L. BRICE, W. CHANG,J. SMITH, AND S. SULLIVAN
2814
Kinetics of the Base-Catalyzed Isomerization of Butadiene and Isoprene Sulfones
by L. K. Brice, W. M. Chang, J. E. Smith, and S. M. Sullivan Department of Chemistry, Viroinia Polytechnic Institute, Blacksburg, Virginia 24061 (Received January 17, 1967)
The rates of the base-catalyzed isomerization of a- and p-butadiene sulfone and of a- and 0-isoprene sulfone have been measured a t several temperatures between 25 and 55" in aqueous sodium hydroxide (0.1-0.5 M ) . I n addition, the simultaneous rates of hydration of a- and 8-butadiene sulfones have been measured under the same conditions. Kinetic and thermodynamic parameters for the reactions have been calculated.
Introduction A number of olefin isomerization reactions of the type X-CH+2H=CH-Y
J_ X-CH=CH-CH2-Y
have been studied,' both for cyclic and open-chain compounds. Rate measurements have shown these reactions to occur via a carbanion intermediate, the proton transfer being either inter- or intramolecular, depending upon the structure of the olefin, the medium, and the catalyst. Equilibrium measurements have revealed a wide variation in relative thermodynamic stabilities of the two isomers with respect to changes in the structures of X and Y. Few such systems, however, have been subjected to accurate measurement of both forward and reverse rates and the equilibrium states. The purpose of this work is to provide this kind of data for further study of the effect of molecular structure on the kinetics and thermodynamics of olefin isomerization. Certain unsaturated sulfones isomerize in basic so1ution.1b~c~2 The two isomerization reactions studied here are
1
2
3
The Journal of Phyaicd Chemistry
The isomerization of p-butadiene sulfone (1) and abutadiene sulfone (2) is complicated by the simultaneous hydration of the isomers to the alcohol (3).
Results The Isomerization and Hydration of a-and @-Butadiene Sulfone. Reaction 1 is a pseudo-first-order parallel consecutive reaction, the mathematical analysis of which has been discussed by several author^.^ The method of calculation of the rate constants used here is that of Wei and Prater.3a Reaction mixtures containing various initial amounts of 1 and 2 dissolved in 0.300 M aqueous NaOH were prepared. The mixtures were analyzed for 1 and 2 by gas chromatography and the mole fractions of 1, 2, and 3 were calculated. The results for kinetic runs a t 45" are shown in Figure 1, where the mole fractions of the (1) (a) F. Asinger and B. Fell, Erdoel Kohle, 19, 345 (1966); (b) C. D. Broaddus, J . Am. Chem. SOC.,88,3863 (1966); (c) H. Zimmermannova and M. Prochaaka, Collection Czech. Chem. Commun., 30, 286 (1965); (d) D. E. O'Conner and W. I. Lyness, J . Am. Chem. SOC.,8 6 , 3840 (1964); (e) S. Bank, C. A. Rowe, and A. Schriesheim, ibid., 85, 2115 (1963). (2) (a) W. J. Bailey and E. W. Cummins, ibid., 7 6 , 1932 (1954); (b) J. Boeseken and E. de Roy van Zuydewijn, Koninkl. Ned. Akad. Wetenschap. Proc., 40, 23 (1937). (3) (a) J. Wei and C. D. Prater, Advan. Catalysis. 13, 203 (1962); (b) E. S. Lewis and M. D. Johnson, J . Am. Chem. Soc., 8 2 , 5399 (1960); (c) R. A. Alberty and W. G. Miller, J . Chem. Phys., 26, 1321 (1957).
ISOMERIZATION OF BUTADIENE AND ISOPRENE SULFONES
2815
which neither the P isomer nor the alcohol absorb appreciably. For reaction 1, the initial slope d In ( [llO [2])/dt for a kinetic run with only 1 present initially is equal to kit. First-order rate constants for various hydroxide ion concentrations were calculated from spectrophotometric data in this way and are summarized in Table 11. Figure 2 is a plot of the data in Table I1 and shows that klz is proportional to the hydroxide ion concentration up to 0.5 M between 25 and 45". Table I shows that the rate constants determined in this way are in good agreement with those obtained from the gas chromatographic data.
