscope with and without the reaction cell in the light beam path. The optical density was linear with conwhere the D’s are optical densities with superscripts for centration and the results yielded an effective e s ~ - wave ~ ~ length ~ ~ and subscripts for tinie. of’ 10,200 f 250 a t 24’. Equations 4 and 5’show that the optical densities a t To make sure that the photomultipliers were always ‘both 5780 and 3660 8. suitably plotted as a function set on the same wave lengths before each experiment the of tinie should yield straight lines with the same slope apertures in front of the photomultipliers were realthough ea,- also has a small absorption a t 3660 8. duced to pass a band of 15 A . , a medium-pressure merand although S F - is formed only by reaction 1 whereas cury lanip (Hanovia AH-4) was set in front of the specea,- disappears to a small extent by additional pseudotrograph, and the photoiiiultiplier signals were maxfirst-order reactions also. Our experimental results (halfway between the maxima imized a t 3660 arid 5780 i. have been plotted according to eq. 4 arid 5 in Fig. 2 . A Corning 0-52 filter giving 55% at, 5770 and 5790 i.). The rate constants kl, obtained from the slopes of trarismission a t 3600 i. was placed between the lanip these plots, are given in Table I , and have been corand the reaction cell in all experiments to protect TSAI and SF- solutions from photolysis by the analyzing light beam. Table I : The Rate Constant for the Reaction of eaq- with TNMaMeasured a t 5780 and 3660 Results and Discussion I. Rate Constants and Extinction Coefficient of eaqTh-M -kb--, Light
a.
The Reactivity of eaq- with T N M . When T N J I alone is present in water, one can follow simultaneously both the decay of eeq- a t 5780 8. and the formation of SFat 3660 A. The S F - formation results from reaction 1.
It was observed that the absorption a t 3660 8. reaches a iiiaximuni and then decays to a somewhat lower (11 * 4% lower) plateau. A similar decay occurs with crease due to reaction 1 , SO that we used the maximum or)tical densitv at 3660 8. as D,- for rate constant talc;~atioIls at tiis wave length. F~~solutions colltaining ortly water and TN,M, eq. 2 and 3 niay be written for our conditions d___ (SF-) - 7cl[TX,II][e,,-] dt
-1
_-_d (eaq ~ _ ~
dt
=
kl[TK31][e,,-]
+ k[e,,-]
(2) (3)
where k is the total rate constant for the additional pseudo-Arsf-order reactions consuming eaQ-. If one integrates eq. 3 and then uses the result to substitute The Journal of Physical Chemietry
M
x
105
at
D,
0 145 0 260 0 300 0 380 0 360 0 150 0 330 Average with appropriate weighting
1 30 1 48 1 59 1 96 2 28 2 8 2 8
5780
4 3 4 4 4 4 4 4
A
4 9
7” 9c 9c
2 1 6
at 3660
4 4 4 4 4 3 4 4
A
6 2 9 9 9 7 8 7
path, cm
48 32 32 48 48 48 48
or more experiments. c These are the most recent a n d reliable since: (1) there was no volatility loss of T N M during solution preparation, and ( 2 ) the correction for reactions in pure water was measured instead of calculated.
rected for the reactions of the hydrated electron with other species in water (line A in Fig. 2 ) . Corrections were also made for reactions of ea,- with the SF-, H + , and SO3- initially present and for TSM depletion (up to 6y0 T N l I reacted) during the reaction. All [TSA\I] given in the tables and text are initial concentrations, while avemge [TSAI ] were always used to calculate all rate constants in this paper. It is true that li is not
PULSE RADIOLYSIS
0.7
OF
57
AQUEOUS TETRANITROMETHANE
,
I
I
Table 11: Rate Constant for the Reaction of eaQwith TNM in Aqueous Organic Solutions” [TNM], M X 106
Solute
0.0107 M sucrose 0.1 M sucrose 0.2 M ethanol 0.1 MCH3COONa 0.0002 M CHaCOOH 0.25 M glucose 0,0012 il4 phenol Weighted average
+
Final Dat 3660
A.
----kb---at 5780
A.
2.02 3.0 2.4 3.0
0.930 0.280 0.250 0 210
4.6c 4.4
3.0 4.0
0.500 0.230
at 3660
A.
4.6c 3.7
4.8
...
4.9
4,1
4.5 5.0 4.6
4.8 . . .
4.4
Light path was 16 cm. except for experiment of footnote c. units of 10’0 M-1 see.-’. Light path was 48 cm. Most reliable experiments for reasons listed under Table I. a
* In
\
p scc
Figure 2. Pseudo-first-order disappearance of eaq- and simultaneous formation of S F - using a 48-cm. light path: A, water alone, 5780 B, 1.96 X 10-5 M T S M , 5780 -1.;C, J.96 X 10-5 M T S M , 3660 A. The points at 5780 A. usually showed less scatter about a straight line than those at 3660 time zero at middle of pulse.
