A Quantitative Study of Alkyl Radical Reactions by Kinetic Spectroscopy 111. Absorption Spectrum and Rate

Constants of Mutual Interaction for the Ethyl Radical

HIROYUKI ADACHI, N. BASCO, and D. G. L. JAMES Department of Chemistry, University of British Columbia, Rritish Columbia, Canada

V6T 1 W5

Abstract

Intrinsic spectral and kinetic parameters have been measured for the ethyl radical, which was formed in the gas phase by the flash photolysis of azoethane. Absolute values of the ex- tinction coefficient c(X) were derived from complementary measurements of the yield of ni- trogen and the absorbance of an equivalent concentration of the ethyl radical. The absorption spectrum is broad, structureless, and comparatively weak; f(247) = 4.8 X lo2 I/mol-cm a t the maximum, and the oscillator strength is (9.1 f 0.5) X This is in good qualitative agreement with a spectrum obtained independently using the technique of molecular mod- ulation spectrometry.

The biomolecular reactions of mutual interaction were the only significant reactions of the ethyl radical in this system; kinetic analysis of the second-order decline of the absorbance during the dark period yielded a value of k / c ( X ) for each experiment. The rate constant for mutual interaction was evaluated from the product of corresponding measurements of k / f ( X ) and ((A); individual values are independent of the wavelength of measurement, and the mean value is k = (1.40 f 0.27) X 1O’O I/mol-sec. The rate constant for mutual combination was derived with the aid of product analysis as k 2 = (1.24 f 0.23) X 10’O I/mol-sec; it stands in close agreement with the set of “high” values obtained by direct measurement using a variety of met hods.

Introduction

Absorption Spectrum

The absorption spectrum of the ethyl radical in the gas phase has not previously been characterized with any certainty. The three attempts reported in the literature were based upon quite diverse systems, but the assignments offered are both tentative and conflicting [ 1-31.

Gaydon and co-workers [l] examined the absorption spectra of the flames

International Journal of Chemical Kinetics, Vol. XI, 995-1005 (1979) c 1979 John Wiley & Sons, Inc. 0538-8066/79/00 1 1 -0995$0 1 .OO

996 ADACHI, BASCO, AND JAMES

of diethyl ether and ethane for common regions of absorption. Each spectrum showed a weak band with maxima at 222.8 and 224.2 nm, which these authors assigned tentatively to the ethyl radical.

Wendt and co-workers [2] generated the ethyl radical by four established procedures: the addition of a hydrogen atom to ethylene; the abstraction of a hydrogen atom from ethane; and the mercury photosensitized de- composition of both ethane and diethyl ketone. Each system displayed a similar broad absorption band a t 206 f 1 nm, which was tentatively as- signed to the ethyl radical; but no prominent or persistent band was ob- served at either 223 or 224 nm.

Parkes and Quinn [3] generated the ethyl radical by the photolysis of azoethane in the presence of an excess of nitrogen, and used the molecular modulation spectrometer to examine the transient absorption spectrum. They discovered a weak broad band with a maximum a t 250 nm, which declined by a second-order process with a rate constant of 8 X lo9 l/mol-sec. This result is consistent with the assignment of the spectrum to the ethyl radical, which would have been consumed by bimolecular mutual inter- action. Absorption by azoethane below 230 nm was too intense to allow a search for bands at 224,223, or 206 nm.

No measure of agreement can be found in the results of these three studies, and an independent investigation of the spectrum of the ethyl radical was clearly desirable.

Rate Constant for Mutual Combination

Measurements of this rate constant fall into two classes: (a) direct es- timates, and (b) estimates derived from the rate constant of a related re- action by the use of thermochemical parameters. Each class of measure- ment has yielded a set of values which shows general internal consistency, but attempts to reconcile the representative results of the two classes have generated much discussion.

Absolute Measurements. The three absolute measurements constitute the set of “high” values of the rate constant, and are dispersed about an estimate of 1 X 1 O l o l/mol-sec in the gas phase.

