JOHXH. SULLIVAI;
722
1-01. 65
THE THERMAL REACTIOKS OF HYDROGEX IODIDE WITH ALKYL IODIDES BY JOHN H. SULLIVAN Los Alamos Scientijic Laboratory, University of California, Los Alamos, New Mexico Received J u l y 18, 1960
The experimental data of Oggz on the rates of reaction of hydrogen iodide with methyl, ethyl and n-propyl iodides have been reinterpreted considering the slow rate determining step to be a reaction between an iodine atom and the alkyl iodide. The experimental data are in agreement with the mechanism: R I -+ R I (1); I R I 4 R +,Iz(2); R Iz+ R I I (3); R 4-H I + R H I (4); R R I -+ R'I R H ( 5 ) ; 1 2 21. Independent constants whlch can be obtained from this system are kl, h, k&4, and The rate of reaction 1 for each of the alkyl iodides is shown to be small compared to the rate of (2). For methyl iodide, log kr (mole/cc.)-1 sec.-l = 14.3 - 19,800/4.575T, k3& = 8, and k5/kr = 0.03. For ethyl iodide, log kz = 13.62 - 16,700/4.575T1 and k3/k4 = 8. When the activation energes for (3) are taken to be zero, the C-I bond strengths in CHII and CzH51, as determined from the activation energies of (2), are 55 and 52 kcal., in good agreement with values obtained by other techniques. For n-propyl iodide an unequivocal determination of kz, k3/k4, and kdk4 cou!d not be made, but the ratios ka/ka and k s / k 4 are found to be significantly different from the ratios for methyl 5 ks/lca. and ethyl iodides; the data are fitted by k 3 / k 4G 3
+
+
+
+
+
+
+
+
The rates of reaction of hydrogen iodide v-ith methyl, ethyl and n-propyl iodide were measured by Oggz who showed that the over-all reaction was H I R I -+ RH 12. The over-all rates were shown to be well represerit'ed by the equation
+
+
+ ki(RI)(HI)/[(HI) + which, in a given run, since (HI) + d(Iz)/dt
=
h(RI)(HI)
(12)
(1211
=
(El)
(HI)o,
reduces t o
d(Iz)/dt
=
bb(RI)(HI)
(E2)
where kb is constant only 'during a given run. These equations n-ere considered to support the following mechanism from which they were derived assuming La = lid.
+ R I ---+ R H + RI+R+I R + Iz --+ R I + I R + H I +R H + I
HI
12
I? r,21
(a)
(1) (3) (4)
From the activation energies of (1) Ogg deduced that the C-I bond strength as 43 kcal. for each of the alkyl iodides. Ho\ves.er, from fast flow pyrolysis of these iodides, thermochemical measurements,* and later electron impact data,j these bond strengths are now known to be in the range 30-55 kcal. This discrepancy has thron-n doubt on t'he aboye Since these early experiments. a large body of information on the rates of radical reactioiis has been obtained, and it is n o ~ vpossible to interpret Ogg's extensiye kinetic data in terms of a mechanism which uses some of this information. This reinterpretation yields rate coizsta1it.s and bond htrengt hs which are in agreement with results from (1) This work mas sponsored hy the U. S . ;\toniic Energy Comniission. O g g . Jr., J . Am. C h e m . Sor., 66, 526 (1931). (3) E. T. Biitler and M. Polanyi, Trans. Faraday Soc., 39,19 (1943). C. Ilorrex and R. Lapage, Disc. Faraday Soc., 10, 233 (1951). See also E. K. R . Steacio, "Atomic and Free Radical Reactions," Reinhold Publ. Corp., S e w York, N, Y.. 1951, pp. 81-81, where t h e Butler and Polanyi results are critically discussed. (1) References listed in reference 5 . ( 5 ) C . d. X c l ) o i ~ - d l and B. G. Cox, J . Chem. Piiys., 20, 1496 (1932). (6) E. 75.. R. Stcacie, "Atomic and Free Radical Reactions." Reinhold Publ. Corp., New York, N. Y.. 1954, pp. 264-267. A41aoA. F. Trotman-Dickenson, "Gas IGnetics," Butterworth Scientific Publications, 1953, p. 2 5 8 .