w.;
w.;
accurately first order, but the deviation from first order is small (Fig. 2 ) and the correction due to k is 8 to 18%. The reaction of eaq- with SF- will affect the kinetics at 3660 8. more than a t 5780 8.,but this is only a ininor effect. This difference was neglected here, but corrected for in the calculation of the extinction coefficient. The corrections are discussed in more detail in the sections on ee5780. Experiments were also carried out measuring kl in solutions containing organic solutes as well as T S Y . Again, nieasurenients were made ato5780 and 3660 A. and eq. 4 and 5 applied. At 3660 A , , D, was chosen as the optical density measured a t 3660 A. just at the time when all eaq--had disappeared, this time being determined by examination of the decay curve a t 5780 8. In the experiments with sucrose, corrections were also made for the reaction of sucrose radicals with T N M which occurred before the complete decay of the eaqabsorption (cor. < 15yo). Corrections were made as before for other reactions of enq-. The data are tabulated in Table I1 where the value of kl is in good
agreement with the results in Table I. Since the organic radicals in ethanol or phenol solutions react with TSAI about one-tenth as fast as eaq- does, no k was calculated a t 3660 A. because of this interference. For the other systems also, k , is measured nore accurately a t 5780 A. than a t 3660 8. The organic solutes eliminated OH radicals and acetate suppressed H + as well. I n acetate solutions a weakly absorbing transient was found a t 3660 A. with a half-life under our conditions of about 200 psec. The “final D” in the table is a measure of the pulse intensity and includes the NF- from the organic radical reaction (except for acetate where the radical did not react with TNM). The Reactivity of H Atoms with T N M . Since H atoms also react with T X M to produce NF-, it was essential to measure the rate constant for this reaction before proceeding to an evaluation of e e A . H atoms 1 HClO,, the were produced by pulse irradiating 0.01 A acid converting all eaq- to H. The subsequent reaction of H with TNM, eq. 6, was followed by observing
H
+ C(?JOJ,
+H +
+ C(N0z)S- + S O ,
(6)
the change in optical density a t 3660 A. The rate constant, ks, was calculated as before using eq. 5 for the psudo-first-order reaction plot. Two concentrations of TAX were employed. For 6.1 X M TSM in 0.013 M HC104, k6 was evaluated from the plot as !I1 T N M in 6.1 X lo8 M - l set.-', while 1.36 X 0.01 HC10, gave 5.6 X lo8 M-’ set.-'. -4t 3660 A., the increase in optical density, presunied due to NIT- formation, was followed by a slight decrease to a plateau just as was found for solutions without acid. In one exaniple, D increased to 0.310 in 1 to 2 psec., then decreased to 0.275 after 100 Fsec., arid finally remained constant to 200 fisec. or inore. For our calcuVolume 69, S n m b e r 1
J a n u a r y 1965
58
J. RABAKI,W. A. ~ I U L AAND C , SI. S. MATHESOX
lations of kg we used the maximum optical density as
D,. The possible significance of the optical density decay is discussed later. The reactions H H and H OH occur in parallel with reaction 6. Under our conditions these two reactions contribute about 17% to the initial rate of H atom disappearance in 6.1 X M TKlI and about 8% in 1.36 >( 31 TSAI. This contribution decreases by about a factor of three, as the H atoms are used up since H H depends upon [HI2while for H OH the [OH] can be regarded as nearly constant, and since k,+H 'v k H + O H 1 4 and [HI, 'v [OH],. Correcting for the average contribution of these reactions, we get k.6 = 5.6 X lo8 set.-' and 5.4 X lo8 h1-l sec.-l for the low and high TSSI concentrations, respectively. \Ye see that kl 'v looks and therefore, although H atonis form about 20% of the reducing species15 in neutral solution, reaction 6 did not affect the measurernent of k1.15c T h e Reactivity of eaq- with NF-. It was also necessary in this work to investigate a possible reaction of eaq- with the product SF-. To do this, a 4.0 X .V solution was prepared froin a saniple of I95yopurity) gave, respectively, i c y values of 3.3 x 10'0 and 3.1 x lolo, uncorrected, and2.8 X 10'0 and 2.93 X loLoLU-l see.-', corrected. The Decay of Absorption at 3660 A. If TNRI is irradiated either in neutral water or in 0.01 perchloric acid, the increase in absorption a t 3660 A. due to nitroform formation is followed by a small decay of
+
The Journal of Physical Chemistry
this absorption. Because of the small changes in optical density, plots of log D or 1/D us. time did not show whether the decay was first or second order. I n four experiments (similar to the first experiment in Table 111) the average decrease froin the maxiinum D to the plateau was 11 f 2yGstandard deviation (decreases ranging from 7 to 13%). Addition of 0.01 M HClO, did not nieasurably change the results. ,it neutral pH (no buffer) diluting T S l I 100-fold from 2.3 x lop3M changed the half-life only to -30 psec., with a measured decay in D of 7YG. Increases in electron pulse intensity shortened the half-life in 2.3 x low3M T S M . See Table 111. Because the changes Table 111: Half-Life of D e c a y at 3660 A. a s a Function of Pulse I n t e n s i t y : 2.3 X 10-3 ,M T N N (No Acid)
(&"I
0 0 0 0 a
)"
380/32
=
430/16 302/4
=
840/4
=
=
0 0 0 0
Pulse intensity
012 027 076 210
Half-life,
Decay,
psec
75
18 16 8 4
12 12 14
10 5
(Dmax/l.)
in.half-life are small, the results are not conclusive, but seem to be intermediate betweeri those expected for a first-order reaction or for a second-order reaction of the B, where [AIo = [BIa. type A The first possibility considered was that SO2 absorbs a t 3660 8. and disappears by the reaction KO2 SO2 or S O 2 OH. This explanation of the decay would require that EX^^^^^^ 'v O . ~ E X F - 'v ~ ~ ~1000. " However, the gas phase extinction coefficient is much lower than this. l 6 Further, we pulse-irradiated 2 X lop4M S a S O z in deaerated water saturated with S20 (to convert eaq- to OH) in order to produce the SO2 transient in water through the reaction of OH NOz-. A pulse intensity about fourfold greater than that
+
+
+
+
(14) (a) J. K. Thomas, J . Phys. Chem., 67,2593 (1963); ( b j see also M. S.Matheson, Radiation Res. Suppl.. 4 , 1 (1964j, for rate constants used t o estimate corrections; (e) H. A. Schwara, J . Phys. Chem., 67, 2827 (1963) (2kH+H is t h e rate constant for H atom disappearance). (15) (a) J. T . Allan and G. Scholes, Sat7are. 187, 218 (1960). (bj J. Rabani and G. Stein, J . Chem. Phys., 37, 1865 (1962). (c) NOTE ADDEDI N PROOF. After this paper was submitted, we received a preprint of a paper by K . D. Bsmus, .4. Henglein, A l . Ebert. and J. P. Keene. Ber. Bunsenges. physik. Chem.. in press, on the pulse radiolysis of T N M . Their value for Ic(H f T K M ) determined for the H atoms formed in radiolyzed neutral solution is (2.6 f 0.3) X lo9 .W-'set.-'. whereas our value determined for the larger yield of H atoms in acid solution is 5.5 X 108 J - l set.-'. Two new experiments a t pH -2 yielded k(H f T N M ) = 5.0 X 108 .If-' see.-'. in reasonable agreement with our earlier value. (16) T. C. Hall and F. E. Blacet, J . Chem. Phye.. 2 0 , 1745 (1952).
