Sov., 1960
REACTIONS OF METHYL RADICALS WITH ETHANE AND ETHANE-&
1671
KINETIC ISOTOPE EFFECTS IN THE REACTION OF METHYL RADICALS WITH ETHANE, ETHANE-& AND ETHANE-l,I,I-da BY J. R. MCNESBY National Bureau of Standards, Washington, D.C. Recezved May 8, 1960
Photolyses of acetone46 in the presence of a mixture of C& and CzDsand in the presence of CH3CD3were carried out to C2H6 + CD,H CzHs; ( 2 ) CD3 CHdCD3-P CDSH measure kinetic isotope effects for the reactions: (1) CD, CHzCD3; ( 3 ) CD3 CHsCDs + CD4 CHaCDz; (4).CD3 CzDe + CD4 CsD5. The conclusions drawn from the results is that the relative rate constants are within experimental error: kl/ki = exp( 1500/RT); kz/k3 = 0.73 exp( 1900/RT); &/kt = 1.95 exp( 100/RT).
+
+
+
+ +
+
+
+
The objective of the present study was to evaluate with precision the kinetic parameters of the reactions
The entire system was fitted with brass bellows valves and contained no stopcocks or grease. The acetone-&, ethane-da and ethane-& were obtained from Merck, Ltd., Montreal and were specified 98%.[D/(D H)] in the CD, positions. Ethane was Phillips research grade mateCDJ CzHs +CD3H C2H6 (1) rial and contained 0.05%ethylene. CD3 CHECD, +CD,H CHzCDs (2) Purity of CzD6.-The CZD6 contained 6.5% CzDsH and CD3 CH,CD, +CD4 CHaCDz (3) [CZD,]is considered to mean [CZD~] [CzD5H]. No correction was applied for the CDJH arising from abstraction of CDJ C2D6 +CD4 CPDS (4) from CzD5Hby CD,. There was no CD4or CD3H present The kinetics of the above reactions were obtained H in the C&. Ethylene was present to the extent of 0.05%. relative to those for the reaction Purity of CH3CDs.-The CH3CDa contained about 1% CD4 CD3H. Since the reactions which produced CD3 CDICOCDj +CD4 CDzCOCD3 (5) CD, and CD3H were to be carried out to only a few hunwhose kinetics are known.1-2 Reaction 1 has been dredths per cent. destruction of ethane, this impurity was prohibitively high. I n order to remove the last traces of ( 3 ) 6 and studied3a4as well as the CH3analogs of CD3H and CD4from CHaCDz, it was necessary to add CH4, (4).3,6 However, no comparative study has ap- freeze, pump, melt, freeze, pump, melt, etc. for several peared in which the kinetics of (1) through (4) could days. Finally nitrogen was added and the procedure rebe intercompared. The work mas divided into two peated to remove as much CH, as possible. The final was found by gas chromatography to contain parts; the photolysis of acetone-d6 in the presence ethane-& 1.4% CH4 and 0.5% Nz. No CD4 or CD3H was detectable of mixtures of C2H6and C2D6 and the photolysis of on the mass spectrometer. I n addition an ethylene imacetone-& in the presence of CH3CD3. purity of 1% was found and w a ~considered to have no For the photolysis of acetone-& in the presence effect on the results. Mixtures were made u in reservoirs by adding an apof ethane ethane-& propriate amount of CD380CD3 to the CZHaD3 or CZH6 CZD6 mixture and allowing to mix overnight. After the [cD,l/fCD3HI = (ks[Adsl)/(k~[El required number of photolyses and analyses had been made (k4 [Ed61)/(hi [El 1 ( 1) on representative samples of this mixture, a t different temSince the quantity (li6[Ad6])/(kl[E])is known very peratures, more CD3COCD3was added to the reservoir and of k4/kl is obtained by a second series of photolyses and analyses were run on the a c c ~ r a t e l y ,evaluation ~~~ new mixture. A third mixture was prepared similarly in measurement of [CD4]/ [CD3H]. Evaluation of the reservoir and photolyses carried out as before. I n this kJkl at a number of temperatures permits A4/A1, way the [CZH~]/[CZD~] ratio was kept const?nt while [?cetone-d6]/[C2Hs] was vaned. After terminating a reaction, and E4-E1 to be calculated from the expression the whole reaction mixture was Toepler-pumped through a double-U trap a t 77°K. and into a sample flask for mass spectrometric analysis. The sample flask thus contained carbon monoxide, methane and very small amounts The photolysis of acetone-da in the presence of only of hydrogen. The mass ratio 20/19 gave directly [CD,]/ CH3CD3 produces methane so that [CD3H]. Masses 19 and 20 were rescanned 6 times and average ratios were used. [CDal /[CDJU = (ks[Add )/(h[Edil) h/kz (3) A small amount of the CDaH came from the acetone-& A plot of [CD,] / [CDxH] us. [Ad,] / [Eds] gives k5/k2 impurity. Acetone-& was photolyzed alone a t 280 and and k3/k2 from the slope and intercept, respectively. 