other kinetics investigations, together with new results. A mechaiiism which fits all of Ogg's data for each of the alkyl iodides isi RI+R+I
+ R I +R + Iz R + Iz +R I + I R + H I -+ R H + I R + R I +R'I + R H I
(1)
(2) (3) (4) (5) ( d ) (r)
I 2 f-- 21 Reaction 5 is included since it' occurs in the photolysis and pyrolysis of alkyl iodides8; the present analysis indicates that it occurred in Ogg's experiments to a slight, extent,. R'I is either CHJ, C2H41or C3H61; in the methyl and ethyl iodide systems t'he subsequent reactions of this radical are unimportant since (5) is slow compared to (4) and it is unlikely .that R'I is chain initiating. The slow rate-determining steps are (1) and (2) with the contribution of (1) to the total rate being slight after a small amount of iodine has been produced. Ogg's data, \Then int,erpret'ed using this mechanism, gives yalues of k 2 which are constant, over the total (and very large) range of experimental concentrations. ie., one hundred-fold in CHJ and in HI, thirty-fold in C2HSIand in HI, and fiyefold in H I in the n-propyl iodide r i w where the nC3HiI concentration was relatively vonsta,nt. Further evidence in favor of the present, mechanism comes from the results: (1)the ratio k 3 / k 4for methyl iodide, when calculat,ed using this mechanism, is ill good agreement wit,h that determined iii a different t8ype of experiment by Williams and Ogg9; ( 2 ) reaction 3 is generally considered to have a very low activatioii energy,'" and when this is taken t o hc zero, the artivation energies for reaction 2 are i i i excellent agreement with bond strengths determined from electron impact data.
( 7 ) A similar mechanism, b u t without reactions 3 and 5, is suggested in N. N. Senienov, "Some Problems in Chemical Kinetics and Reactivity," Vol. 11, Princeton University Press, 19.59, p. 11. S. TI-. Benson and E. O'Neal, J . Chem. Phys., 31, 514 (1961), have also q u a n titatively reinterpreted 0 ~ ~ d a' t as with reactions 2-4, d . r. (8) G. R. McbIillan and 11.. .Ilbert Koyes, J r . , J . Am. C h e m . Sor.. 80, 2108 (1958). J. L. Holmes and hllan Rlaccoll, I'roc. C h e m . T o r . . 175 (1957). See also Steacie, pp. 265-270 and pp. 397-404, and A l . Szwarc. Chem. Reus., 47, 75 (1950). (9) R . R . Williams, Jr., and R . .i. O g g , .Jr., . I . Ciiem. I'/t!Js.,16,ti'9li (1947). (10) Pee Ptr:ic:ts I?. 7 $ ? .
THERMAL REACTIOSS OF HYDROGEN IODIDE WITH ALKYLIUUIJXS
May, 1061
Treatment of Data Ogg followed each reaction by measuring the iodine concentration colorimetrically as a function of time. For on'e typical run for each alkyl iodide he presented the initial concent.rations of the reactants and a table (of iodine pressures vs. time. Since more than one hundred runs were made, such det'ailed data for ev'ery run could not be given and, instead, the data were summarized for each run by the presentation of the initial concentrations of hydrogen iodide and alkyl iodide and the experimental values of k a , kb and kl determined from the run. The calculation of the rate constants in the present mechanism are therefore necessarily of two types: (a) calculation from concent,ration vs. time data of each of the three t'ypical runs; and (b) in the case of all other runs, calculation from what will be referred to as the "summarized data" of each run. Calculation from Concentration us. Time Data.The rate equation for the above mechanism, derived with the usual steady state assumpt'ioii d(Rj/dt = 0, is
+
+
d(I)z/dt = [ h ( R I ) WRI)(I)1/[1 ka(L)/ka(HI)[1 k~(RI)/k,(H1)1]4-I~p(1)~bI - k d ( I z ) ( M ) - ki(R1)"
+
033)