PULSE
RADIOLYSIS OF
!lQUEOCS
TETRANITROMETHANE
which yielded D, = 0.350 with TXRI gave D o = 0.025 in the N2O-iYOz- system. The EN^^^^^^ of -100 in water estimated from this result agrees with the gas phase value. l6 The half-life of this decay, probably due to the NOz reaction alone, was about 100 psec. From this result the decay of KOz absorption cannot account for the decay at 3660 8. Another possible explanation of the decay is that eaq- reacts with TYAI to give an intermediate with about 10% greater absorption than NF- at 3660 8.
+ C(NOz), +C(NOz)4c(N02)4c(xOz)3- + NOz eaq-
(8)
+
+
--r~--$
Hz, HzOz, H, OH, ea,-, H3Oaq+, OHw-
(10)
sufficiently reactive toward ethanol and sucrose. H can M TNJI its half-life be eliminated since in 2.3 X is less than 1 psec. and therefore it cannot account for a decay of 10 to 20 psec. The transients ea,-, H30aq+, and OHaq- can also be eliminated by other arguments: eaq- also has a half-life less than 1 psec. in 2.3 X l o p 3M TNM, added H30a,+does not affect the decay, and NFis relatively stable in high concentrations of OHa,-. Thus the possibility that OH reacts with NF- to form nonabsorbing products must be examined more closely. OH
+ C(N0z)3-+nonabsorbing products
crudely measured value. Before proceeding with the estimate, it may be noted that most or all of the species designated as OH radicals really may be accepted as being such.17 In the steady radiolysis of T K J I in water, G(NF-) N 3 was fo~nd.58~Since the reducing species are presumed to account for the S F - formation, and since the yield of G, G H N 3 , it appears that OH does not react appreciably with KF- in the relatively low-intensity steady radiolysis. The NF- may be protected from OH attack by NOz- or KO2. If NOz hydrolyzes rapidly then NOz- would be the protective
+
NO2
(9)
However, we would expect reaction 9 to be first order with a half-life independent of intensity. Further, to check this possibility, 2.3 X lop3 M TSAI 0.2 M ethanol or 0.104 M sucrose was pulse-irradiated (D, = 0.31, 1 = 32 cm.). No decay was observed at least up to 500 psec. These two experiments suggest that NF- may react with other products formed by the radiation but is protected by ethanol or sucrose. These other products should be among those listed on the right-hand side of eq. 10 and should be reactive toward ethanol and sucrose. Only H and OH qualify as Hz0
59
(11)
An attempt was made to measure kll. An NFsolution (1.8 X M ) was saturated with NzO and irradiated with a pulse such that the absorption decreased about 25Oja with a half-life of -20 psec. (2 = 16 cni.). (-4pulse of the same intensity gave D,,, = 0.400 in 2.3 X M T N J I in water also using a light path of 16 cin.) From this experiment, assuming [ N F - ] essentially constant and [OH] governed by the recombination reaction, we calculate crudely kll 3 X lo9 M - I sea.-'. It is possible to make another estimate of kll using certain assumptions, which would disagree with the
-
+ NO2 H10_ 2H+ + NOz- +
r\To3-
(12)
agent. From Schwarz18and Schwarz and Allen,Ig we can calculate IC13 = (55 f 20) X ICl4 = 55 X 4.5 X lo7
+ NOS- +OH- + KO2 OH + HzOz + HzO + HOz
OH
(13) (14)
= 2.5 X lo9M-l set.-'. From eq. 12 each NOz gives l/zNOz-so that G(NO2-) = 1/2 (G, G H ) 'v 1.5, while from eq. 13 one OH consumes l/zSOz- or N 1.2 so that the steady-state excess nitrite yield is -0.3 or [r\TO2-] N 0.1 [NF-1. Assuming that 20% of the NF- formed is destroyed by OH (an unreasonably high fraction in view of the measured G(SF-)), then k13[i\roz-] = 4kll[NF-] and k13 = 40kll. Thus kll 5 6 X lo7 M-' set.-', and since in the pulsed radiolysis experiments [NF-1, = 1 to 2 X loW6M e [OH]oand2kls= 1 X 1O1O M-l set.-', then about 40/,or less of the OH would
+
OH
+ OH + HzOz
(15)
react with NF-. Whether or not NO2- reacts with OH to protect N F in low-intensity steady-state radiolysis, it is probable that the hydrolysis of NOz is too slow to form KOz- as a protective agent in these pulsed radiolysis experiments. In any case, we prefer the higher experimental value of k l l . ,4possible alternative protective mechanisin for SOzin steady radiolysis, and one which could reconcile the experimental facts known to us, is the following. Reaction 11 is rewritten OH
+ C(NOz)3- -+-OH- + C(S02)o
(lla)
and is followed by c(NOz)3 f NOz- + c(Noz)3-
+ NO2
(16)
Reaction 16 should proceed to the right, since the reac(17) A. Hummel and A. 0. Allen, Radiation Res., 17, 302 (1962). (18) H. A. Schwara, J . Phys. Chem., 66, 255 (1962). (19) H. A. Schwarz and A. 0. Allen, J . Am. Chem. Soc., 77, 1324 (1955).