The rotating sector method was applied to the study of the mutual combination of ethyl radicals formed by the low-intensity photolysis of diethyl ketone at 323,373, and 423 K [4]. A t 323 K the value of the rate constant was (1.5 f 1) X 10’0 l/mol-sec. Unfortunately the value increased with an increase of reaction temperature, implying an activation energy of 2 f 1 kcal/mol, which is unlikely for the mutual combination of ethyl radicals.

The increase at the higher temperatures may be due to a departure from the simple mechanism by the introduction of a chain propagation sequence involving the formation and dismutation of the C2H&OC2H4* radical.

ALKYL RADICAL REACTIONS 997

The technique of very-low-pressure pyrolysis was applied to the gener- ation of the ethyl radical from azoethane, and the yields of the ethyl radical and n-butane and the consumption of azomethane were monitored by mass spectrometry [5]. The n-butane was formed exclusively by the second- order combination of ethyl radicals with a rate constant of 4.5 X lo9 1/ mol-sec a t 860 f 17 K under very-low-pressure conditions; this value was extrapolated to 1 X 1O’O l/mol.sec a t infinite pressure.

The technique of molecular modulation spectrometry was used to monitor directly the absorption attributed to the ethyl radical, which was generated by the periodically interrupted photolysis of azoethane [3]. The result of (8 f 2) X lo9 l/mol-sec, measured a t room temperature, is not significantly different from the value of 1 X 1O’O l/mol.sec, estimated by extrapolation of the results obtained by very-low-pressure pyrolysis a t 860 K; this agreement supports the expectation that the activation energy for the combination is negligible.

These indirect methods fall into three classes: (a) rate studies of the reverse re- action, the pyrolysis of n-butane [6], (b) product analysis of radical buffer systems [7], and (c) rate studies of reactions of the ethyl radical, including metathesis and dismutation [8].

Each method requires an accurate knowledge of the entropy and the heat of formation of the ethyl radical a t appropriate temperatures in the range from 300 to 1100 K. The evaluation of the entropy has been based upon the assignment of frequencies given by Purnell and Quinn [9] and by O’Neal and Benson [lo], with free internal rotation of the methyl group. The value of 26.0 f 1 kcal/mol for the heat of formation of the ethyl radical a t 298 K has been generally accepted for over 20 years [ l l ] , although the estimate of the uncertainty is probably too low [12].

A value of 4 X lo8 l/mol-sec for the rate constant for combination was selected by Hughes and Marshall as representative of a large body of studies by the indirect methods. This “low” value is only 1/25 of the representative “high” value derived from direct methods. Golden and co-workers have shown that this value could be raised to 2 x lo9 l/mol.sec if a barrier of 2 kcal/mol were assigned to the internal rotation of the methyl group [5]. Tsang has recently shown that the representative value could be raised to 8 X lo9 l/mol.sec if a value of 28.5 kcal/mol were assigned to the heat of formation of the ethyl radical a t 298 K, with the retention of free internal rotation [13]. His model predicts a decrease in the Arrhenius parameters for the homolysis of the central bond of n-butane with an increase of tem- perature from 300 to 1100 K; the preexponential factor decreasing by a factor of 15, and the energy of activation by 4 kcal/mol.

A new evaluation of the rate constant for mutual combination seems desirable in view of the diversity of current estimates.

Methods Involving the Thermochemistry of the Ethyl Radical.

998 ADACHI, BASCO, A N D JAMES

Experimental

The low extinction coefficient of the ethyl radical required an increase of an order of magnitude in the sensitivity of absorbance measurement above the level attained previously by us using kinetic spectroscopy with plate photometry [14]. This increase was achieved by using a photoelectric apparatus with a pulsed xenon lamp as the analytical light source and a dual-beam optical system with twin cells and balanced photomulti- pliers.

The reaction and reference cells were made of Pyrex glass and fitted with Suprasil end windows to transmit monitoring light down to below 200 nm. Each cell was cylindrical in shape, with a length of 914 mm and an internal diameter of 20 mm. The use of Pyrex for the cells served the double pur- pose of restricting the photolytic radiation to X > 280 nm and of virtually eliminating scattered light from the photoflash in the wavelength region used for monitoring the absorbance of the ethyl radical. Furthermore a double gas filter containing chlorine and bromine was placed before the slit to remove radiation between 280 and 520 nm, which could have been scattered within the spectrometer. These precautions made it possible to monitor the absorbance of the ethyl radical during the period of the photoflash, and this capacity was used in the evaluation of the extinction coefficient by the extrapolation procedure described below. Kinetic measurements of the mutual interaction of ethyl radicals began when the photoflash was virtually extinct, some 25 psec after the firing.