The methyl iodide run was at 280', the et'hyl iodide run a t 260". As will be shown later, the rate of reaction 1 at these temperatures was negligible compared to the rate of (2) after a small amount of iodine had been formed, and in integrating this equation for these tfworuns kl(RI) was taken t'o be zero. Further, to facilitate integration, the slowly varying quantity IRI)/(HI) was set equal t'o time average values [(RIj/HI) Iav. The slowly varying concent,ration of .the reactant present in the larger amount, (RI) in these two runs, was also set equal to time average values. With these subst'itutions and with (I) = H:D(I~)~/~ where K D is the dissociation constant' for I&, the integrated equation is kZ
= ~-
2
KD(RI)svt
[(12)t1/2- (12)01/21
+
2 3 -~ X k4 k~(RI),vtIl ([RI)/(HI)la&s/kil [(H12)01/z log (H:[)01/2 (L)t'/z (HI)01/2 - (1z)o;jl (H.t)o'/*- (Iz),'/2 (HI),'/? (Iz)o'/g
+ +
[(Ip)tl/z
-
(I2)0'/21]
+
= y(t)
+
IC3
x ( t ) (E41
In using this equation zero time was considered to be a t Ogg's first optically measured concentration, Le., for methyl iodide at 480 sec. aft'er mixing, and for et,hyl iodide, at 600 sec. after mixing, during which times d f k i e n t iodine had been formed so t,hat kz(R1j(I) >:> k,(RI). Each subsequent time was measured from either of these zero t'imes. The time average values of concentrations n-ere taken to be one-half the sum of the initial and final values for each time interval. Iodine equilihium constants R:n = 8.51 X lo-* and 15.6 X lo-* (rnole/cc.)'/?at 260 and 28Oo.l2 (11) I a m indebted t o a referee far pointing out t h a t this Pqiiatiori is more accurate tlisn the equation originally derived. (12) ''Selectee. Valuesi of Chemical Thermodynamic Properties," Series 111, Natio-ial Riireau of Standards, Washington, D. C . , March 1, 19.54.
723
When y(t) was plotted against ~ ( t for ) the methyl iodide run and the ethyl iodide run, good straight lines were obtained from which k3/k4 and k2 were obtained as the slope and the intercept at r(fj = 0. As kglk4 could not be determined from these runs, we used in these calculations kS/k4 = 0.03 for CH3I and k6/k4 = 0 for CzHsIobtained from treating the summarized data below. The dependence of concentrations on time was also given for one n-propyl iodide run at 290'. However, fewer measurements were made on this run and the scatter in the data does not permit k3/k4 and kz to be determined accurately. Calculation from the Summarized Data.-Rates for each alkyl iodide were measured by Ogg a t 10" intervals in the ranges; methyl iodide 270-320" , ethyl iodide 250-300', and n-propyl iodide 260300'. The following data were given for each run: temperature, initial concentrations of hydrogen iodide and alkyl iodide, and the calculated values of Each run was followed until "at k a l kb and k1. least one-half of the reactant present in the smaller amount was consumed," and measurements of the rates were started when the "reactions had proceeded some 10% toward completion." In principle, these data from four or more runs at each temperature permit the calculation of k1, IC,, k 3 / k 4 and k5/k4 from an integrated form of E3. However, the approximations used in deriving E4 are not valid for many of the runs and without these approximations the integral of E3 is too complicated to be used in determining the rate constants. Rate constants were therefore obtained with the following method. ogg's value of kb WAS strongly dependent on thc initial concentrations (as was shown by him), but was fairly constant over the time intervals of each run. If the present mechanism is correct, kb in each run must have been an average value of a slightly varying function k ( c ) of the concentrations of the reactants. Thus, if we set the rate expresqion E2 equal to E3, we obtain k ( c ) = k b = [ki ks(RI)/k4(HI)II