Volume 69, .Vumber 1
January 1966
J. RABANI,W. A. MULAC,AND 11.S. ~\IATHESOK
60
+
tion of ea,T N M gives as products the entities on the right-hand side of reaction 16 and not those on the left. The higher value of kll (>lo9)could then be consistent with the steady radiolysis results. However, S O z - probably does not form rapidly enough in the pulsed radiolysis experiments to play a protective role. In this case ( l l a ) could well be followed by reaction 17 arid/or 18, so that some nitroform is destroyed in the pulse radiolysis experiments if an OH scavenger is not c(NOz)3 2c(r\'02)3
+ N0z
-+
+C(sOz)4
nonabsorbing products
(18)
-
+
+
+ RHz +HzO + R H H + RHz Hz + R H
OH
-+
RH
+ C(K0z)r
(19)
(20)
-+
c(r\'o2)3-
+ KO2 + H f + R
(21)
(a) The decay of light absorptions a t 5780 and 3660 A. were followed simultaneously, the absorption a t 5780 8. being due solely to eaq- while that a t 3660 8. is mainly due t o S F - with a smaller contribution froin the hydrated electron. For the organic The Journal of Physical Chemistry
e,,-
+ H202-+OH,,- + OH kzz =
ea,-
(17)
present. Other species such as HzO+, 0- (unlikely in acid solution), or 0 atomsz0could be invoked to explain the absorption decay a t 3660 8.)but such speculations are not warranted with our present knowledge of this system. Our present conclusion is that reaction 11, OH S F - , with a value of kll lo9 may explain the observed decay. I n any case, regardless of the detailed explanation, the measured rate of decay or the experiment on OH SF- (NzO NF-) above both indicate that the decay can be corrected for in the estiniations of eeX. This is particularly true if the optical density changes during a Dshort time interval are compared a t 3660 and 5780 A., since the correction for the decay may then be less than 2% of e,'. The Reactivity of Several Organic Radicals with T N M . A suitable organic solute may be added to an aqueous T S J I solution in sufficient concentration to react with all H and OH radicals with the resultant formation of an equivalent number of organic radicals (reactions 19 and 20). The organic compounds used in this work are not reactive toward eaq-,12s21 so that eaq- still disappears by reaction I. When a TSlI-organic scavenger solution is pulseirradiated, both the ea,- and organic radicals formed react with TYJI to form NF- and thereby increase the optical density a t 3660 8. Reactions 1 and 21 can be separated by three different experimental procedures.
+
radicals examined kl 2 10kZ1,and, therefore, ICzl could be determined a t 3660 8. after all eaq- had disappeared, while kl was deduced froni the decay a t 5780 A. (b) By the use of an appropriate concentration of HzOz or XZO all e,,- were converted according to eq. 22 or 23. In the case of HzOz,the ratio of RHz to
+ NzO
1.2 X 1OO '
Nz+ OH,,-
sec.-l
(22)
+ OH
(23)
HzOzwas made sufficiently high so that all OH radicals were converted to RH. The OH radicals probably do not react rapidly with NZO. In this system about 90% of the R H radicals result from reaction 19 and about 10% from reaction 20. With this ratio, even if the products of the two reactions differ, the complication should be minor. Of course, reaction 19 itself might involve parallel reactions, giving different f o r m of the R H radical. However, in the case of ethanol the a-ethanol radical seems to be the only important radical formedJZ2 and, in any case in the systems studied, no complications were observed which could be attributed to the simultaneous production of two forms of RH. Thus, it appears that reaction 19 in these systems gives essentially only one radical or that the different radicals formed have similar reactivities toward T S l l . The rate constants for ea,HzO2, eq. 22, and OH H,Oz, eq. 14, are and that for reaction 1 has been determined in this work as 4.6 X 1O1O M-' set.-', so that the adjustment of the HzOz concentration to ensure that eaq- reacts only with HzOz and not with TNAI is rather easy. Of the compounds used to form R H , only for ethanol was it known in advance that k19 was sufficiently high.23 (c) An acid solution can be used for pulsed radiolysis, so that all e&,- are converted to H atoms by eq. 24, and then (19) and (20) will occur to approximately the
+
ea,-
+ H3Oa,+
+H
+
+ HzO
2.3 X 10'O M-' set.-' (ref. 3)
(24)
same extent to produce RH. In procedure (b), H atoms were of minor significance, but here they somewhat exceed the OH radicals in number. Further, the concentration of RHz required here is less than in (b), since H reacts but slowly with the electron scavenger H+,24and H T K l I we have found to be about
+
(20) A. 0. Allen, Radiation Res. S u p p l . , 4 , 54 (1964). (21) E. J. H a r t , J. K. Thomas, and S. Gordon, ibid.,4 , 74 (1964). (22) I. A. T a u b and L. hl. Dorfman, J . Am. Chem. Soc., 84, 4053 (1962). (23) J. Rabani and G . Stein, Trans. Faraday SOC.,5 8 , 2160 (1962).
61
PULSE RADIOLYSIS OF AQUEOUS TETRANITROMETHANE
+
100-fold slower than eaqTNM. However, procedure (c) cannot be used when RH2 reacts with H + as is the case for sucrose. Ethanol has been used as a source of RH using all three procedures. The concordance of results for k21 among the three methods supports the discussion and mechanism above (Table IV). The rate constant
I .o
0.9 0.8 0.7 0.6
0.5
0.4 0.3
-
0
I
e
0.2
Table IV : Rate Constant for Reaction of Ethanol Radicals with TNM
Concn. of ethanol, M
0.1
0.1 0.2 0.5 0.5 0.1 0.1 0.1 0.45
0.I
TNM concn.
Other additive , . . I . .
...
0.1 N HzSOa 0.03N H&Oc 0.02M Hz0z 0.02M HzOz 0.02M HzOz 0,09M Hz0z
x
106,
D,"
M
12 3 31 24 29 29 17 31 4 4 12 3
0 0 0 0 0 0 0 0 0
47 38 25 54 54 37 36 45 46
kb
6 6 5 5 5 5 4 6 5
3 3 0 4 8 4 5 0 1
In units of 109 M-1 sec.-1 Each Light path was 16 cm. value is an average of 2-5 experiments. 0
is also independent of T N M or ethanol concentration. The formation of NF- in a solution of 0.2 M ethanol M T N M (procedure (a)) was plotted and 2.4 X as a first-order reaction according to eq. 25, with quantities similarly defined as for eq. 5 . The oscilloscope In [(Dm3660 - Dt3660)/Dm3660] = -kzl[TNM]t
(25)
trace a t 5780 8. showed that the electron disappeared in 4 psec. Equation 25 is then valid for times greater than 4 psec. In experiments similar to those for ethanol discussed above (procedure (a)), rate constants were measured for the reaction with T N M of radicals derived from sucrose, glucose, and phenol (Table V). For these solutes the reaction of RH TNXl was more easily separated froin the reaction of eaqTNnl than was the case for ethanol and no additives such as H30+ or H202were used. In the case of sucrose, experiiiients were also done with added N20. The final optical density is not changed by the presence of NzO. In Fig. 3, the absorption changes in pulse-irradiated TNAI-sucrose solutions with and without added NZO are plotted according to eq. 25. In the presence of K20 the extrapolated D, (D, - D, at zero time) agrees with the measured value, but in the absence of NzO (line b) the extrapolated D, is less than the meas-
+
+
0.06
0.05 ..