420". The [CD3H]/[CDa]ratio was, in both cases, 0.04 and is a measure of the acetone-& contained in the acetone&. Corrections of CD3H formed from mixtures of CD3Experimental CzD6 apd C2H6 were made on the basis that to a The light source was the full arc of a Hanovia medium pres- COCD3, approximation all CDaH came from reaction 1 and the sure mercury lamp. A cylindrical fused silica reaction 6rst from 5 could be calculated, since (k,[Ad$]) / ( k t vessel 4 X 4 cm. was placed in the center of a hollowed five CD, [CZH,])is known. Now, 4% of the CDd from reaction 5 inch aluminum cylinder. The latter was fitted with two was subtracted from the total CDsH as the contribution of quartz windows on one end and was heated electrically. acetone-& impurity. The quantity [CD&OCD31 Temperature gradients across the reaction vessel varied the means [CD8COCDs] [CDZHCOCD~].A similar from about two degrees a t the lowest to five degrees at the here correction was made to CD3H in the acetone-&thane-dq highest temperature. The average temperature was used system except that kl/kt was assumed to be equal to 2.0 in all calculations. and independent of temperature. That this correction is justified is borne out by the results to be described. (1) J. R. McNesby, T. W. Davis and A. S. Gordon, J . Am. Chem.
+ +
+
+
+
+
+ + + +
-
+
+
+
(a),
+
+
+
+
+
Soc., 76, 823 (1954).
(2) J. R. McNesby and A. S. Gordon, ibid., 76, 1416 (1954). (3) 3. R. McNesby and A. S. Gordon, %bid., 77,4719 (1955). (4) M. H. J. Wijnen, J . Chem. Phys., 28, 1357 (1955). (5) F. 0. Rice and T. A. Vanderslioe, J . Am. Chem. Snc., 80, 291 (1958). (81 F. 0. Rice and R. E. Varnerin, ibid., 77, 221 (1955).
Results A. The CD3COCD3-C2HB-C2DaSystem.-The quantity (k5(Ad6])/(kl[E]), having been precisely measured over a temperature r a ~ ~ g ecan , ~ be , ~ subtracted from [Cb,] / [CDaH] and k4/k1 evaluated.
J. R. MCNESBY
1672
Vol. 64 1.1
1.0 0.9 0.8 a'
"C
8 0.7
-
0.5 0.4
0.3
Fig. 1.-Demonstration of linearity of CD4/CD&I us. Ads/E for the system acetone-dsethane-ethane-de; ethane/ e t h a n e 4 = 0.137.
'
02t 0.1 0
I
1
I
.5E
(Ad,)
Fig. 3.-Evaluation .56
.50
I
-. . 4 8 W
.46 .44 .4 2
evaluation of kl and k4 and are shown in the Arrhenius plot in Fig. 2 where the drawn line is for the CnHe C n D s system. "he slope and interce t were measured by a least mean squares calculation ancfthe values obtained m E, El = 1.47 f 0.05 kcal. and A4/AI = 1.0 f 0.2. B. The CDaCOCDr CDaCHIlSystem.-Since none of the rate constants in the CD3CHI expenments were known relative to kb,direct application of equation 3 waa required for the evaluation of all relative rate constants. In order to know the ratios [CD,l/[CD+] at the same temperature but at three compoations it IS neceesary to interpolate in the experimental data. For this reason, were made for each of the three mixtures of [CD4]/IC81°te &I us. T. For the purposes of interpolation the beat smooth curves were drawn through the data and all subsequent data used for analysis were taken directly from these curves. Experimental precision is such that a maximum error of 1% in any of the sixteen [CD4]/[CDJH] ratios would place it directly on the appropriate curve. The data are presented in Table I1 and obedience to equation 3 is shown in Fig. 3. The plot of 1 log k 8 / h us. 1jT included in Fig 4 e v e s Ea E% = 1.87 f 0.05 kcal. and As/At = 1.4 f 0.2. Analysis of the slopes of the plots of equation 3 gives ASIAt 1.6 and Ez Es = 0.3.
+
Y
-+
of ks/kz and k&.
-
.52
9
I
3
+
.54
.
/
I
2 ( E d , 1.
COMPOSITION Ad6/E = 2.19
Fig. 2.-Arrhenius plot for isotope effect in reaction of methyl-& radical with C?Hs and C~DB.