+ kz(I)]/(HI)[l + kdIz)/kd(HI)[l + + [kr(I)'(M) - h ( I z ) ( M ) - ki(RI)I/ ( H I ) ( R I ) (E5)
Equation E5 may be used to calculate A.1, A.2, k 3 / k 4 ,and ks/k4 from the values of k b given by Ogg. Since k ( c ) was fairly constant over the periods of rate measurements, we may take kb for each run to be a time average of the slowly varying k ( c ) and equal to the time average of the right hand side of E5. If we replace (I) by (I) = [[kl(RI) kd(1,) (&I)]/kr(iU)]''2 and take the time average of the> right hand side of E5 to be equal to the algebraic. combinations of the time averages of the individual terms, then
+
+
k ~ [ l / ( I z ) ' / * ] ~ ,L~KD= h-1 li4
lib
[(HI)/ILJ"~]
+ $ [(RI)
[(1:)'/>ITx/[1
LI
+
-
Thiq equation is in the form of a straight line, with [1,/(12)'/2]a7,as a b c i w i , t h e righi hand i i d ~ (RHSE6) as ordinate and kl as .lope. The last term, a rewlt of the steady state (I) bring qlightly
724
J o m H. SULLIVAN
greater than K(12)'/*,is negligible in most runs and is appreciable only in runs a t the highest temperatures and lowest Iz concentrations. Values for kd were determined from the data on iodine atom recombination of Bunker and Davidson (M = 12) and of Engleman and Davidson (M = C2H51,cH31 and HI). l 3 At temperatures (320, 300' for CH3I and 300, 290' for CsHJ) where the range of concentrations was large E6-was used to determine k2, k3/krl and a rough value of kl from the values of kb14 and the initial and final concent.rations given by Ogg. RSHE6 was calculated for each run for a pair of values of k 3 / k 4 and k5/k4 and then was plotted each point representing one against [ 1/(12)'/z]av, run. This was repeated. systematically varying the trial values of k3/k4 and kj/k4 in order to choose the pair for each there was a minimum scatter in the experimental points about a linear plot as required by E6. The scatter in the data was such that k6/k4could not be determined from these runs; however, ka/k,< was in good agreement with k3/k4 = 8 determined a t lower temperatures, kl was obtained within a factor of 3, and k 2 K ~mas obtained a t the intercept 1/(11)~'~ = 0. At t,emperat,ures where the variation in ICl[ 1/ (I2)'/zIav over all the runs was small compared to k 2 K ~equation ( E T ) was used
1.01. 65
RT) gives k3/k4
The value of k 2 = 8.7 at 280'. is in good agreement with that determined below, kz = 2.04 X lo6 (mole/cc.)-l sec.-l, from the data on all runs a t 280'. When calculations were made from the summarized data, the variation in [1/(Iz)'/2]av over all runs a t 270, 280, 290, and 310' was too small to allow kl to be determined. An extrapolation using kl = Alexp(-55,00O/RT) of a rough value of kl obtained from the 320' data indicated that kl ( l/(I)l/z)at these lower temperatures was at the most (i.e., at 310') about 2% of k h . Since the variation in k1[1/(12)'"]a~ over all runs at a given temperature was less than 0.4% of kzKr,, it was justifiable to use equation E7 in determining k3/k4,k6/k4,and k2. For these temperatures, then, E7 was used with the following trial values, k3/k4 = 5, 6, 7, 8, 9, 10, 11 and k5lk4 = 0.0, 0.03, and 0.05. The values which fit the data most closely were Temp., "C.
Xa/ka
ha/kr
9 10 6 G
0.03 .03 .03 .03
270 280 290 310