0
I50
IO0
50 t
( p sec)
Figure 3. Pseudo-first-order formation of NF- in solutions of 2.02 X 10-6 M TNM in 0.0107M sucrose: 0 , argon saturated; 0, NzO saturated; time zero is middle of pulse.
ured one. This difference is due to the rapid reaction of eaq- with TNRl which is practically instantaneous on the time scale of Fig. 3.
Table V : Rate Constants for Reaction of Organic Radicals with TNM TNM concn.
Time" t o D,,
Source of radical
Concn., M
x lo6,
Sucrose Sucrose Sucrose Sucrose Glucose Phenol Phenol
0.1 0.1 0.0107 0.0107 0.25 0.0012 0.0012
3.0 12 2.02 2.02 3.0 3.0. 9.0
usec.
kb
250-500 60-100 250-1000 250-1000 120-200 120-200 50-100
0.83 0.71 0.90 LOe 2.6 1 2 1.2
Dm
M
0.27OC 0.300' 0.920d 0.930d 0.490c 0.225~ 0.260c
0 Change in D less than 37, in indicated time interval. * Each number is average of 2-5 experiments, in units of logM-l set.-'. Light path was 48 cm. Most reliable Light path was 16 cm. because there was no T N M volatility loss. e Saturated N 2 0 .
If the reactions in the presence of organic solute are as proposed in this section, then the ratio of the final optical density to the optical density at the end of the eaqTSRl reaction should be (GoH G, GH)/G, * 2.1. This expected result was confirmed in two ways. (1) In Fig. 3 both lines are experiments of equal pulse intensity, and the ratio of the extrapolated D, in
+
(24)
+ +
M .S.Matheson, Ann. Reo. Phya. Chem., 13, 7 7 (1962).
Volume 69,,\'umber
1
January 1.985
J. RABANI,W. A. MULAC,AND 21. S.MATHESON
62
the presence of S 2 0 to the difference in the extrapolated values in the presence and absence of NzO should be equal to the ratio of G values cited above. The observed D, ratio of 2.4 is slightly greater, perhaps because a few per cent of eaq- reacted otherwise than with T N I I . (2) The final optical density a t 3660 8. in the ethanol experiments divided by the optical density at 3660 A. found at the time of eaq- disappearanceoh sucrose experiments (this time determined a t 5780 A,) should again be ~ ~ 2 .since 1 , the eaq- T N M and R H 4-T K M reactions are nearly separate in sucrose solutions. Comparison of several experiments done with equal electron pulse intensities showed that the optical density due to the total reaction of CHaCHOH and elrq- was about twice that due to the reaction of eaqalone, in agreement with ( G H G, GoH)/Ge ‘v 2.1. This shows that the a-ethanol radicals reacted essentially only with TNRI. In support of this, comparison of the rate constant for recombination of a-ethanol radicalszzwith the rate constant for a-ethanol radical T X M shows that under our conditions radical reconibination was negligible. The value of k l is so high that almost all eaq- must be scavenged by TXM. The Evaluation of in Aqueous T N M . In this evaluation it is assumed that NF- is the immediate product of reaction 1. Then, if all eaq- react in ( l ) , and if the absorption at 3660 8. is due only to NFand eaq- and that at 5780 only to eaq-, eq. 26 is valid, where exx is the extinction coefficient of the species
+
+ +
+
ce5780
___
E:FF- 3660
-
AD5780
AD5780= AD3660X e1/(U - crA) where The Journal of Physical Chemistry
(27)
D
5780
- D 6780
AD3660= (D23660 - D13660)(cor., see below) er =
ce6780/cNF-3660
+ k7[KF-] + k~[H30,,+10+ kzs[NOa-lo + k n s [ ~ o 2 ]+ kw) eaq- + KO3K03-2 (28) eaq- + NO2 * NOS(29)
U = kl[TNR/I]/(kl[TNRI]
-
[H30aq+Jo and [NO3-Io are the concentrations just before the pulse while [NF-] is the average concentration during the time interval used and includes the initial concentration, [NF-I,, as well as the radiolytic SF-. The NO2 is wholly radiolytic. I; is that fraction of all electrons which disappear by reaction 1 to form NF-. The calculation of U is discussed later. The data to be used in eq. 27 to evaluate cr were taken from Tektronix 555 oscilloscope traces similar in appearance to those in Fig. 4. All such photographs
-,.I
p sec
100%
z
0 v)
22
0%
Ji 100%
(D16780 - Dz5780) (D23660 - D13660) + A(D15780 - D25780) (26)
x a t wave length A, where A is defined as ~ e ~ and where D,’ is the optical density a t wave length X at time t , after the pulse. The decay of D5’8O and the increase of D3660were observed siniultaneously after an electron pulse, so that the possibility of variations in pulse intensity from one pulse to another cannot affect the result. However, it appears to be impossible with the present equipment to use a concentration of T N N high enough to ensure that all the e,lq- react with T X l I and yet have a reaction slow enough that it can be followed accurately as a function of time. (It niay be noted that the situation would be appreciably worse without the multiple reflection cell.) Therefore, it is necessary to correct the calculation of ets5780for electrons disappearing in reactions other than (I). Equation 26 corrected for the various side reactions to be discussed below becomes eq. 27.
