2946
R. WANDER,P. NETA,AND L. M. DORFMAN
Acknowledgments. It is a pleasure to acknowledge the partial financial support provided by Grant 315l-A5 from the Petroleum Research Fund of the American Chemical Society. The author also wishes to thank Professor P. J. Flory of Stanford University, who sug-
Pulse Radiolysis Studies.
XII.
gested the possibility of using thermochemical results to evaluate interatomic potential functions, and Professors L. s. Bartell and L. 0 . Brockway of the University of Michigan for several helpful discussions.
Kinetics and Spectra of the Cyclohexadienyl
Radicals in Aqueous Benzoic Acid Solution
by R. Wander, P. Neta, and Leon M. Dorfman Department of Chemistry, The Ohio State University, Columbus, Ohio .@%lo (Received February 10, 1968)
The pulse-radiolysis method has been used t o determine the optical absorption spectra of the cyclohexadienyl radicals of benzoic acjd in aqueous solution. The kinetics of formation and decay have been determined in a pressurized NzO solution. The uv absorption bands and extinction coefficients are: (OH)CsHsCOOH: Xmax 347 mp, €847 3600 f 500 &-'cm-I; (OH)&H&OO-: Amax 330 mp, €330 3600 4 500 Cm-l; (H)C6Hscrn-l. The values of the rate constants, at 2 5 O , are: k = (4.3 ct COOH: hmaX352 m p , €362 3700 f 500 0.8) X l o 9 M - I sec-' for OH CGHsCOOH; 27c = (1.2 =t0.4) X lo9 M - l sec-l for (OH)C6HsCOOH (OH)&,H&OOH; 2h = (5 i 2 ) X IOs .k-' sec-I for (OH)6Q"COO(OH)d&COO-.
+
Introduction The kinetics of hydroxyl radical addition t,o benzoic acid and several other aromatic compounds in aqueous solution have been determined in pulse-radiolysis The rate constants were determined from the formation curves of the hydroxycyclohexadienyl radical. Although the absorption spectrum of the OH-adduct free radical for benzoic acid has been reported,2 there has been some uncertainty about the absorption spectrum of the H-adduct free radical. This is resolved for benzoic acid in the present workl as it has been for several other aromatic compounds in recent articles3-5 in which it has been shown that the H-adduct free radical has a similar and equally intense uv absorption band to that of the OH-adduct free radical. This.observation is also pertinent to the question of the validity of the OH-addition rate constant. It, therefore, appeared worthwhile to determine for benzoic acid, which may be used as a reference reaction in competition kinetics, the absolute rate constant for OH addition in a system in which the hydrogen atoms have been essentially eliminated, or a t least sharply reduced in concentration. This was done a t pH 5 3 , well below the pK of 4.19 for benzoic acid16by pressurizing with nitrous oxide to 3-4 atm, which gives a T h e Journal of Physical Chemistry
+
+
sufficiently high concentration of NtO to scavenge the hydrated electrons. In addition to the absorption spectra of the cyclohexadienyl radicals and the rate constant for OH addition, we have also determined the rate constant for the reaction of the hydroxycyclohexadienyl radical with another like radical for both benzoic acid and the benzoate ion. Experimental Section The detailed technique, using a Varian V-7715A linear accelerator, has been outlined.' These methods are similar to those of our earlier work.2i8 Electrons of 3.5-4-MeV energy were used with a pulse duration of 0.1-0.4 psec. The pulse current was generally in the (1) L. M. Dorfman, I. A. Taub, and R. E. Btihler, J . Chem. Phys., 36, 3051 (1962). (2) L. M. Dorfman, I. A. Taub, and D. A. Harter, ibid., 41, 2954 (1964). (3) E. J. Land and M. Ebert, Trans. Faraday SOC.,63, 1181 (1967). (4) K. D. Asmus, B. Cercek, M. Ebert, A. Henglein, and A. Wigger, ibid., 63, 2435 (1967). ( 5 ) M. C. Sauer and B. Ward, J . Phys. Chem., 71, 3971 (1967). (6) "Handbook of Chemistry and Physics," 47th ed, The Chemical Rubber Publishing Co., Cleveland, Ohio, 1966, p D-86. (7) W. D. Felix, B. L. Gall, and L. M. Dorfman, J . Phys. Chem., 71, 384 (1967). (8) M. 9. Matheson and L. M. Dorfman, J . Chem. Phys., 32, 1870 (1960).