Within the error of this analysis we take k3/k4 = 8 2 independent of temperature and consistent with the results of Williams and Ogg and the comkl (I/(I~)l/z) + k z K ~ RHSEG (ET) pletely reported run at 280'. At each temperature where (1/(12)'/9 is a mean value over all tlie kSfk4 is determined primarily by the data of only runs at a given temperature. The values of k 3 / h one or tJwo runs in which (RI)/(HI) >> 1. Aland k6/k4 which best fit the data were those for though its value is therefore uncertain, the data which the sum of the squares of the residuals from each temperature indicate that k5/lc4 is 2[(RHSE6)i - RHSES]' was a minimum. The definitely in the range 0.02-0.06. The large perceiitTTalue of k1 was obtained by extrapolation from a age uncertainty in 1cs/k4 has only a negligible effect higher temperature value; k 2 K ~was then deter- on the values of the other constants. mined by subtraction of the small quantity kl. At 300 and 320' [ 1/(12)1/2]av varied by a factor of (1,/(12)"2), of the order of a few per cent. of k 2 k ~ , 11 and 7, respectively. When R H S E G , using from R H S E G . k3/k4 = 8, &/k4 = 0.03 was plotted against [ 1/ I n each run, the average values in E6 or E7 were (I?)'jZ]av, the scatter of points around the best calculated for the same time interval over which t,he straight lines was large and the precision in the value of kb was determined by Ogg. This int'erval slope lil was low. However, at 320', within a fncmas taken to be that in which the reactant present. tor of 3, kl = 5 X set.-', and the value of kl in the smaller amount varied from 0.9 to 0.5 of at 300' was obtained from this using kl - Alexpits concentration a t zero time.15 Values of Kn12 (-55,00O/RT). With these values and k3/k4 = 8, which were used at 250, 260, 270, 280, 290, 300, k5/k4 = 0.03, k 3 K ~was calculated for each run a t 310 and 320" were 6.23, 8.51, 11.66, 15.6, 20.8, 300 and 320' from E6. The values of k 2 K and ~ liz 27.4, 35.6 and 46.0 X l o 4 (mole/cc.)'/2. from the individual runs show no trend with concentration of either rcactant over a hundred-fold Results Methyl Iodide.-The slope of E4 for the com- range in concentration a t 300' and a forty-fold pletely reported run corresponds to k3/k4 = 8.7 range a t 320". The mean values of k 2 K ~and k2 together with and the intercept a t z(t) = 0 is kz = 1.89 X lo6 the probable errors in k2 are given in Table I. (mole/cc.)-l set.-'. The value of k3/k4 is in agreement with the results of Williams and Oggs on the For 270, 280, 290 and 310' the mean values of photolysis of methyl iodide in the presence of hydro- RHSE6 as calculated from E7 using ka/k4 = 8, gen iodide. Their equation ka/k4 = 4.4 exp(750/ kb/k4 = 0.03 are given in column 2 . Values of k1 extrapolated from kl = 5 X Eec.-' at 320' (13) D. L. Bunker and N. Davidson, J . Am. Chem. Soe., 80, 5085 are given in column 3. The small corrections, (1958); R. Engleman and N. Davidson, ibid., 82, 4772 (1960). k1(1/(1)2''z), column 4, were subtracted from the (14) A deciuial error is present in ref. 2 and t h e values of k~ ( X values of RHSE6 to obtain lc2Kn. The uncertainty in ref. 2) are too larre by a factor of 10. (15) Since explicit data u'cre n o t given for the initial and final conin kz arising from uncertainties in the other coiicentrat,ions of each run, these limits, based on Ogg's descriptions of the stants (mainly k3jk4) is about 1 5 2 0 % . runs, were used far all runs. This procedure introduces scatter in tlie The Arrhenius equation for k2, plotted in Fig. 1, is results, b u t little absolute error. If we assume the reactant in smaller amount varied from O.!) t o 0.4 of its concentration at zero time, the calculated value of k d k 4 is lowered by about 7% and kzKD is unchanged within 17?.
*
log kt = 14.3
If we assume E3
=
-
19,800/4.575T
0, then D(R-I)
=
E2
+ D(1-I)
May, 1061
THERM.4L
REACTIONS OF HYDROGEN IODIDE
T ~ B I ,IE METHYL IODIDE,
RHSEG, Temp,
(mole/ cc )-','2
105 k ; ,
WITH
ALKYLI O D I D E S
1.3
kjlka = 8, kg/ki = 0.03 kdl/
k2KD, (mole/cc.)-1/2sec
-1
0.160 318 588 0 99 1 79 3 12
\
12
10-6 kz, (mole/cc.)-l sec.-l
(12)1'2),
OC. sec see.270 0 161 0 06" 0 001 280 320 .17' 002 290 ,i92 4" 005 300 1 0' 310 1 132 2 3" 03 320 5 a Extrapolated froin kl at 320'.