=
z a
II:
t~
~
~
/
~ 1
0Oo/
e I
~ I
~ I
L
~
~
I
I
I
I
I
1
-
\ I psec TIME Figure 4. Simultaneous rate curves of NF- (upper, 3660 A.)
and eag- (lower, 5780 A.); argon-saturated solution of 2.02 X 10-6 M T N M in 0.0107 M sucrose; 48-cm. light path. The “noise” (light emission) caused by the electron pulse begins a t 2 psec. and terminates a t 3 psec. in this figure.
were enlarged to a graticule size of 10 X 18 cni. for easier reading. The two independent beanis of this scope were used to record the changes in D, and since in eq. 27 the AD’S at 3660 and 5780 8. are for identical time intervals, it was necessary to locate a point on each trace corresponding to the same instant. This was done by recording the same signal on both traces @iultaneously. Such a signal was recorded for 3660 A. with a shutter closed between the lanip and the re-
PULSE RADIOLYSIS OF AQUEOUS TETRANITROMETHANE
action cell. This signal showed effectively an increase in light transmission and is believed to represent Cerenkov radiation plus the decay of a small amount of fused silica luminescence. Total duration of this light emission signal a t 3660 A. was 1.1 psec. for a 0.4-psec. electron pulse. At 5780 .&., the signal is smaller and narrower and is probably due only to Cerenkov radiation during the pulse. Such traces with a closed shutter between lamp and cell also showed the point in time a t which this "noise1' ended. Therefore, only those parts of the oscilloscope traces later in time than this point were used for rate constant or er evaluation. In evaluating Lr, the corrections for reactions occurring in pure water are first considered. Figure 2 showed the decay a t 5780 and 3660 A. in the presence of 1.96 X M TNAI for an experiment similar to those used in the er evaluations. Line A shows that for pure water irradiated with a similar electron pulse, the 5780-A. decay is very close to first order, a t least during the time required for complete ea,- decay in the 1.96 X M TNAI. We shall define k , as the apparent pseudo-first-order rate constant for ea,- disappearance, which is derived from the slope of the pure water plot and which is valid for the specific conditions of our experiments. The value of k , obtained is 1.3 X 105 set.-', and it includes contributions of reactions 22, 24, 30, 31, 32, and 33, ie., of e H202, e H+,
+
+
+ OH +OH,,(30) ea,- + H 2 H2 + OH,,(31) ea,- + ea,H2 + 20H,,(32) e,,+ H 2 0 +H + OH,(33) e + OH, e + H, e + e, and e + H2O. k , should deea,-
=
pend on the time and pulse intensity since of these reactants only [HzO] is constant. However, in all experinients using eq. 26 (or its corrected form eq. 27) for determining -36e0, the same pulse intensity was used, and further, since the correction introduced by k , in the value of eF is not large, small variations in k , change ee only by a quite small amount. In the presence of T N M the electrons may have other side reactions in addition to those grouped in k,. Corrections for these must also be applied. NOz and NF- are products of reaction 1. I n reaction 7, whose rate constant k7 was measured as 3.0 X 1Olo M-l set.-', not only is an electron used in a side reaction iiot forming SF-, but the effect of an electron which had previously reacted in (1) is cancelled. Half of the correction for reaction 7 appears in U ; the other half is applied as discussed below. For reaction 29 we have no nieasurenient, but 3 X 1O1O M - l sec.-l might be a
63
reasonable value for k29. Correction for (7) and (29) also requires a knowledge of the effective concentrations of KF- and SO2 in the time interval used. Froin experiments described elsewhere (or even from an estimate with a bimolecular decay constant of 5 X 1Olo M-' set.-'), the decay of SO2 is much slower than the formation of NF- in these experiments, so that [SO21 will closely parallel the [NF-] resulting from reaction 1. A small amount of thermal hydrolysis of TS&Min the solution before the experiment produces KF-, H +, and NO3-. For these three products the concentrations produced by hydrolysis should be [H+]o = 2 [XF-lo = 2 [NOs-Io and they were determined from the absorption of NF- a t 3500 8. using a 5-cm. cell in a Beckman spectrophotometer. The rate constants are known for (28) and (24) to be 1.1 X 1Olo and 2.3 X 101O M-1 set.-', r e s p e ~ t i v e l y . ~The ~ ~ rate constant for reaction of H with NF- is unknown, but, even if it were as high as 3 X 1Olo M-I set.-', the correction would be only 1 to 2%, so, in the absence of definite data, this correction was neglected. The value of A in eq. 27 was obtained by measuring simultaneously, in pure water which w y pulse-irradiated, the absorption a t 3660 and 5780 A. A was determined as 0.145 with a standard deviation of 0.001, using ten different pictures. In eq. 27, AD5780was used as experimentally measured ; however, the experimental A D e e 0 was corrected for: (1) the loss of SF- via reaction 7 ; (2) the formation of small amount! of NF- via reaction 6 ; and (3) the decay a t 3660 A. which has previously been discussed. For correction (l), an average concentration of NF- was used in combination with k7 = 3.0 X 1O'O M-' see.-' to calculate the decrease in N F due to the reaction of ea,NF- during the appropriate time interval. Since this correction of er is small (0.5-2%), the error introduced by use of a constant [YF-] is negligible. Actually, [SF-] changed during any time interval used by a factor of two or less. To make correction (2), it was assumed that GH/G, N 0.2 and that G, E GoH. Rate constants for reactions involving H atom disappearance were talren14 as ks4 = 1.0 X 1Olo and kaj = 1.2 X 101oM-lsec.-l, T S M (reacOur value for the rate constant of H
+
+
H+H+Hz H
+ OH +HzO
(34) (35)
tion 6) is 5.5 X lo8 M-I set.-'. It can be shown that initially under our conditions the rate of formation of H atonis by ea,H30aq+,reaction 24, and eaqH20, reaction 33, is slightly greater than the rate of H atom disappearance. On the other hand, only about
+
+
Volume 69, S i i m b e r 1 January 1965
J. RABANI,W. A. MULAC,AND 31, S.MATHESON
64
5% of the eaq- will eventually form H atoms since most eaq- will decay by reaction with T N l I and other species not forming H atoms. Considering these facts, it is a sufficiently good approximation to assume [HI constant during the short time intervals used in evaluating er or kl. With these data and assumptions, T N M was calthe XF- formed by the reaction H culated and the appropriate amount subtracted from AD3660in each of the time intervals used in eq. 27. Correction (3) is for the decay at 3660 ‘1.and was estiM mated from plots of the decay measured in 2 X T N l I with a pulse intensity equal to that used in the er experiments. This correction of AD3660 varied from 0 to +3.5% and opposed the effect of correction (2). Values of AD5780as measured are plotted in Fig. 5 against the corresponding corrected values of AD3660. These points were compiled from four different experiments. The AD values plotted in Fig. 5 were obtained by the following procedure : the oscilloscope traces from an experiment, such as shown in Fig. 4, were divided into approximately equal time intervals in the region of changing D by selecting the same six points in were measured a t time on each trace. DS750 and D3660 erich point. Then each pair D15780 - D 1 57g0 , D3 3660 D,3660 (cor.) were plotted in Fig. 5 where i = 1, 2, 3, 4, and j = 2, 3, 4, 5, 6 and all pairs of i and j (i < 1) were taken for which AD3660was greater than 0.03. All experiments corresponded to the conditions of Fig. 2 (1.96 X 10-j M T S N 48-cm. light path) for which b’ was calculated to be 0.85. The conditions determining C were: = [SO,-]O = 1.85 X lop7 M ,[Hf],, = 3.0 X lo-’ -11 (corrected for dissociation of water), [SF-],, including [SF-]o = 7.8 X lop7 .If, [NO2] = [KF-I,, - [NF-lo, and k’s as previously quoted. The slope in Fig. 5 should correspond to cr/ (I; - er=l) from which er = 0.975 was determined. Adding together the errors (for the slope of Fig. 5, 2%; for L-, .5c7,; and all others, 2 7 3 , and correcting er for the fact that k , includes a sinal1 contribution of eaq- which is second order and considerably ebqdiminished in the presence of TNJI, one obtains er = 0.98 i 0.09. Thus ee5” = 10,000. TWO earlier experiments plotted as in Fig. 5 gave = 11,200 and 12.000, respectively. The average is 11,100. The diff erences between experiments are unexpectedly large. Evaluation of ee5780 in TNM-Sucrose Solution. Since the reactions of the H and OH radicals complicate the determination of eeS780 in water-TNN solutions, sucrose was added to react with and eliminate these radicals. Thus the measured P 6 0 values no longer are corrected for the H T K M correction, or for the decay a t 3660
0.300
1
+
+
+
The Journal of Physical Chemistry
Figure 5 . Evaluation of in aqueous TSM. Points were obtained from four separate experiments.