Figure 1. Reaction triangle for a-butadiene sulfone (2), @-butadiene sulfone (l),3-hydroxytetrahydrothiophene 1,l-dioxide (3)system (reaction 1) a t 45' in 0.300.M aqueous NaOH: 0,experimental points; 0 , the straight line reaction path. The smooth curves are reaction paths calculated from the integrated equations for reaction 1 using the relative rate constants in Table I.
Table 11: First-Order Rate Constants (sec-1) at 25,35, and 45' for the Base-Catalyzed Isomerization of a-Butadiene Sulfone (klz) and of P-Isoprene Sulfone (k45) to Their Respective a Isomers in Aqueous Sodium Hydroxide -250-
[NaOH]
three components of the reaction mixture are plotted on a triangular diagram. The relative rate constants 921 = k21/k12, 923 = k23/h2, and 913 = k13/k12 were calculated from these data using the method of Wei and Prater (see Appendix). The absolute values of the rate constants were calculated by a method also described in the Appendix. The results are summarized in Table I. Good agreement is found between reaction paths calculated4 for reaction 1 using these rate constants and the experimental points, as illustrated by the reaction triangle at 45" in Figure 1.
-350-
kiz X
krs X
kiz X
10'
10'
10'
0.10 0.15 0.20
0.120 0.305
0.426
0.25 0.30
0.153
0.591
0.35 0.40 0.45 0.50
0.136
0.180
0.472 0.577
0.266 0.725 0.262
0.790 0.951 0.958
7
-
4
5
0
7
kiz X
krs X
10'
10'
0.525
0.663
0.905 0.908 1.29 1.36
1.09
1.00 1.96 2.54
kra X 104
1.73 1.47 1.81 1.92 1.84 2.18
1.54 1.59
2.28
3.36 3.94 3.97 4.47 4.33 5.05 5.22
2.40
~~
Table I : First-Order Rate Constants for the Base-Catalyzed Isomerizqtion and Hydration of the Isomeric Butadiene Sulfones in 0.300144 Aqueous NaOH (Reaction 1) -klz
Temp,
-Relative
OC
ea1
35 45 55
0.622 0.615 0.618
rate constantsQ&a
0.402 0.382 0.397
X 104,sec-1-
e12
Go methodb
0.038 0.055 0.033
0.605 1.77 4.98
uv
methodC
0.600 1.73
...
a Calculated from gas chromatographic data by the method of Wei and Prater.3. Calculated from gas chromatographic data as described in the Appendix. Calculated from ultraviolet data as described in this section.
'
The concentration of a-butadiene sulfone in the reaction mixture can also be determined spectrophotometrically by measuring t h e optical density of the reaction mixture (after quenching with HCI) a t 220 mp, a t
The Isomerization of a- and P-Isoprene Sulfone in Dilute Aqueous Sodium Hydroxide. The rate of isomerization of P-isoprene sulfone (4) to a-isoprene sulfone (5) in dilute aqueous NaOH (reaction 2) was also measured spectrophotometrically and by gas chromatography. The reaction is first order in sulfone and first order in hydroxide ion over the concentration ranges studied (0.02 and 0.2 M sulfone; 0.10-0.5 M NaOH). The results are summarized in Table I1 and Figure 2. Table I11 and Figure 3 show the results of a typical kinetic run. The reaction approaches an equilibrium point independent of the hydroxide ion concentration. The (4) The reaction paths were calculated from the integrated equati0ns3~for reaction l with the aid of a n I B M 7040 computer. The authors are indebted to Dr. Clyde Kramer of the V P I Statistics Department and Mr. James Nash of the V P I Computing Center for writing the computer program.
Volume 71, Number 9 August 1967
L. BRICE, W. CHANG,J. SMITH,AND S. SULLIVAN
2816
50
0 0
1
3 [NaOHl.
2
100
150
Time, min.
5
4
Figure 2. Hydroxide ion dependence of the first-order rate constants for the base-catalyzed isomerization of @-butadienesulfone ( 0 )and of 8-isoprene sulfone (0)to their respective a! isomers in aqueous NaOH a t 25, 35, and 45". Data in Table 11.
Figure 3. Determination of first-order rate constant (k45) for the reversible isomerization of &isoprene sulfone to a-isoprene sulfone in 0.500 M aqueous NaOH at 35". Data in Table 111.
sodium hydroxide concentrations of 0.1, 0.2, and 0.3 Table I11 : Typical Kinetic Run for the Reaction 4 Time, min
@ 5"
The rate constants obtained agreed with those in Table 11,indicating that the salt effect on reaction 2 is negligible.
