737
NOTES Methyl Red Dissociation Kinetics in
t o an increased rate of
2L
+ CHsOH -+
4HI
+ CO (surface)
Because of the surface sensitivity of the rate, no attempt was made to measure IC&. Z, and we conclude that 26.0 kcal/mol is at least a lower limit to the activation energy of the homogeneous part of step 1, in view of the observed A factor. This value of El leads4to a C-H strength of 95.5 f 2 kcal/mol for XeOH, which is greater than the limits ( 92 Ikcal/mol) set by the study2 of the photobromination of &OH. Recent work by Loucks and Laidlerlo yields the value of -91 kcal/mol for the C-H bond strength in dimethyl ether which may be expected to be similar to that in methanol. The 0-H bond strength in MeOH is 103.6 kcal/mol'l and the a-bond strength in formaldehyde is defined as AH for the reaction
Dilute Aqueous Solution1 by L. P. Holmes, A . Silzars, D. L. Cole, L. D. Rich, and E. M. Eyring Department of Chemistry, University of Utah, Salt Lake City, Utah 8 4 I l Z (Received August 1 5 , 1 9 8 8 )
Methyl red is a frequently used acid-base indicator in temperature-jump relaxation method2kinetic studies, and a knowledge of the specific rates in eq 1 is unnecessary if the sample system equilibrium has a relaxation time 7
CHzO -+ CHz - 0
methyl red anion (1)
i.e., the difference in AH for the reactions
+ H. CH20H +CH2O + Ha CH30H +CHIO.
+
(y)
which is 103.611- 2912J3 ( f 2 ) = 74.6 f 2 kcal/mol. This is exactly the same as DT0(acetone)l4(74.6 kcal/mol) and substituents seem, therefore, to have in contrast to the little or no effect on the value of Owo, situation for olefins
Dwo( CH2= CH2) = 59.1 kcal/mol DTo[(Me)2C= CHz]
=
long compared to that of this methyl red equilibrium. However, in studying diff usion-controlled reactions, such as A10H2+ 3. H+ APf HzO characterized ,~ by relaxation times of the order of 4 ~ s e c known values of kD and k R are needed for a reliable interpretation of spectrophotometric temperature-jump relaxation data. Values of kD and kR have been determined by an electric field-jump (E-jump) relaxation method2 and are reported here to meet this need,
55.8 kcal/mol
A possible reason for the invariance of DToin the ketones is that in the carbonyl T bond, the electrons are as far removed from the C atom as they are in the biradical formed, when the 7r bond is broken. There will, therefore, be no change in the stabilizing effect of substituents such as methyl groups as the r bond is broken. This would imply that the sp2 C atoms in propylene and in the butenes are probably slightly more polar in the biradical than in the ground-state olefins, so that there is decreased energy in a bond formation. This is not an unreasonable conclusion. Acknowledgments. The authors wish to thank Drs. D. 31.Golden and G. R. Haugen for helpful discussions. (10) L. 33. Loucks and K. J . Laidler, Can.
J. Chem., 45, 2785 (1967). (11) S. W-.Benson and R. Shaw, Advances in Chemistry Series, No. 75, American Chemical Society, Washington, D. C . , 1968,
Experimental Section Dilute aqueous solutions of Xational Aniline Division methyl red recrystallized from water, mp 183-185" (lit,4 181-182"), were subjected t o an electric field jump of 2 x lo5 T'/cm in the form of a single, square, high-voltage pulse of 2 to 3 ysec duration. A block diagram of the E-jump apparatus is shown in Figure 1. The sample cell was fashioned from Plexiglas with stainless steel electrodes spaced 2 mm apart. White light from a 300-W zirconium arc passed through a 320-nm interference filter and through 1 cm of solution in the sample cell before striking the photocathode of a 1P21 photomultiplier tube. The photomultiplier tube was operated below 500 V to avoid saturation. The distance from the sample cell to the photomultiplier tube was made large (4.5 m) t o minimize the need for shielding from stray electromagnetic fields. The exponential decay in per cent light transmitted as a function of time was observed through a Tektronix Type W preamplifier on a Type 545 oscilloscope. The
p 288.
(12) The flgure 29 kcal/mol is derived from the experimental data a s follows: A H p (CHsOH) = -48.0 kcal/molls and AHf" (H.) =52.1 kcal/mol, whence AHfo ( a CHZOH)=D(H-CHzOH) +AHp (CHsOH) -AHP (R.)= -4.6. A H p (CHZO)= -27.7 kcal/mol,~4 so t h a t A H = -27.7 f 5 2 . 1 +4.6=29 kcal/mol. (13) 9. W. Benson, "Thermochemical Kinetics," John Wiley and Sons, Inc., New York, N . Y.,1968. (14) R.Walsh and S.W. Benson, J.Amer. Chem. SOC.,88,3480 (1966).
(1) Supported by Grant AM 06231 from the National Institute of Arthritis and Metabolic Diseases. (2) M .Eigen and L. DeMaeyer, "Technique of Organic Chemistry." Vol. V I I I , P a r t 11, S. L. Friess, E . 9. Lewis, and A. Weissberger, Ed., Interscience Publishers, New York, N. Y., 1963, Chapter 18. (3) L. P. Holmes, D. L. Cole, and E. M. Eyring, J. Phys. Chem., 72, 301 (1968). (4) H.T . Clarke and W. R. Kirner, Org. Syn., 2, 47 (1922). Volume 73, Number 9 Mawh 1969
738
NOTES
-43 P
n
4-
C,R, 0.