x., which was shown not to occur in sucrose solutions. (In an S z O saturated solution 0.0104 111 in sucrose and 3.87 X lop5 JI in NF-, no decay at 3660 8. (16-cm. optical path length) was observed after irM sucrose radiation by a pulse which gave 5 X S F - (> The desired conditions were in fact closely approached, although complications due to reactions 43, 44, and 41 do introduce a small error. If H202is added to an oxygenated T N M solution so that [HzOz] >> [TNM], then eaq- will react with it forming OH. Reaction 22 will be followed by reaction 14 to form HOz. The H atoms will eventually yield HOz radicals whether they react with O2 or HzOZ. Above its pK the HOz will dissociate to H f and 0 2 - . In this system the reactions of HOz OH (43) and 02- OH (44) are eliminated. If [TYAI] is chosen low enough so that k45[T1;M] is much smaller than
+
+
+
+
(25) A. 0.Allen and H. .4.Schwxrz, Proc. 2nd Intern. Conf. Peaceful Usee At. Energy, 29, 30 (1958). (26) A. 0.Allen, "The Radiation Chemistry of Water and Aqueous Solutions," D. Van Nostrand, Inc., New York, N . Y., 1961,p. 40. (27) G. Czapski and L. M. Dorfman, J . Phys. Chem., 6 8 , 1169 (1964). (28) J. H.Baxendale, Radiation Res., 17, 312 (1962). (29) B. H.J. Bielski and E. Saito, J. Phys. Chem., 66, 2266 (1962). (30) G.Czapski and B. H. J. Bielski, ibid., 67, 2180 (1963). (31) K.Schmidt, Z..Vaturforsch., lbb, 206 (1961).
PULSERADIOLYSIS OF AQUEOUS TETRANITROMETHANE
both k14[H202]and k41, then the rate of formation of XF- can be used to measure Sincels k14 = 4.5 X lo7 M-' set.-', the half-life for the reaction of OH H202is1*about 1 psec., using 0.02 M H202. We estimate the half-life for H 0 2 -F H + 02-to be of the same order. Defining K = k41/k42, the limits of K are 1.6 X (pK = 4.8) and (pK = 4.0). By analogy with similar neutralization reactions, it seemed reasonable to assume k 4 2 = (2 to 10) X 10'O M-1 sec. -l, and therefore the limits of k41 may be 3 X lo5 to lo7 set.-', and the corresponding half-life limits 0.06 to 2 psec. These considerations suggest that the results in Table VI represent kd5 with only minor
+
+
Table VI : The Reactivity of 02- with TNM5 [TNMI, M X
icr
101
1 2 3 7 17 18 30 35 58 69
5c 9 7c 5c 2 5 8 8 6 0
kra, M - 1
Final
[HzOz1
0 0 0 0
02 02 02 01
I
optical density
0 0 0 0 0 0 0 0 0 0
18 65 18 19 64 40 62 71 71 68
seo. -1 pHb
x
6.2 6.2 6.1 6.1 6.0 6.0 5.7 5.8 5.8 5.6
2.65 2.0 1.9 1.5 1.9 2.0 2.3 1.6 1.45 1.65
10-B
a Solutions 0 2 saturated except where otherwise stated ; 16-cm. light path used. * Measured before pulse. Air saturated.