PULSE-RADIOLYSIS STUDIES
2947
range 310-330 mA. The detection system used was as described.7 The irradiation cell was 2 cm long, using a double pass of the analyzing light beam, 1.2 cm high and 0.8 cm deep in the direction of the electron beam. The electron beam had a diameter of about 1.5 ern at the point of incidence on the cell wall. The irradiation dose was required in the determination of the molar extinction coefficients. This was , ~ using a measured in situ, as previously d e ~ c r i b e dby modified Fricke dosimeter for which the yield of ferric ion at the high dose ratesl0V1l is 15.6 molecules/lOO eV. This dosimetry was also checked by measuring the optical absorption of ozonide ion at 430 mp in an oxygen-saturated solution of 0.1 M potassium hydroxide and taking the extinction coefficient of 0 3 - as 1900 M - 1 cm-1,' which is itself referred to the Fricke dosimetry. With unchanged accelerator settings, the dose per pulse was found to be constant to within 3%, and, therefore, no external pulse monitoring was done. Each result was an average of 4-6 measurements. The dose per pulse for the 0.1-psec pulse, used in the determination of the OH-addition rate constants, was 6 X 1 O I 6 eV/g at the highest pulse current. Taking GOH G,,,- = 5.2 gives an initial OH concentration of 6 X M. The pH of the solutions was adjusted with sulfuric acid or sodium hydroxide and was measured either with a Beckman research pH meter or by titration of the highly basic solution with standardized HCl. The benzoic acid, sodium hydroxide, potassium hydroxide, ferrous sulfate, and sulfuric acid were Baker Analyzed reagents. The nitrous oxide was passed through two successivc alkaline pyrogallol solutions and through triply distilled water before being bubbled through the reaction solution to deaerate it and finally to pressurize it. The K20 pressure was generally 3-4 atm, which gives an equilibrium concentration higher than 8 X M , estimated from the solubility and Henry's law. For solutions not containing NzO, argon was used to pressurize the deaerated solution to 1 atm, and a standard syringe technique12 was used to handle the solutions. The argon was of high purity (99.99%) and was used without further purification.
*
+
Results and Discussion Since the pK for the benzoic acid-benzoate ion equilibrium is 4.2, the kinetic studies and spectral determination on the benzoic acid system were carried out a t pH 3 or lower. In order to scavenge the hydrated electron effectively at this pH, the P I T 2 0 pressure was selected to give an N20 concentration in excess of 8 X M . Under these conditions, the competition between the reactions eaq-
+ NzO
=
N20-
(1)
and eaq-
+ H+ = H
(2)
is overwhelmingly in favor of reaction 1, approximately 3% of the hydrated electrons reacting by ( 2 ) . Following reaction 1 the hydroxyl radical is formed very rapidly7~13-~6 relative to the ensuing kinetics, and the hydrated electron is thus converted to OH. The reaction of esq- with benzoic acid eaq- 4- C6HsCOOH = CaHsCOOH-
(3)
has been neglected since its rate is very much slower than that of reaction 1, as the concentration ratio [NzO]/ [C6H&OOH] is always greater than 80 in these experiments, while Icl and k3 are probably comparable,16 judging from the value of the rate constant for the reaction of the hydrated electron with benzoate ion. Under these conditions then, the ratio of the total hydroxyl radical yield to the hydrogen atom yield is approximately 10, so we may regard the system, to a good approximation, as a one-radical system. The OH-Addition Rate Constant. The absolute rate constant for the reaction OH
+ C&COOH
= (OH)C&COOH
(4)
was determined from formation curves observed at 340 mp in the NzO-pressurized system. The values found -~
~~~
Table I: Absolute Rate Constant for the Reaction OH
+ CsHbCOOH a t 25'"
Benzoia acid
Rate constrtnt, M-1 sec-1 X 10-8
concn, M x 104
2.0 2.0 3.1
4.5 6.0 5.0 2.9
4.6 5.2 9.5 9.8
4.9
3.7 3.2 Av 4 . 3 + 0 . 8
NOTEADDEDI N PROOF.The correction for the effect upon the value for ka (as determined graphically) of the two reactions H f C0H;COOH and OH OH has been estimated using an Electronic Associates Incorporated Model TR-20 analog computer, and is included in the table. It ranges from +lo% a t the highest benzoic acid concentration to +S% a t the lowest, where OH ranges from 0 to -2%. the correction for OH @
+
+
(9) L. M. Dorfman and I. A. Taub, J . Amer. Chem. Soc., 85, 2370 (1963). (10) J. Rotblat and H. C. Sutton, Proc. Roy. SOC.,A25.5, 49 (1960). (11) J. K. Thomas and E. J. Hart, Radiat. Res., 17, 408 (1962). (12) C. B. Senvar and E. J. Hart, Proc. Intern. Conf. Peaceful Uses Atomic Energy, 29, 19 (1958). (13) G.E.Adama, J. W. Boag, and B. D. Michael, Proc. Roy. Soc., A289, 321 (1966). (14) J. Rabani and M. S. Matheson, J. Phys. Chem., 70, 761 (1966). (15) P. Neta and L. M. Dorfman, Advances in Chemistry Series,
in press. (16) M. Anbar and P. Neta, Int. J . Applied Radiat. Isotopes, 18, 493 (1967) Volume 72, Number 8 August 1968
2948
R.