Ethyl radicals were generated by the flash photolysis of azoethane in the presence of n-pentane as a moderating gas. The temporal variation of the absorbance of the reacting system was displayed on the screen of an oscil- loscope. This display comprised the currents I and l o generated by the photomultipliers monitoring the beams transmitted by the reaction and reference cells, respectively, and their difference I0 - I . This combination of data allowed the precise measurement of absorbance a t a comparatively low signal-to-noise ratio. The display was recorded on Polaroid film from the screen of a Tektronix model 7704 oscilloscope with 7A12 and 7A13 plug-in units, the former being a dual trace and the latter a differential comparator unit.

The only significant products of the photolysis were nitrogen, ethene, ethane, and n-butane. The products were separated into two fractions and a residue by fractional distillation under vacuum, and the number of moles of each fraction was estimated by measuring its pressure in a known volume with a McLeod gauge. The first fraction was nitrogen, and was isolated a t 73 K; the second fraction comprised ethane and ethene, and was isolated at 112 K; the residue comprised n-butane, n-pentane, and azoethane. The yield of n-butane was estimated as the difference between the molar yield of the first fraction and one half of the molar yield of the second fraction. At 25°C the rate of consumption of the ethyl radical by metathesis or by

ALKYL RADICAL REACTIONS 999

reaction a t the wall is negligible in comparison with the rate of mutual in- teraction when the ethyl radical concentration is of the order of molh and the total pressure is 0.060 atm. The rate constants for metathesis with n-pentane and with azoethane are approximately 4 and 340 l/mol-sec, re- spectively a t 25°C [15], and we estimate that the rate of mutual interaction exceeds the sum of the rates of metathesis by a factor greater than lo5 in our system. Accordingly we have assumed that the C2 fraction comprises ethane and ethene a t a molar ratio of unity, and on this basis we have de- rived a value of 0.14 f 0.01 for the ratio of disproportionation to combi- nation, which is fully consistent with the accepted value [16].

Azoethane was supplied by Merck Sharp and Dohme (Canada) Ltd.; analysis by vapor phase chromatography showed that the sole impurities were traces of nitrogen, methane, ethene, ethane, and butane, and these were removed by exhaustive degassing in freeze-thaw cycles under vacuum. The n-pentane supplied by Matheson Coleman and Bell Manufacturing Chemists was only 98% pure. It was purified by two successive distillations, the first with a 50-cm long distillation tower, and the second with a 100-cm tower in a stream of nitrogen. The product was shown to be pure by vapor phase chromatography, and stored over Linde molecular sieve 4A.

The ethyl radical shows a weak, broad absorption between 230 and 260 nm, and no fine structure was revealed by observations a t the wavelengths listed in Table I. The resolving power of the spectrometer was sufficient to achieve a partial resolution of the maxima a t 215.8 and 216.4 nm in the absorption spectrum of the methyl radical under similar conditions, and yet the Beer Lambert law was shown to be valid for the absorbance centered on 216.4 nm when a band pass of 0.16 nm was used in this apparatus [17]. The resolution of fine structure by this spectrometer should be less com- plete for the ethyl radical than for the methyl radical as the former has the greater number of vibrational degrees of freedom. Accordingly there is no reason to doubt that the Beer Lambert law will be valid for the ethyl radical when the band pass has the value given above for the methyl rad- ical.

Each experiment was performed with a photoflash energy of 1080 J and a band pass of 0.16 nm. A value of k/t(X) was obtained by kinetic analysis of the decline of the absorbance during the dark period. The separate evaluation of ( (A) , and thereby of k , was achieved by combining an ap- propriate extrapolation of the absorbance with a measurement of the yield of nitrogen, and allowed the absorption spectrum to be expressed in abso- lute units. Greater accuracy was maintained by restricting these mea- surements to a range of wavelengths near maximum absorption, extending from 234 to 255 nm. The concentrations of azoethane and n-pentane were 5.46 X and 1.91 X lo-:% mol/l, respectively. The percentage of azo- ethane decomposed was 0.23%.