7-35
\ \*\\
37&0.03 04 f 07 82 i .1 62 i 45 5 06 i 06 6 77 & J
1 2 2 3
0
o
08
and the C-I bond strength in methyl iodide is 55 kcal. Ethyl Iodide.-The slope of E4 for the completely reported run at 2610" is k3/k4 = 7.7 and the intercept o 0.6 is kz = 5.1& X 106(mole/cc.)-l sec.-l. The summarized data of all the.260' runs gave k3/k4 = 10 and ka = 6.80 X lo6 (mole/cc.)-' see.-'. In calculating from the summarized data for 0.4 250, 260 and 270', the variation in [ 1/(Iz)1/2]5v over all rum a t each temperature was too small to allow kl to be determined. From extrapolation using k , = A I exp(-52,000/RT) of the value of k, = 1 X Lsec.-' obtained from the 290' 02 data, the lalues of kl(l/(I~)l/z)at these lower temperatures were les. than 3% of k 2 K ~ . The O 01 3 I variation of kl[ 1/ ,IJ1/~Iav over all 'runs a t a given I I I I temperature was less than 1.3% of k 2 K ~ .At these 1.65 1.70 1.75 180 1.85 1.90 I95 temperatures, thcii. equation E7 was uced to determine ka/lc4 and k?. lo3/T. Trial values k3,'k4 = 6, 8, 10, 12 and Ic6/k4 = Fig. 1.-Determination of the activation energies of 0, 0.05, 0.1 were wed in E7; lc5/k4 could not be reaction 2 . determined :idtEe best values of kB/li4were TABLE I1 Temp,
250 260 270 2E 0
O C
kdh
ETHYL IODIDE, ks/k4 = 8, k6/ka = 0
> 12'6 10,12 8, 10
68 At 290', the variation in [ l / ( I ~ ) ~ / ~ ] awas v sufficiently large to abtain the rough value kl = 1 X 10-4 from equation E6 and good fits to E6 were obtained with k3/1:4 = 6 or 8 and k5/lc4 = 0.05 or 0.1. Considering the results from all temperatures we take k3/k4 = 8 f 2, independent of temperature, and k4/k5 = 0. The values of kl, based on the 290' value, are in column 3 of Table 11. For the 290 and 300' data, kzK= and k2 were calculated for each run from E6 using lc?/k, = 8, kS/kq = 0 and the appropriate value of kl. The lL?sfrom individual runs show no trend over a twenty-fold change in concentration of either reimctant a t 280, 290 and 300'. The mean values and the probable errors in k, are given in Table 11. The values of RHSE6 a t 250, 260, 270 and 280' in Table I1 are means, the individual values for each run having been calculated from E7 using k3/k4 = 8, h / k q = 0. The small corrections k1 (l/(12)1/z) wece applied to RHSE6 to obtain the mean values given in columns 5 and 6. The uncertainty in kz arising from uncertainty in the other constants (mainly k1/k4) is about 1 5 2 0 % . (16) Only three runs were made, a n d t h e d a t a are insufficient for a determination of m / b .
250 0.307 0.03' 0.005 260 .503 .07" ,011 270 .947 .IS" .031 280 1.87 .43" .12 290 1.o 300 2.3" Extrapolated from hi at 290".
0.302 4.85 f 0 . 6 ,492 5 . 7 8 3 ~. 4 ,916 7.86rrt . 3 1.75 1 1 . 2 0 & . 2 2.87 13.8 rrt .8 5.00 18.3 rrt 1 . 1
(1
The Arrhenius equation for kp,plotted in Fig. 1,is log
ki
13.62
- 16,700/4.575T
+
If we assume Ea = 0, then D(R-I) = E , D(1-1) and the C-I bond strength in ethyl iodide is 52 kcal. n-Propyl Iodide.-In these runs: t'he variations in initial concentrations of propyl iodide were less than 20% and in almost every run (RI) < (HI). Since the variation in kl[ 1/(12]'/2)av over all the runs at a given temperature was small compared to k2KDJ equation E7 was used in analyzing the data. The concentration range over which these runs were made was too Pmall to allow ka/k4 and ks/k4 to be separately evaluated, but the calculations show that on the basis of t'he above mechanism, the rates in this system differ significantly from those in the methyl iodide and ethyl iodide systems. Thus, if we let k&( = 8 in E7 a t each of the five
i26
JOHSH. SULLIVAN
Vol. 65
temperatures, the values of kg/k4 which fit the data best are 0.5, 0.9, 0.9, 0.9 and -1.5 a t 260, 270, 280, 290 and 300'. If we take k5/k4 = 0 in E7, the best values of k3/lc4 are then 3, 3, 2, 3 and 3 a t these temperatures. The data are also satisfied by suitable pairs of values for which, roughly, k,'k4 = 3 4- 5 Ics'k4. Rate constants kz were calculated using 1c3/k4 = 3, k5/k4 = 0 in equation E7, and are given in Table 111. The values of' RHSEG are averages taken over all runs a t a given temperature. In calculating the small quantities, k1(1/(12)1~2), the values of kl at each temperature were taken to be equal to those for ethyl iodide. The values of k2 are averages over all the runs at each temperature.