The product ratio [CD,] / [CDBH]was measured a t a / [C2De]ratio and a t three different constant [C2H6] [Ad6]/ [E] ratios. Other methanes CHzD2, CHsD and CIIr were looked for and found to be absent over the entire temperature range. The most meaningful measurements are those a t low [Adc]/[E],since here the CD4 comes mainly from abstraction from CIDa. A t the highest of the three ratios the precision of k4/kl is poor and experiments on this mixture were only used to demonstrate the linearity of the [CD,]/ [CDsH] us. [Ada]/[E] plot (Fig. 1). The thirteen measurements made on mixtures I and I1 (Table I) were used in the
-
-
+
-
Discussion
While least mean squares calculation of the *probableerrors in the ratio of A factors and A (activation energy) produces the illusion of great precision, the fact is that a systematic error of =t2% in the measurement of k& can give an error of *40% in Aa/Aa and *25% in A(activation energy). It is, therefore, questionable to attach significance to differences of the indicated magnitudes. It is perhaps more instructive to weigh the sum of the evidence. For the reaction of CD, with acetone,'S2 s-n-butane,' CzHs C2Ds and CHaCDs the values of AD/AH are 1.25, 1.65, 1.00 and 1.38. It is possible that AD/AH generally exceeds'unity.l If departure from unity is real, quantum mechanical tunnelling may provide an explanation. Tunnelling would be expected t o give departures of AD/AH from unity
+
(7) J. McNesby and A. Gordon, J . Am. Cham. Soc., 78,3570 (1956).
Nov., 1960
REACTIONS OF METHYL RADICALS
WITH
1673
ETHAXE AND ETHANE-&
0.60 0
0.55
0.50
Y
0.45
\
n
r
0
0
0.40
-I
-+
0.35 0.30
0
CD3+ CH3COCH3t CD3COCD3
e
GD3+ S-CH3CH2CH2CH3 t CH3CD2CD2 CH3
o
C D 3 + CH3CD3
0
G D 3 t CzHgt C2Dg
A
C H 3 t CH3CD3(Ref.5)
0.25 I
I
I
1.4
1.6
Fig. 4.-Isotope
2.o
2
lO3/T, effect for reaction of methyl-d3 radicals.
TABLE I PHOTOLYSIS O F A C E T O N E d e I N THE PRESENCE O F
TABLE I1 ETHANE PHOTOLYSIS OF ACETONE-ds I N THE
T,"C.
M k I : Ad& 1.01 1.oo 0.99 .99 .97 .96 .95 .94
1
I
I .8
= 0.89
260 286 314 349 385 396 444 490
2.56 2.65 2.75 2.90 3.07 3.03 3.17 3.24
0.90 .89 .88 .88 .86 .85 .85 .84
2.66 2.75 2.85 3 .OO 3.18 3.14 3.28 3.35
290 331 338 393 487
Mix 11: A d e m = 2.19 3.72 1.oo 2.19 3.85 0.99 2.17 .99 3.81 2.17 4.07 .96 2.10 4.30 .94 2.06
4.08 4.22 4.17 4.44 4.68
277 294 310 339 387 392 422 428 482
Mix 111: Ads/E = 3.62 1.oo 3.62 4.33 4.33 1.oo 3.62 4.59 0.99 3.58 4.59 .99 3.58 4.89 .97 3.51 4.90 .96 3.48 4.92 .95 3.44 4.92 .95 3.44 5.09 .94 3.40
5.06 5.06 5.36 5.36 5.69 5.69 5.71 5.71 5.89
in the observed direction and also give anomalously large values for ED-EH. However, the temperature of the present experiments seems too high t o permit tunnelling to be important.
T ,'C.
[CD&'[CDrH] obsd.
290 328 344 396 462 266 270 337 393 433 464 270 307 347 403 459
0.485 .511 .527 .550 .595 .700 .704 ,736 .760 ,787 .810 .926 .954 .960 .981 1.014
PRESENCE O F
[Adsl/fEdrl 0.109 .109 .109 ,109 .109 .221 .221 .221 .221 .221 .221 .334 .334 .334 .334 .334
CHnCDr . .
ICD~I/[CDIHI corr.
0.489 .515 .531 -554 .600 ,712 ,716 .749 .773 .800 .824 ,950 * 979 .985 1.007 1.040
The view can also be taken that departures of AD/AH from unity merely reflect experimental error. If it is assumed that AD/AH = 1, an additional point at 1/T = 0 is available for the Arrhenius plot. If a straight line is drawn through this point and the experimental points, the slope gives A (activation energy). It is interesting that when the data for the attack of CD3 radicals upon C2H6 C2D6, CHaCD3, CD3COCDa CHICOCH,, CH3CHzCHzCHa CH3CD2CD2CH3 (secondary attack) are plotted, a single line can be drawn which may be within experimental error for all of these systems. This is shown in Fig. 4. The slope of the line corresponds to 1.50 kcal. for ED - E H . It is thus possible to predict k D / k H for any of the above systems at any temperature by the expression
+
+
+
J. R.
1674
Vol. 64
hiCxESBY
TABLE I11
SUMMARYOF ISOTOPE EFFECTS Reaction
CD3 CD3 CD3 CD3
+ CZHa CD3H + CzH6 + CH1CDa CDsH + CHiCDS + CH~CDS CD4 + CHaCDz +
+ C d h * CD4 + CzD6 --*
+
kD/kH = exp[-1500/(RT)]
-ExperimentalE, kcal.