[4 1
0.0200 0.0153 0.0120 0,0098 0.0078 0.0066 0.0053 0.0044 0.0022
0 20 40 60 80 100 120 140 m
M and in which the total ionic strength was maintained constant (0.4 M ) by addition of sodium chloride.
Discussion From the data in Tables I and IV, the thermodynamic and kinetic parameters for the two isomerization reactions 1 and 2 were calculated and are summarized in Table V. Further comparison of the two reactions can be made by calculating the specific rates of isomerization relative to the conversion 1 -P 2, taking lc12/2 =
a Initial concentration of @isoprene sulfone, 0.0200 M ; concentration of NaOH, 0.500 M ; temperature, 35".
same equilibrium point is reached starting with the pure CY isomer. Rate and equilibrium data obtained a t four temperatures are summarized in Table IV. Additional kinetic runs were performed a t 35" with Table IV : Second-Order Rate Constants and Equilibrium Constants for the Base-Catalyzed Isomerization of a!- and 8-Isoprene Sulfones in Aqueous Sodium Hydroxide k'46
x lo',
Temp,
M-1
OC
8ec -1
K46
25 35 45 55
0.135 0.450 1.29
7.33
...
The Journal of Physical Chemistry
... 7.00 6.68
Table V : Kinetic and Thermodynamic Parameters" at 25" for Base-Catalyzed Sulfone Isomerizations in 0.300 M Aqueous Sodium Hydroxide AS
*,
ASo,
Reaction
kcal/ mole
call mole deg
kcall mole
kcal/ mole
call mole deg
1+2 4+5
20.1 20.4
24.6 26.1
-0.29 -1.21
0 -2.2
0.9 -3.3
AH*:,
AGO,
AH',
' Activation parameters (A. A. Frost and R. G. Pearson, "Kinetics and Mechanism," John Wiley and Sons, Inc., New York, N. Y., 1961, p 99) were calculated from k = (RT/Nh)eAS*/Re-AH*/RT. Standard state is 1M in all cases. Mackle (H. Mackle and P. A. G. O'Hare, Trans. Faraday SOC., 57, 1873 (1961); also, private communication) has measured the enthalpies of combustion a t 25" for sulfones 1, 2, 4, and 5, from which the enthalpies of isomerization of the solids can be calculated. The results are -1.1 f 1.6 kcal/mole for 1 2 and -0.9 f 1.6 kcal/mole for 4 + 5.
'
-
ISOMERIZATION OF BUTADIENE AND ISOPRENE SULFONES
1. The statistical factorJ of '/z is included since sulfone 1 has two equivalent reaction sites. The results at 45" are
The effect of the methyl group is to increase the rate of conversion of the @ to the CY isomer and to decrease the rate of the reverse reaction, thus resulting in a net increase in thermodynamic stability of the CY isomer. Table V shows that the latter effect results from a decrease in the enthalpy of isomerization which overcomes a small decrease in the entropy of isomerization. Similar results have been reported for reactions 1 and 2 in various alcoholic media,'" where the average values of K l z and Kd5a t 23' are 1.3 f 0.2 and 2.4 f 0.2, respectively. It should be noted that the change from alcoholic media to water has a greater effect on the equilibrium constant for the isoprene sulfone system than for the butadiene sulfone system. The kinetic data for reactions 1 and 2 are consistent with a carbanion intermediate mechanism. Recent worklb on the deuterium exchange of sulfones 1, 2, and 3 has shown that exchange takes place at a rate comparable to isomerization and hydration, so that the proton transfer accompanying the isomerization reaction is intermolecular.