WANDER,
P. NETA,AND L. ni. DORFMAN
; l T 1 0 3000 4
2000 10
0.0
4 m
Figure 1. The plot of the first-order rate law of the formation curve of the carboxyhydroxycyclohexadienyl radical, observed a t 340 mp, with a benzoic acid concentration of 9.8 X 10-4 M . D, and D are the optical densities a t the plateau of the formation curve and at any time, respectively.
3000
ZOO0
0
I
300
are shown in Table I. Each value shown in the table is an average of two runs. In each case, the rate curves were found to fit very closely to a first-order rate law. An example is shown in Figure 1. Since the initial concentration of the OH radical is 6 X lo-" M , at the lowest benzoic acid concentration the ratio [OHIO/ [CeHd2OOH] = 0.03 initially and falls lower during the observed formation. The effect of OH recombination on the addition rate constant is thus about 2% for the lowest benzoic acid concentration. The averagevalue is k4 = (4.3 & 0.8) X lo9M-l sec-' a t 25". This is significantly higher than the value (2.1 f 0.3) X lo9 M-' sec-' previously reported.2 The difference is very likely due to the concurrent observation, in the earlier work, of the H-atom addition reaction which has a lower value than the OH addition in the case of phenol3 and b e n ~ e n e , ~as, 'well ~ as benzoic acid.'l It should be noted that the OH-addition rate constant for the benzoate ion is slightly higher,I5 having a value of (6.0 f 0.7) X lo9M-I sec-l. T h e Cyclohexadienyl Radical Spectra. The radical formed in the NnO-pressurized system at pH 3 should be almost entirely the OH adduct with not more than 10% of the H adduct present. The uv absorption band of the OH adduct is shown in Figure 2a. The maximum is a t 347 mp. The molar extinction coefficientla of this carboxyhydroxycyclohexadienyl radical, taking Ge,, GOH GH = 5.8,l9is €341 3600 & 500 M-I cm-l at 25'. The extinction coefficient of the hydroxycyclohexadienylcarboxylate radical, which has a m a x i r n ~ m at~ 330 mp, is €330 3600 f 500 M - l cm-l in neutral solution a t 25". The absorption spectrum of the H-adduct free radical was determined in two separate ways. I n the absence of N20,a t pH 1.8-2, where reaction 2 competes favorably with reaction 3, both the H adduct and the
+
The Journal of PhysieaE Chemistrzl
+
350 )r
40(
(ms)
Figure 2. The uv absorption bands in pulse-irradiated aqueous benzoic acid solution about 1 pBec after pulse: (a) the carboxyhydroxycyclohexadienyl radical a t p H 3, with [NnO] = 8X M and [CeHSCOOH] = M ; ( b ) the absorption of both the OH adduct and H adduct without N,O, a t pH 2 and [CBHSCOOH]= 10-3 M (for comparison with a, the optical density is given on the right); (c) the carboxycyclohexadienyl radical; 0, calculated from a and b as explained; 0, determined directly using CD,OH, [C&COOH] = 5 X M , pH 1, and [CDaOH] = 0.2 M ; e is the molar extinction coefficient.
OH adduct are formed in comparable yields, depending upon the values for GOH, GH, and G,,,- at t,he particular pH. The H-adduct spectrum may thus be determined from the optical density ratio observed in the presence and in the absence of NzO, at a fixed pulse intensity. Alternatively, as a check on the foregoing method, the OH was scavenged by CDsOH, as reported for benzene and t ~ l u e n eand , ~ the remaining H-adduct radical was observed directly. A correction was made for the weak absorption of the .CD20H radical. The absorption band for both species, without NzO present, is shown in Figure 2b. From this observed band and from the ratio of the optical densities with and without NzO, the band for the H adduct alone is determined from the relationship
~ (17) ~ ~ P. ~ Neta and L. M. Dorfman, to be submitted for publication. (18) It is of course clear that no attempt has been made to distinguish among the possible isomeric forms of the cyclohexadienyl radicals which may be formed and that the reported molar extinction coefficients may very well be a weighted average of the separate coefficients for the ortho, meta, and para isomers. (19) L. M. Dorfman and M. S. Matheson, Progr. Reaction Kinetics, 3 , 237 (1965).