11.5 13.0 11.6 13.5 (4)O
The experimental values obtained in this work, together with values obtained on the basis of the above argument are given in Table 111. It is appropriate to comment on the paper of Rice and Vanderslices in which a study was made of the isotope effect for the reactions. f CH3CD3
CH3
CH3D
CHsCD2
+ CHpCD3 +CH4 + CHzCD3 f
(7) (8)
The quantity ETE, was found to be 0.6 kcal. Since this value is in very poor agreement with the present work, possible Sources of the disagreement must be sought. In the work of Rice and Vanderslice, one part of CH3NaCH3was decomposed in the presence of 100 parts of C H ~ C Dand, I under these conditions, lc7/k, is given directly by [CH3D]/ [CH,] in the products. The important assumption was that the reaction CH, + C H ~ N ~ C+ H ~ C H ~+ CH~C~CH, (9)
is negligibly slow. Evidence cited in upp port of this assumption consists of the observation that changing the concentration of aomethane from 15% produced an error of only 0.3 kcal. in E7-Ef. However, certain other evidence indicates that it might have been occurring t o an important degree. First, only minor deviations from AD/AH = 1 are to be expected, while the extrapolated value of Rice and Vanderslice gives AD/AH = 0.48. The ratio of rates of reactions 9 and 8 can be calculated from known rate constants8 and the assumption that k, has the same kinetics as reaction 2. This calculation reveals that reaction 9 must have been proceeding from 13 to 22% as fast as (8) under the conditions of the experiments. Further objection to the values obtained by Rice and Vanderslice is seen by extrapolation of kD/kH for attack G f CHI on CH3CD3, CHsCD,CH3 and (CH3)&D which Herck and Szwarc, J. Am. Chem. SOC, 89, 3558 (1960),have obtained for abstraction of H and D from CsHsCHDCHs, kH/dD = 1.28 exp (-1560/RT). This agrees with equation 4 wlthin their experimental error. (8) P. Ausloos and E. W. R. Stearie, Can. J . Chem.. 33, 31 (1955).
,---Assumption: AD/AH = 1-E, koal. A , mole-1 ee. see.-'
A, mole-' ce. aec.-l
4.3 4.3 2.2 3.0
x x x x
lO'PT'/Z 10'OT1/' 10'OT 1 2 101'T'/Z
11.5 13.0 11.5 13.0
4.3 4.3 2.2 2.2
x x x x
10'OT1/* 10""~ 10'OT'/~ 10'OT1/2
gives AD/AH = 0.48, 0.22 and 0.31, respectively, on a per atom basis. These deviations from Unity are uniformly in the direction of too much H abstraction and can be understood if an extraneous Source of CH4 is Present. Two investigations of the reaction CH:
+ CsD6 +CHaD + CzDs
(10)
have been reported with widely differing results.3** It is possible t o compare (10) with (1) CDI CzH6 +CD3H CsHs (1) studies* According to the for each Of the Of Rice and Varnerin6
+
+
klo/kl = 0.46e+3W/RT
while according to McNesby and Gordon klo/kl = 3.6e-3300/RT
Although these two results are in very poor agreement, the high temperature measurement of kio/ki, in each case, is probably within experimental error of the value predicted by kD/kH = eXp[ - 1500/(RT)]
Judging by the large deviations of A d A 1 from unity it is probable that both studies were subject to systematic errors of unknown origin. While it is possible that CHz and CD3 exhibit very different kinetic behavior, this seems unlikely in view of evidence obtained in other systems. A comparison has been made for the reactions2
+
CH3 CHsCOCHs +CH4 CD3 CH3COCH3 +CDdH
+
and for CD3 CH3
+ CHzCOCHd + CH&OCHa
+ CH4 +CD3H + CH3' + CH4 +CH4 + CH3"
(11) (12) (13) (14)
No difference could be detected in the kinetics of (11) and (12) while at 625"K., I C I ~ / ~=U0.6. (9) J. R. McNeaby and A. S. Gordon, J. Am. Chen. Soc., 76, 4196 (1954). (10)F.S. Dainton, K. J. Ivin and F. Wilkinson, Trans.Forodapl SOC., 66, 929 (1959).