I
T
I
Figure 1. Block diagram of the electric field-jump relaxation method apparatus. RI = lo7 ohms, RI = 200 ohms. The triggered spark gaps G are both E, G, and G. Nodel GP-15; T, trigger pulse generator and time delay; L, zirconium arc and interference filter; S, sample cell; P, photomultiplier,
Table I: Electric Field-Jump Relaxation Data for Aqueous Methyl Red a t 25" Go,' 10-6 M
pHb
41,9
5.146 5.163 5.164 5.600 5.145 5.805
31.4 23.5 7.51 3.59 3.27
p.sec
T , ~
0.62 3t. 0.10 0.73 f 0.16 0.83 f 0.11 1.16 3t. 0.10 1.24 f 0.04 1.67 f 0.58
=H+ + kn
nd
4 3 3
4 3 5
a Total methyl red molarity of sample solution calculated from the measured molar absorbance a t the 460-nm isobestic point assuming a molar extinction coefficient of 15,300 1. mol-' cm-1. b Glass electrode pB of the sample solution. 0 Average electric field-jump relaxation time with standard deviation calculated from the range of n independent, measuremente. d Number of independent determinations
of
lom486 is in good agreement with the literature vahie6J of 10-5.00a t zero ionic strength and 25'. This value of lc~lis approximately a third of that ealculated from the Smoluchowsky-Debye-Eigen phenomenological equation2 for diff usion-controlled reaction between H+ and a spherical monoanion in water a t 25". Very similar differences between experimental and theoretical values of k R have been observed2 for such acids as p-nitrophenol, carbonic acid, and acetic acid and attributed largely to steric factors. The k~ for methyl red is also significantly smaller than values of 8 X 1O1O M--' sec-l and 7.2 X 10loM-l sec-l reported6 for the indicators bromocresol purple and phenol red, respectively, in water at 15" from similar E-jump relaxation method experiment . This difference can be ascribed almost entirely to the greater attraction of a dianion for a proton in the equilibrium
7.
resulting relaxation times are given in Table I. The estimated experimental error in the individual measurements of T is =tl5%, The electrical resistance of the sample cell in all cases exceeded lo4 ohms so that the jump in temperature incident to the E-jump was negligible. The reliability of the apparatus was verified by reproducing the kinetic results of Ilgenfritz6 for aqueous bromocresol purple. Since the ionic strength of our sample solutions never exceeded 2 X 10-6 114, we were able to approximate the hydrogen ion molarity by the relation [H+] = 10-pH where the glass eIectrode pH was determined with a Reckman 1019 meter.
Results and Discussion The relaxation time 7 attributable to equilibrium 1 is given by2
HA-
A2-
(3)
kR
which is under observation in the case of these two sulfonephthaleins. The value k~ = 4.8 X lo6 sec-l for methyl red is much larger than the corresponding constants 2.4 X lo4 sec-' and 4.9 X 102 sec-l found6 for aqueous bromocresol purple and phenol red, respectively. However, methyl red proton dissociation is from a resonance stabilized, zwitterionic acid,' whereas, in the sulfonephthaleins a phenolic proton dissociates. Thus, R more instructive comparison is that between methyl red and benzoic acid ( I c D = 2.3 X lo6 sec-1)8 as well as the three isomeric aminobenzoic acids. The values8 k D = G,4 X 106, 7.4 x lo6, and 4.4 x lo5 sec-' for o-, m-, and p-amino benzoic acids, respectively, indicate that the difference between k~ for benzoic acid and methyl red can be accounted for entireIy in terms of zwitterionic forms of protonated methyl red that do not involve significant intramolecular hydrogen bonding. Where intramolecular hvdrogen bonding is important as in N N-dimethylo-aminobenzoic acid, k~ drops tos -, 1 X lo2 sec-l. Successful measurements of 7 as short as 0.2 psec with this spectrophotometric E-jump device suggest the feasibility of measuring the rate of the helixrandom coil transition in aqueous poly-L-glutamic acid and poly-L-tyrosine. Previous studiesQ have shown that the relaxation time for this transition in these polyanions lies between 0.05 and 2.0 psec, which is too fast for measurement by the more common Joule heating temperature-jump relaxation method. (5) G. Ilgenfritz, Doctoral Dissertation, George August University, Goettingen, Germany, 1966. (6) I. M.Kolthoff, J. Phys. Chem., 34, 1466 (1930).
The least-squares straight line drawn through a (7) 9. W. Tobey, J. Chem. Educ., 35, 514 (1958). (8)-M. Eigen and E. M. Eyring, J. Amer. Chem. Soc., 84, 3254 (1962). 7-1 us. ([H+] [A-1) plot of the data of Table I has (9)G. Schwarz, J. Mol. Biol., 11, 64 (1965): R.Lumry, R. Legare, a slope k~ = 3.5 x 1O1O M-1 sec-' and an intercept and W. G. Miller, Bdopolymers, 2, 489 (1964); and E. Hamori k~ = 4.8 X 106 sec-l. The quotient K , = k ~ / =k ~ and H. A . Scheraga, J. Phys. Chem., 71, 4147 (1967).
+
The Journal of Physical ChemiutTy