Experimental Section Materials. p- Butadiene sulfone (sulfolene) (1) and p-isoprene sulfone (3-methylsulfolene) (4) were obtained from the Special Products Division of the Phillips Petroleum Co., Bartlesville, Okla. The crude sulfones were crystallized from methanol and vacuum dried. Melting points were 63.5-64.5' for 1 (lit.2863.5-64.5') and 62-63' for 4 (lit.2b62-63'). The CY isomers (2 and 5 ) were prepared from the corresponding @ isomers by standard laboratory procedures.2 Nelting points were 47-48' for 2 (lit,2* 4849') and 77-78' for 5 (lit.2b79'). The compound 2-methyl-4,5-dihydrothiophene 1,ldioxide ( 6 ) , used as an internal standard in the gas chromatographic analysis, was obtained from Dr. J. A. Rigney in this laboratory; mp 69.5-70.0" (lit.6 68-69"). Kinetic Measurements. For monitoring reaction 1 by gas chromatographic analysis, reaction mixtures having a total initial sulfone concentration (1 plus 2) of 0.200 M and a sodium hydroxide concentration of 0.300 M were prepared and thermostated. Samples
2817
were removed periodically and quenched with an equal volume of a solution containing 0.320 M HC1 and 1.100 M sulfone 6, which was used as an internal standard. Each sample was then injected into an Aerograph Model 204 gas chromatograph (hydrogen flame ionization detector) with a 10.0-p1 capacity syringe, the injection sample size being 1.4 pl in all cases. From the peak areas and previously determined calibration curves of peak area vs. concentration, the concentrations of 1 and 2 were calculated. Good separation of sulfones 1, 2 and 6 was obtained by using 6.3% Carbowax 1500 on Gas Chrome Z (mesh size 80/100) in a 4.3-ft length of 1/8-in. 0.d. stainless steel tubing. Column, detector, and injector temperatures were 135,240, and 175", respectively, with a helium carrier gas flow rate of 46 ml/min. Retention times for sulfones 1, 2, and 6 under these conditions were 1.5,4.0, and 2.2 min, respectively. Reaction 1 was followed spectrophotometrically using a Beckman DU spectrophotometer. Sulfone 2 absorbs strongly at 215 mp (molar absorbancy index, 193 M-' cm-l) whereas sulfones 1 and 3 have negligible absorbancies above 210 mp. Reproducible results were obtained at 215 mp even though the absorbance vs. wavelength curve for sulfone 2 is rather steep in this range. Reaction mixtures were quenched with standard HC1 before spectrophotometric analysis. Initial sulfone concentrations of 0.0100 and 0.0200 M were used and gave identical kinetic results. Reaction 2 was followed in a similar manner by gas chromatography and spectrophotometry. Since only the ratio of isomer concentrations was needed, an internal standard was not used in the gas chromatographic analysis. Retention times for sulfones 4 and 5 under conditions comparable to those described above were 2.7 and 7.9 min. The molar absorbancy index of sulfone 5 at 223 mp is 155 M-l cm-l. Sulfone 4 does not absorb appreciably at this wavelength.
Acknowledgment. This work was supported in part by grants for undergraduate research from the National Science Foundation and the Petroleum Research Fund of the American Chemical Society.
Appendix Let al, a2, and a3 represent the mole fraction concentrations of sulfones 1,2, and 3. Then the rate equations for reaction l can be expressed by the matrix equation ~
~~
~~
(5) S. W.Benson, J . Am. Chem. SOC.,EO, 5151 (1958). (6) S. F. Birch and D. R. McAllan, J . Chem. SOC.,3411 (1951).
Volume 71, Number 9 August 1967
L. BRICE,W. CHANG,J. SMITH,AND S. SULLIVAN
2818
d-a- Ka dt
(3)
where CY is the composition vector (4)
and where K is the rate-constant matrix
K
- (kl2 + h 3 )
=
(
k21
- (k21
k12
k13
+
k23
k23)
:)
(5)
0
As shown by Wei and Prater,' eq 3, 4, and 5 can be transformed to another coordinate system, called the characteristic coordinate system, where the variables in the rate equations are completely uncoupled so that solutions to the equations are more easily obtained. The matrix rate equation in the characteristic system is dp _ -- Ab dt where
b =
(i!)