1000 ADACHI, BASCO. AND JAMES

TABLE I. Values of €(A) and k for the ethyl radica1.a

x *ma,(') 1O-l0k

-1 -1 emole-lcm-l emole sec -1 nm cm sec

234 2.3120.08 0.069 303 0.70 235 2.9820.07 0.061 271 0.81

3.4220.10 0.066 292 I .oo 236 3.11f0.12 0.071 315 0.98 237 3.2520.10 0.080 3 54 1.15

237.5

238 239 240

241 242 242.5

243 244 245

246 247 247.5

248 249 250

2.92fO. 05 3.34f0.07 3.13AO. 09 3.24A0.09 3.97A0.14 4.25fO.12 3.6520.10 2.81f0.07 3.2420.08 3.7520.14 3.47f0.14 2.2720.37 2.70fO.07 2.3520.07 3.14f0.09 3.06fO. 13 3.4620.10 3.2420. 14 2.7420. 08 3.5420.11 3.0120.10 3.2620.11 3.00f0.10 3.1820.20 3.3520.16 3.42f0.13 3.5420. 11 3.3020.12 2.97t0.12 3.55f0.12 2.41 f 0 . 08

0.074 0.078 0.084 0.089 0.094 0.099 0.100 0.077 0.083 0.097 0.096 0.092 0.098 0.090 0.107 0.105 0.103 0.103 0.096 0.109 0.104 0.108 0.108 0.107 0.109 0.108 0.115 0.108 0.091 0.102 0.097

329 346 373 393 417 439 444 342 366 432 426 4 08 435 399 475 467 457 457 426 483 463 478 478 475 483 479 510 478 404 452 428

0.96 1.15 1.17 1.27 1.65 1.87 1.62 0.96 1.19 1.62 1.48 0.92 1.17 0.94 1.49 1.43 1.63 1.48 1.17 1.71 1.39 1.56 1.43 1.51 1.62 1.64 1.81 1.58 1.20 1.61 1.03

251 3.10f0.09 0.094 418 1.30 252 3.24t0.12 0.091 4 03 1.31 253 2.48tO. 09 0.087 385 0.95 254 2.59f0.10 0.084 371 0.96 255 2.65f0.15 0.076 335 0.89

2.83tO. 09 0.074 330 0.93 2.3120. 10 0.078 348 0.80

a C,,, = 2.47 X mol/l for each experiment. Statistical analysis of 31 values of k measured at wavelengths from 237.5 to 250 nm yields the result k = (1.40 f 0.27) X 10'0 I/mol-sec.

ALKYL RADICAL REACTIONS

Results

1001

Absorption Spectrum

Ethyl radicals were generated by the flash photolysis of azoethane:

(1) C ~ H S - N = N - C ~ H ~ + h v - 2C2Hj + N2 and consumed in the second-order reactions:

(2) 2C2Hj - C4H10

(3) 2C2H; - C2H4 + C2H6 The concentration of ethyl radicals was monitored by the measurement of absorbance:

A(X) = c(X)[C2Hj]l

where ((A) is the decadic molar extinction coefficient, and 1 = 914 mm, the length of the reaction cell.

Absolute values of the extinction coefficient € ( A ) were obtained at a series of wavelengths between 234 and 255 nm from the equation:

= A max(X)/Cmaxl

by evaluating A,,,(X) and C,,, for each experiment. C,,, is the hypo- thetical value of the concentration that would have been obtained if all the ethyl radicals formed by the flash had been present simultaneously in the reaction vessel, and is evaluated from the yield of the product nitrogen as:

C,,, = 2[N2] = 2.47 X molh

A,,,(X) is the corresponding absorbance at the wavelength X and is eval- uated by an extrapolation procedure.