(20) D. F. Sangster, J . Phys. Chem., 70, 1712 (1966).
2949
PULBE-RADIOLYSIS STUDIES where DN%O and D are the optical densities in the presence (Figure 2a) and absence (Figure 2b), respectively, of N20, and (OH and EH are the molar extinction coefficients of the OH adduct and the H adduct, respectively. The appropriate correction for the small amount of reaction 2 in the presence of i S 2 0 was made. The value for t H may then be determined from the observed optical density, and the value of course depends upon the selected values for the yields. The absorption band for the H adduct is shown in Figure 2c. The G values used in determining this band from eq 5 are GOH = 2.65, G,,,- = 2.6, and GH = at p H 3 and pH 7. At pH 1.8-2, for the experiments without NzO present, the values used were G,,,GH = 3.25, and GOH = 2.75.21 The data for the H-adduct absorption band, determined directly with CD,OH as scavenger for OH radicals, is also shown in Figure 2c. There is excellent agreement on both the maximum and the shape of the band, considering the uncertainty in the XtO method, which is essentially a difference determination. The molar extinction coefficient for the carboxycyclohexadienyl radical, determined at pH 1 from the direct experiments with CD,OH, is €852 3700 f 500 M-' cm-' a t 26", taking GH G,,,- = 3.70 molecules/100 eVSz1
+
+
The Radical-Radical Rate Constants. Since the NzO-pressurized system approximates to a one-radical system, we may determine the rate constants for the bimolecular combination reaction of both (OH)CeHjCOOH with a like radical at pH 3 and (OH)&H,COO- with a like radical at pH 7. The decay of the OH-adduct free radical in the case of both benzoic acid and the benzoate ion was found to fit a secondorder rate law, as may be seen in Figure 3. The bimolecular rate constants may be determined from 2ic = (slope)q,Z
(6)
where I is the length of the optical absorption path. The values22a t 26" are (OH)&H&OOH
4- (oH)C:,H,COOH; 2k
=
(1.2 f 0.4) X lo9 M-* sec-l
(OH)&H&OO- f ( O H ) ~ 6 H 5 C 0 0 - ;
2k = (0.5
=I=
0.2) X loB
sec-1
It is interesbing to note that in a comparison of the encounter-controlled rate constants for the neutral species and the ionic species, the Coulombic interaction factor in the Debye equationz3
0
taking r 5 A, gives a ratio of 0.45 for the rate constant of the carboxylate ion species to that of the neutral benzoic acid radical, in accord with the experimental ratio. This simple comparison assumes that the interaction distance, r , and the diffusion coefficient are the same for the ion and the neutral free radical,
0
ZOO
100 t
300
400
(psec)
Figure 3. The plot of the second-order rate law of radicalradical decay curves. The reciprocal of optical density is plotted against time. Lines a-c show the carboxhydroxycyclohexadienyl radical a t pH 3, M . Lines [CsH,COOH] = lo-* M , and [NzO] = 8 X d and e show the hydroxycyclohexadienyl carboxylate radical anion at pH 7 , [CpHsCOOH] = 5 X 10-4 M, and [NzO] = 2 X M . The temperature is 25'.
Acknowledgment. This report is based upon work supported by the U. S. Atomic Energy Commission. It is also a pleasure to acknowledge the following assistance available to us during part of this work. One of the authors (R. W.) was the recipient of a fellowship under the National Defense Education Act; one of the authors (P. IS.)was supported as a visiting scientist under the university postdoctoral program, administered by the Graduate School of The Ohio State University. We are indebted to Mr. E. G. Wendell for his operation and maintenance of the linear accelerator and the detection equipment. (21) J. W. T. Spinks and R. J. Woods, "An Introduction t o Radiation Chemistry," John Wiley and Sons, Inc., New York, N. Y., 1964, pp 259, 263.
(22) Since the isomeric radicals may be formed, these rate constants may represent a composite value of the individual rate constants for the separate reactions. (23) P. Debye, Trans. Electrochem. Soc., 82, 265 (1942).
Volume 78, Number 8 August 1968