(Actually, the reaction rate-constant matrices K' = K/k12 and A' = A/X2 are more readily obtained, as described below.) The matrix X can be determined from a knowledge of (i) the reaction path along which al/u2remains constant throughout the reaction (the straight line reaction path; see Figure 1) and (ii) the equilibrium composition of the subsystem 1 z=t 2. For reaction system 1, all reaction paths converge to the straight line path, as shown in Figure 1. The initial composition of the reaction mixture for this path a t 45" is a1" = 0.432 and azo = 0.568. The equilibrium composition for the subsystem 1 e 2 can be obtained as follows. Let ut, be the mole fraction of species i in a reaction mixture containing only species j initially. Then from the integrated equationsae for reaction 1, it is easily shown that a21/a12 is equal to the equilibrium constant for the reaction 1 2, K12 = l/&, where a12and a21 are measured a t corresponding times. In particular, a12 and a21 can be accurately determined a t their maxima (which occur a t the same time t), as can be seen by plotting the data in Table VI for kinetic runs at 45". From these data we obtain (u12)msx= 0.252 and (u21)max= 0.410, so that Kl2 = 1.63. The equilibrium mole fractions for the subsystem 1 Ft 2 then are al* = 0.381 and u2* = 0.619. The matrix X calculated from these data is
*
and
0 A = (0 0
x=
0 --XI
0
The matrices and A represent the composition vector and the rate-constant matrix in the characteristic system. The solutions to the three rate equations in the characteristic system are thus seen to be of the form
b, = b,"e-A*t
(6)
The transformation from the natural to the characteristic coordinate system is effected by a 3 X 3 square matrix X whose elements are the coordinates in the natural system of the three unit vectors in the characteristic system. The matrix X is used first to transform the real composition vectors CY a t each time t into the characteristic composition vectors p
p
x-'a
=
(7)
The rate constants X1 and A:, in the Characteristic system can then be evaluated by means of eq 6. The rateconstant matrix in the natural system is t.hen calculated from A as
K
=
XAX-l
The Journal of Physical Chemistry
(8)
0.000 0.000 1.000
(
0.430 0.570 -1.000
1
0.447 -0.549 0.102
and is used to transform the a-composition vectors into the p-composition vectors according to eq 7. The results for a kinetic run at 45" with only 1 present initially are summarized in Table VI. From eq 6 it is easily shown that a plot of log bl vs. log bz has a slope of X 1 / X 2 . The results for the kinetic run a t 45" just described are shown in Figure 4, from which we obtain XI/XZ = 0.133. The rate-constant matrix in the characteristic system is then A = -A*(!
0 g.133
H)
Transformation of A to K by means of eq 8 and normalizing to a relative rate of 1 for reaction 1 + 2 yields -1.055 1.000 0.055
0.615 -0.997 0.382
0.000 0.000 0.000
(7) See ref 3a for details of the method outlined here.
ISOMERIZATION OF BUTADIENE AND ISOPRENE SULFONES
0.15 0.08
1
2819
Table VI: Composition Data Used to Evaluate Kls and XI/Xn for Reaction 1 at 45O in 0.300 M NaOH d
t,
min
(aSo
-
4) 1
(ado
-
1
8(0°
0
10
I
t
#
t
*
I
0.4
0
a
0.8
t
1
1.2
20
-Log br.
Figure 4. Determination of XI/X, ratio for reaction 1 in 0.300 M aqueous NaOH at 45'. in Table VI. Slope gives XI/&, = 0.133.
0.0555
Data
1.0000
35 0.0330 55
80
0.6125
1.0000
(0.2310) 0.5100 0.2790
(0.5180) 0.3800
(1.0000) 0.9250
0.1020
0 * 2690
0.2995
0.1475
0.1694
0.3395
0.1800
0.1215
0.2490
0.3700
0.4060
0.2600
100
120
60
0
140
160
100
Time, min.
Figure 5. Determination of kla for reaction 1 in 0.300 M aqueous NaOH at 45'. Data in Table VI.
160
from which the relative rate constants a t 45" in Table I are calculated. The value of k12 can be obtained as follows. By dividing the integrated equation for a1 by that for a2 for a reaction in which only compound 1 is present initially, we obtain
' Calculated from a ( t ) for (a&
0.0644
= 1, by means of eq
Whent-*co,(ul/as)-*(P+Q-Bia-
7.
1); s o e q 9
upon rearrangement becomes
(9)
where
P -and
+ e21 + e23 +
013)
Since Q and (aI/&)- can be calculated from the relative rate constants et, (Q = 0.784 and (al/ae).. = 0.758 a t 45", for example), Iclz can be obtained from the slope of the left-hand side of eq 10 plotted against time. Figure 5 shows a plot of eq 10 using data at 45" for reaction 1.
Volume 71, Number 9 Auuuat 1967