Each extrapolation of the absorbance was performed over the initial period of 36 psec. The absorbance curve between 0 and 36 psec was divided into 4-psec intervals, and the mean absorbance (Ai ) was estimated for each interval from the smoothed curve. The decrease in absorbance due to mutual interaction during the interval i is given to a good approximation by

6A, = A t ( - d A / d t ) = (4 X ( A i ) 2 G where G = d ( l / A ) / d t = 2k/c(X)-1, and is the gradient of the corresponding second-order plot. The corresponding total decrease in absorbance AA 36

during the initial period was obtained by summing over the nine 4-psec intervals, and the extrapolated value A,,, is the sum of the value of the absorbance a t 36 psec and AA36:

9

i = l A,,, = A36 4- AA36 = A36 + (4 X lov6) G X (Ai)'

1002 ADACHI. BASCO, A N D JAMES

The error in A,,, due to the approximation in the estimate of 6Ai is less than 1%.

The absolute values of c(X) are plotted as the absorption spectrum of the ethyl radical in Figure 1. This spectrum has a maximum a t 247 nm with ~(247) = 4.8 X lo2 l/mol-cm. A curve was fitted to all 43 values of c(X) with the aid of a computer program, which examined all polynomials of degree less than 11 and selected one of the fourth degree as giving the best fit to the data. The maximum was characterized more precisely by fitting a curve to the 24 values measured between 242 and 252 nm.

The oscillator strength of the ethyl radical was estimated as (9.1 f 0.5) x lo-".

There is an indication that the value of E ( A) rises again for X < 225 nm, but accurate measurement in that region is hindered by the increasing absorption of azoethane.

Rate Constant for Mutual Combination Rate measurements were based upon the decline in the absorbance

during the dark period following the extinction of the photoflash. This decline was due to the second-order reactions (2) and (3), and conformed to the rate equation

2 k +-.---.t 1 - 1 A(X) ( (A) Col I ((A)

- . 230 240 250 2 6 0

Figure 1. Absorption spectrum of the ethyl radical. .-this work, using flash photolysis and kinetic spectroscopy; 0-Parkes and Quinn, using molecular modulation spectrometry [3].

ALKYL RADICAL REACTIONS 1003

where k = k z + k s and CO is a constant. A series of measurements of k / c ( A ) was made to complement the measurements of €(A) described in the pre- vious section. At each wavelength the absorbance A (A ) was measured a t a series of delay times in excess of 25 psec, and the corresponding value of k / c ( A ) was derived from the gradient of the second-order plot and the value of 1.

Values of the rate constant for mutual interaction were calculated as the product of corresponding values of k l c ( A ) and €(A) obtained from each experiment, and are listed in Table I. The most accurate values of k were obtained from 31 measurements a t wavelengths from 237.5 to 250 nm, and statistical analysis of these values gave the result

k = (1.40 f 0.27) X 1Olo l/mol.sec

No correlation was found between the value of k and the wavelength used for its measurement, as r2 = 0.15 for a trial linear regression; this inde- pendence provides general support for our procedure.

The disproportionation-to-combination ratio was calculated from the yields of the stable products:

in agreement with the accepted value of 0.14 [16]. The rate constant for mutual combination is therefore

k z = (1.24 f 0.23) X 1 O ' O l/mol-sec

The total pressure of the reacting system is 0.060 atm, and it is reasonable to assume that this estimate of k2 represents the high-pressure limit.

Discussion

Characterization of the Absorption Spectrum

The measure of agreement between the results of this investigation and those obtained by Parkes and Quinn [3] may be assessed from Figure 1 and Table 11. Agreement is excellent a t the qualitative level of locating the position of the maximum and estimating the approximate half-width AA of the absorption band. At maximum absorption our estimate ~ (247) = 4.8 X lo2 l/mol.cm exceeds the value ~ (248) = 3.3 X lo2 l/mol-cm, which is equivalent to the cross section a(248) = 1.25 X 10-'8 cm2/molec given by Parkes and Quinn. However, these estimates do not differ significantly if each is assigned a standard deviation of 0.2 E,,, by analogy with the

1004 ADACHI. BASCO, A N D JAMES

A Ah max

nm nm

Authors

Parkes and 248 2 0 Quinn [3]