errors introduced by other reactions. The agreement found in the presence of H202 with only HOz formed initially, and in the absence of H202 with mostly 02formed initially, supports the idea that the measured reaction is not limited by the dissociation of HO2. Further, the fact that the same rate constant is obtained over a 50-fold variation of [TNM] also indicates that complications due to competing reactions were n:t significant. H202 absorbs enough light at 3660 A. to make it difficult to work with more than 0.02 M H20z with a light path of 16 cm. Therefore, in the experiments with H202, in order to avoid photolysis, a filter eliminating light below 3400 A. was used and the solutions were not exposed to the analyzing light beam for more than 1 min. while making the necessary oscilloscope adjustments. Indeed, these precautions were followed also where no H2Oz was present. Each value for in Table VI is the average of two to four experiments. For each experiment, the variation of optical density, D, with time, t, was plotted ac-
cording to eq. 47, and
67
k45
was calculated from the slope
In [(DmassO - D13860)/Dma660] = -k45[TNM]llt (47) of the resulting line. In experiments without added H202there was a fast initial rise in D, due to the direct reaction of cap- with T N N , and this was followed by a slower rise due to the reaction of Oz- with T N X The ratio of the optical density a t the end of the rapid rise to the increase in optical density during the slower reaction agreed with the ratio deduced from the known rate constants for eaqT N M and eaq02.38*4,9 However, in oxygenated solutions some loss of oxygen occurred during transfer of solution to the cell (usually 10-2073 (see ref. 9 for transfer technique) as this transfer was not carried out under an oxygen atmosphere. Further, there was not a sharp limit ("noise" immediately following the pulse tended to obscure this limit) between the first rapid rise and the subsequent slow increase in D. Therefore, our directly measured kl is considered to be more accurate than the value deduced from the competition with 0 2 , as determined from the ratio of optical density changes discussed above. From this ratio of optical density changes kJk37 = 2.3 f 0.7 was obtained assuming [02]= 8 X loW4 M in the oxygenated solutions. The pH values in Table VI were measured with evacuated solutions subsequently exposed to air during the pH measurement so that C02 absorption probably occurred. Therefore, as the solutions were evacuated before oxygenation, these pH values are lower limits since no buffer was added. If the actual acidities of the evacuated solutions before irradiation were due to hydrolysis of TNAI, then the measured absorptions due to XF- definitely would indicate higher pH values than those in Table VI. On the other hand, hydrogen ions are formed by the pulse of electrons in coiicentrations M (see optical densities, Table VI), of -1 to 4 X so that in some experiments the effective pH was only about 1 pH unit above the pK of HOz. However, this would still mean 90% Oz- to 10% HOz at equilibrium, while G values indicate'5b that with only O2 present the originally formed yields would be --85Q/, 0 2 - and -15% HOz. Our conclusion is that kdj in Table VI is not lowered by more than 10% by the presence of some of the radical in the H 0 2 form. The effect in low intensity experiments would be much less than 10%. KO correction has been made for this effect. Each value of in Table VI, being the average of a number of experiments, n, was given a weight n, and the over-ail least-squares average was calculated as (1.9 f 0.4) X l o 9M - sec.-'. The Effect sf p H in Oxygenated Solutions. For the pseudo-first-order reaction of 02- with T S l I where
+
Volume 69,Number 1
+
January 1.966
J. RABANI, W. A. MULAC,AND M.S. MATHESON
68
the absorbing species NF- is formed, eq. 47 was used to calculate k46 under conditions such that little if any HOz was present. If both 0 2 - and HOz react with TNM, then the rate of formation of NF- is given by
+
d[NF-l -- k46[TNM][02-] k4e[TNM][HO2] (48) dt
If reactions 45 and 46 are slow compared to reactions 41 and 42 so that 0,- and HOr are always in equilibrium, then one can substitute [02-][H+]/K for HOz in eq. 48. d~[NF-] dt
{ k46
+
k46
[H+]/K ] [TNM I [?,-I
(49)
One can manipulate the equilibrium equation for 0 2 and HOz to obtain (50), where the subscript, 0 3 , refers [Oz-]
+ [02-1>/(1 + [H+l/K) = ([NF-1, - [NF-])/(1 + [H+]/K) =
([HOz]
(50) to final concentration and the other concentrations are at time t. Substitution of (50) into (49) yields d_-[NF-] dt
IC' + k46[HfJ/K[TNM]([NF-1, - [NF-I) 1 [H+I/K
+
(51)
which integrates, if [TNM], the pH, and the ionic strength are constant, to
Table VI1 : The Reactivity of the 02--HOz Equilibrium Mixture with TNM [TNMI, M x 10'
34.3b 34,5b 37.2b 34.5b 35.7b 1.46c 3.61" 3.610 7.3~ 7.4* 15.00 4.ld 11.2 37.2 50.5 43.4 14.5 15.2 58.0 43.4 14.4 43.4
DmO
Acid added
0.70 0.61 0.65 0.57 0.67 0.26 0.41 0.10 0.11 0.15 0.36 0.15 0.25 0.24 '0.33 0.31 0.16 0.18 0.21 0.26 0.14 0.17
HzSO4 His04 HzSOr HzSOc
PH
5.0 4.9 4.57 4.51 4.22 2 X 10-4A~HzSOa 3.70 2.75 1 . 9 X 10-3N 1 . 8 X 10-zNHzSOc 1 . 8 5 1 . 9 X 10-2N HzS04 1.83 2 . 0 X 10-2NHzS04 1.81 2 . 0 X 10-2N 1.81 2 . 0 X 10-2NHC104 1 . 7 0 0.1N 1.17 0.1NHzSOa 1.17 0.08 N HClO4 1.10 0.2NHClO4 0.70 0.8 N 0.32 0.8NHz804 0.32 0.8NH2S04 0.32 0 . 5 N HClO4 0.30 1 . O N HC104 0.00 1 . O N HClO4 0.00
Q,M-' 8ec. - 1
1.1 X lo8 1 . 2 x 109 6 . 9 X lo8 1 . 0 x 109 4 . 5 X.108 2 . 8 X 10' 4 . 4 X lo' 7 . 3 X 10' 6 . 5 X 10' 7 . 2 X 10' 5 . 7 X 10' 4 . 8 X 10' 1 . 9 X 108 2 . 3 X 108 1 . 6 X 108 7 . 5 X 106 5 . 5 X 106 5 . 6 X 106 4 . 8 X 106 3 . 8 X 106 2 . 0 x 106 1 . 9 x 106
a A 16-cm. light path was used unless otherwise stated. 02saturated, all other experiments air-saturated. e [HzOZ], 0.02 M ,added. d Light path was 48 cm.
or
D, D, - D
In -= Q[TNM]t
+
(53)
where Q is defined as Q = (Kk46 kte[Hf])/(K 4[Hf]). I n a given experiment, a plot of In (D, Dj vs. t yields a straight line from whose slope the effective rate constant, Q, may be determined. At higher pH values above the pK of HOz, K >> [ H f ] and Q = k45 since experiments showed k46 > k46. Under these conditions Q should be independent of [H+]. However, as can be seen from the previous discussion, it is difficult to maintain a constant pH near neutrality without the use of a buffer and we preferred not to use buffers in order to avoid possible complications in the mechanism. The JournaE of Physical Chembtry
If [H+] >> K and if [H+]k46were much greater than Kk46, then again Q would be independent of pH and equal to k46. However, even at a pH as low as 0, Q was found to be pH dependent showing that IC46