stants kl, k ~ k&4 , and k5/k4 and also, very likely, the small differences in the activation energies E3-E4 for both the methyl and ethyl iodide systems. n-Propyl Iodide.-The differences between the calculated rate ratios in the propyl iodide system and those in the methyl and ethyl iodide systems may he real, or the result of a different mechanism in the n-propyl iodide system. Such a mechanism could occur by the isomerization of the propyl radical, R, to the secondary radical, sR.17 The subsequent reactions 3, 4, 5 of the radical R would then be accompanied by the similar reactions, 3', 4', 5' of sR. In determining the kinetics we may consider that a fraction f of the total number of reactions 2 give sR and a fraction 1 - f give R. The data are not sufficiently TABLE 111 extensive to obtain an unequivocal value of f n-PRoPn IODIDE, k3/k4 = 3, k5/k4 = 0 but it is possible to show from these and other literature data that: (1)f # 1, Le., the radical R does not isomerize in a time short compared to its reaction half-life in this system; and ( 2 ) if we 260 0.296 0.07 0.013 0.283 3.32 f 0 . l consider that the rate constant ratios for the n270 0.569 .18 ,030 ,539 4 . 6 2 3 ~. 2 propyl radical should be equal to those for methyl 280 1.00 .43 .OS0 .92 5.9 f . 5 and ethyl radicals, k3/k4 = 8, kb/k4 0, the n290 2.00 1.0 .18 1.82 8 . 7 rt . 1 propyl iodide data then can be explained if 10 to 300 3.45 2.3 .44 3.01 11.1 f .2 20% of the propyl radicals isomerized to secondary a Taken equal to the ethyl iodide values. propyl before reaction with iodine or hydrogen When k3/k4 = 8, lc&4 = 1 are used in E7 to iodide. With isomerization, the products of (4')and ( 5 ' ) calculate IC,, the values are about 30y0 higher than t8hose in Table 111. The assumption of a likely would be the same as those of (4) and ( 5 ) , but revalue for k , does not affect the determination of action 3' would produce sec-propyl iodide, sRI, k 3 / k 4 and k5/k4 since all runs had the same average which then would react further with iodine atoms values of (Iz); different kl's merely change k , by (2') slightly. SR + Iz +sRI I (3') The activation energy for (2) is: if k3/k4 = 3, I BRI+SR 1 2 (2') Ez = 19.3 kcal.; if k 3 / l i = 8, k5/k4 = 1, then EZ = Holmes and Maccol118 have shown that (2') is fast 18.0kcal. Taking E3 = 0 the C-I bond strengthin even with trace amounts of iodine at 214 and 236'. n-C3H71is then 53-54 kcal. At Ogg's higher temperature runs the rate of (2') Discussion would be faster by a factor of (I)280~/(I)220~ = [KD. Methyl and Ethyl Iodide.-The mechanism sug- (IZ)'/zat 280']/[K~(12)~/'a t 220'1; the ratio of the gested here explains some of the qualitative two dissociation constants is 10, and Ogg's iodine observatioii made by Ogg; (1) the reaction was concentrations were larger than the trace amounts usually "abnormally slow" at the start of the of Holmes and Maccoll by at, least a factor of 2, reaction; ( 2 ) this effect was enhanced by large ex- PO that the rate of (2') at 280' would be a t least a cess of HI; and ( 3 ) values of kt, were constant in factor of 20 greater than (2). If every R isomerized the l0-50% completion range for each run. On before reacting with iodine reaction (3') would be the basis of the present mechanism we see from E5 nullified by (2') and the inhibition of the over-all that kb is a function of concentrations and can be reaction by iodine molecules would be absent. calculated as a function of the extent of reaction Since the over-all reaction is inhibited to a t least from our values of kl, k,, k3/k4and k51k4. Such cal- an extent corresponding to k3/kq = 3, the half life culations (with k 3 / k 4 = 8.5, k5/k4 = 0.03 to obtain for isomerization cannot be short compared to the precise agreement with ogg's kbS) were made for time between formation of R by (2) and reaction of two CzHsI 300' runs, run 31b with a high value of R by (3). (HI)/(RI), and run 29b with a low value of (HI)/ Assuming that the ratios k2ik4 and k5lk4 for the (RI). In a given run ogg determined kbs from propyl radical