This work 2 4 7 25

E mX k~’E max k2

t mole-‘ s e c - l - 1 L mole-’ cm-’ cm s e c

3 . 3 x 102 2 . 4 10’ (8 : 21 lo9

4 . 8 x 102 2 . 5 10’ ( 1 . 2 0 . 2 ) 1o1O

Rate Constant f o r Mutual Combination

Remarkably close agreement is found between the mean value k2/6(247) = 2.5 X lo7 cm/sec of the present work and the estimate of the ratio k2/ ((248) = 2.4 X lo7 cm/sec which may be derived from the values of k2 and ~ ( 2 4 8 ) reported by Parkes and Quinn [ 3 ] . The corresponding mean values of the rate constant for mutual combination are (1.2 f 0.2) X 1 O l o and (0.8 f 0.2) X 1O1O l/mol-sec, but with such limits of error these results cannot be said to differ significantly. The ratio of these mean values is commen- surate with the mean value of 1.7 f 0.3 observed for the ratio of corre- sponding pairs of estimates of c(X) between 235 and 255 nm. Both esti- mates of the rate constant belong to the set of “high” values, clustered about 1 X 1 O l o l/mol.sec, which were obtained by direct measurement by other techniques [4,5]. They are an order of magnitude greater than the estimate of (1.2 f 0.2) x 109 l/mole.sec obtained by Hickel for combination in aqueous solution a t 298 K [18]. However, this estimate is associated with an activation energy of 3.9 f 0.4 kcal/mol, which is approximately the value expected for the activation energy of diffusion of ethyl radicals in water. Accordingly it is probable that the combination of ethyl radicals is con-

ALKYL RADICAL REACTIONS 1005

trolled by the rate at which a random pair of independently formed ethyl radicals can diffuse to an encounter within a common solvent cage. We conclude that the estimate of the rate constant in aqueous solution is qualitatively compatible with the value measured for the gas phase in the present investigation.

Acknowledgment

This work was supported by the National Research Council of Canada.

Bibliography

I 1) A. G. Gaydon, G. N. Spokes, and J. van Suchtelen, Proc. R. SOC. London, Ser. A, 256,323

[2] H. R. Wendt, D. Wyrsch, and H. E. Hunziker, Ber. Bunsenges. Phys. Chem., 78,201

[3] D. A. Parkes and C. P. Quinn, J . Chem. SOC., Faraday I , 72,1952 (1976). [4] A. Shepp and K. 0. Kutschke, J . Chem. Phys., 26,1020 (1957). [5] D. M. Golden, K. Y. Choo, M. J . Perona, and L. W. Piszkiewicz, Int. J . Chem. Kinet.,

IS] D. G. Hughes and R. M. Marshall, J . Chem. SOC., Faraday I , 71.413 (1975), and references

17) R. Hiatt and S. W. Benson, J . Am. Chem. SOC., 94,25,6886 (1972). [8] R. M. Marshall and J. H. Purnell, J . Chem. Soc., Chem. Comm., 764 (1972). [9] J. H. Purnell and C. P. Quinn, J . Chem. SOC., 4049 (1964).

(1960).

(1974).

8,381 (1976).

therein.

[lo] H. E. O’Neal and S. W. Benson, Int. J . Chem. Kinet., 1,221 (1969). 1111 A. F. Trotman-Dickenson, “Gas Kinetics,” Academic, London, 1955, p. 15. [12] S. W. Benson, J . Chem. Educ., 42,502 (1965). 1131 W. Tsang, Int. J . Chem. Kinet., 10,821 (1978). 1141 N. Basco, D. G. L. James, and F. C. James, Int. J . Chem. Kinet., 4,129 (1972). [15] A. F. Trotman-Dickenson and G. S. Milne, “Tables of Biomolecular Gas Reactions,”

[16] J. A. Kerr, “Free Radicals,” J . K. Kochi, Ed., Wiley, New York, 1973, Ch. 1. [17] H. Adachi, N. Basco, and D. G. L. James, unpublished results. [18] B. Hickel, J . Phys. Chem., 79, 1054 (1975).

National Bureau of Standards, Washington, D.C., 1967, pp. 71-72.

Received January 18,1979 Revised April 16, 1979 Accepted April 26,1979