should be equal to those for the the extents of reaction in the time intervals t 2 - tl et,hyl radical and that the apparent differences in where t z is a running variable and tl is the time for rates arise from isomerization, we may calculate 10% completion. Our calculated values corre- what fraction f of the R radicals isomerized to sR sponding to these clearly show the apparent rate and reacted by ( 3 9 , (4') and (5'). Taking kdk4 = (i.e., k b ) to be low a t the start, and this effect to 0 and also k5'/k4' = 0, a steady-state treatment with be enhanced by Pxcess H I ; the average taken over d(R)/dt = 0, d(sR)/dt = 0, d(sRI)/dt = 0, gives the 10-50% completion range was for each run the rate equation equal to the kb reported by ogg. (17) D P. Stevenson, Trans. Faradag SOC.,49, 867 (1953), has given It should be mentioned that Ogg's data are so endence t h a t s-CaH7 radicals are present In the mass spectrum of nextensive that a treatment of the primary data hexane. 118) J L. Holmes and A. Narcoll, Pror C h m . Soc., June (1957). would give much more precise valiies of the con-
-
+
+ +
THERMAL REACTIOKS OF HYI)ROGES IODIDE KITH
May, 1961
+
tl(I)a/dt = [ki(RI) kz(I)(RI)I [(I - f)/(l
+ kdId/k4(HI)) + fl
When this rate :is equated to E2 and k b is considered a time average of a fuiict,ion of the concentrations ~z'KD =
hb
[[(HI)/'(Iz)'/21av4-- [(Id1~21~vl,/ k3 [l k4
C3Hs
Iourr,~,b
i2i
reaction.
I n the pyrolysis of s-propy122 and niodide a t these temperatures, propylene is a stable product and does not react with either iodine or the alkyl iodide. The propylene, if formed, then reacted wit,h hydrogen iodide
+ I + H I +s - C ~ H+~ I
+ S 2 [ ( I d / ( H I ) l a ~ ~ ] Similar reactions have been proposed to explain(9)the C3Hs
The data fit this equation a t each temperature for li3/k4 = 8 and f := 0.1 to 0.2. If radical isomerizat.ion did not occur and if the ratios of rate constants for R are k3/k4 = 8, k5/k4 = 1, the rate equat'ions E3 and E8, from which these figures were obtained, may be incorrect. Since t'he rate of (5) is now appreciable, it is necessary to derive rate equations taking into account the reactions of the C3HsI radical subsequent to reaction 5 . The most probable reaction of the C3H61 radical would be bimolecular reactions with hydrogen iodide, n-propyl -iodideor iodine, or a unimolecular decomposit,ion GH61-+
.%LIhan1.4 x lov4 for the rate of t,he unimolecular decomposition of C2HL If, in Ogg's runs, reaction 7 had predominated over (8), the propylene was not a stable product^ since t,here was no increase in pressure during the
+
+
(19) C. E. McCauley, W. H. Hamill and R. R. Williams, Jr., J . Am. Chem. SOC.,76, 6263 (1954). (20) R . A. Ogg, Jr., ibid., 68, 607 (1936). (21) L. B. Arnold, J r . , and G . B. Kistiakowsky, J . Chem. Phys., 1 , 166 (1933).
These equations, when we take k3/k4 = 8, agree with the experimental data for k6/k4 = 0.15, 0.25, 0.25, 0.25 and 0.4 a t 260, 270, 280, 290 and 300'. If we take kslk4 0 then kJk4 = 3 is in agreement with the data a t each temperature. These ratios apply if no isomerization took place and if the rate of reactioii 7 was greater than the rate of (8). In summary, the kinetics of the n-propyl iodide system differs significantly from the kinetics of the methyl and ethyl iodide systems. Either the ratio k3Ik4 for n-propyl iodide is about one-third that for ethyl iodide and methyl iodide or the ratio k5/k4 for n-propyl iodide is much larger than that for methyl and ethyl iodide. If these ratios for all three alkyl iodides are about equal, the data for npropyl iodide are in agreement with a mechanism in which l0-20% of the n-propyl radicals isomerized to s-propyl radicals before reacting.
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(22) Reference 13. Also .J. L. .Jones and R . .4. Ogg, Jr., J . Am. Chem. SOC.,69, 1939 (1937); J. V. 8. Glass and C. N. Hinshelwood, J. Chem. Soc., 1817 (1929). (23) J. L. Joner and R.A. Ogg, Jr., .I. A7n. Chem. Soe., 69, 1931 (1937). (24) C. E. McCauley and G. J. Hilsdorf, ibid., 80, 5101 (1958).
