2400
NOTES Protolysis Kinetics of Diamines i n Sulfuric Acid
treated with silver oxide to form a quaternary hydroxide. This, when mixed with sulfuric acid, gave the desired quaternary sulfate salt in a solution of known by Donald E. Leyden* and J. M. McCall, Jr. acidity. Stock solutions of sulfuric acid were prepared Department of Chemistry, University of Georgia, by dilution of 96% sulfuric acid (J. T. Baker, AR), Athens, Georgia 80601 (Received Januaru 26, 1971) and standardized with potassium hydroxide. Publication costs borne completely by The Journal of All pK, values were determined by potentiometric Physical Chemistry titration using a Corning Model 12 pH meter and NBS standard buffers. The titrant used was standardized, carbon dioxide-free potassium hydroxide. The temExcept for several papers concerned with protonation perature was maintained a t 25.0 f 0.1”. thermodynamics, previous study of acid-base reacExchange rate values were calculated by matching tion kinetics of amines has been almost exclusively concomputer simulated curves to the experimental spectra. cerned with monoamines and amino carbonylates. The equation used to simulate the curves was similar Considerable work has been done on the protolysis to those given by Arnold for spin-coupled systems in kinetics of tertiary amines using high-resolution nuclear which the coupling is small relative to the chemical magnetic resonance and spin-echo technique^.^-^ Conshift difference of the coupled nuclei.” In all cases the sidering these systems fairly well known, there should line shape of the methyl proton resonance was used to be similarities between these results and the protolysis calculate the proton exchange rate. The value of T 2 reactions of diamines when the amino groups are sepwas measured frequently as the line width a t halfarated by long chain lengths. Yet significant influence height of the methyl protons in solutions of low acidity of the second amino group may be expected as the and was assumed to be controlled by inhomogeneities separation of the amino groups is decreased. These in the magnetic field. Computer processing was done differences could arise from steric and coulombic effects on an IBM 360/65 remote terminal Model 2741. and possibly proton chelate formation. Accordingly, Kinetic data were taken for I and I1 over a concenthe protolysis kinetics of N,N,N’,N’-tetramethyl-l,2tration range of 0.1-0.7 M . The concentration dediaminoethane (I) and its monoquaternary methyl pendence of the rate of exchange was nonlinear and the sulfate (11), N,N,N’,N’-tetramethyl-l,3-diaminoproapparent rate increased only slightly at low concentrapane (111),and N,N,N’,N’-tetramethyl-l,4-diaminobution and rapidly increased above 0.4 M . The change tane (IV) were studied. The acid dissociation conin rate with concentration was not related to concenstants of these compounds vary sufficiently to require a tration or viscosity in any simple manner. It was wide range of acidity for the study. The study was concluded that an accurate representation of the acidity undertaken using a sulfuric acid-water solvent system could not be made using acidity function values under to take advantage of Hammett acidity values in the these conditions. Therefore, the apparent rate was highly acidic region. lo The investigation yielded determined over the above concentration range and kinetic parameters and dissociation constants for these extrapolated to zero concentration. The rate constants compounds and interesting observations related to the reported were calculated from the extrapolated data. chain length.
Experimental Section All spectra were recorded using a Hitachi-PerkinElmer R-20 high-resolution nuclear magnetic resonance spectrometer equipped with a variable temperature probe. A standard temperature of 25” was chosen for all the compounds and was checked frequently to ensure accuracy to f1 ” . Care was taken to avoid saturation during each experiment. The compounds used, with the exception of I and 11, were obtained from Aldrich Chem. Co. I was obtained from Eastman Organic Chemicals. No further purification was necessary. The quaternary salt (11) was prepared from the tetramethylamine and methyl iodide. The resulting iodide quaternary salt was then T h e Journal of Physical Chemistry, Vol. 76, N o . 16, 1971
Results and Discussion A number of reactions have been shown to apply to the study of proton exchange in aqueous solu(1) F. Holmes and D. R . Williams, J . Chem. Soc., A , 478 (1967). (2) A. Vacca and D. Arenare, J . Phys. Chem., 71, 1495 (1967). (3) A . Loewenstein and S . Meiboom, J . Chem. Phys., 27,1067 (1957). (4) E. Grunwald, J . Phys. Chem., 67, 2211 (1963). (5) E. Grunwald, ibid., 67, 2208 (1963). (6) 2.Luz and S.Meiboom, J . Chem. Phys., 39, 366 (1963). (7) E. K . Ralph and E. Grunwald, J . A m e r . Chem. Sac., 89, 2963 (1967). (8) E. Grunwald and A. Y. Xu, ibid., 90, 29 (1968). (9) E. Grunwald and E. K. Ralph, 111, ibid., 89, 4435 (1967). (10) E. M . Arnett and G. W. Mach, dbid., 86, 2671 (1964). (11) J. T. Arnold, P h y s . Rev., 102, 136 (1956).
2401
NOTES tions.S~6~9112-~~ The potentially significant reactions for diamines are
+ HzO +HBB + H30+ +HBBH+ + OH- "2, +HBB + HzO +HBBH+ + +HBB -% +HBB + +HBBH+ +HBBH+ + H2O + +HBB -% +HBB + HzO + +HBBH+ +HBBH+
+HBB ka_ BBH+
(1) (2)
(3)
+ HS04- ka_ +HBB + HzS04 +HBBH+ + SO?- k?_ +HBB + HS04-
ks.
+HBBH+---HOH
+ HzO k-
+HBB---HOH
(5)
B
+HBB---NOH
(4)
where +HBBH+ represents the diprotonated amine. Since the system also contains sulfuric acid, other mechanisms of proton exchange involving sulfate and bisulfate ions acting as bases should also be considered.16 +HBBH+
r e a ~ t i o n 7 ~ Q ~ l " 1The ~ - ~first ~ step is a transfer of the proton from a hydrated amine molecule to the solvent water with retention of the N . . "OH hydrogen bond. This is followed by complete breakage of the N. .HOH bond in a second step. The two steps are shown in the following equations.
+ H30+
(sa)
"a, +HBB + HOH
(8b) The first equilibrium is that process identified with the acid dissociation constant of the compound. The second step is the process detected using nmr observation of the amine. Equation 9 may be obtained from eq 8 after applying a steady-state approximation to the concentration of +HBB---HOH
(6)
(7)
Consideration of the medium enables us to immediately reject several of these reactions. Reaction 2 has been shown to be negligible in solutions of very low pH because of the extremely low concentration of hydroxide ions.16 Also, reaction 3 has been shown to be negligible for trialkyl monoamines due to steric factors.* Reactions 6 and 7 were considered even though a 10-100fold greater amount of water is present. However, the protolysis rate was observed to increase sharply as the concentration of both HS04- and sod2- decreased; thus they could not play an important part in determining the overall rate. Experimentally, a variation in the concentration of the amine a t constant acidity produced no effect on the observed rate which demonstrated that no mechanism second order in amine was important. Therefore, reactions 3 and 4 may be neglected. Reaction 5 represents the transfer of a proton from one side of the diamine to the other by formation of a ring structure. This is deemed unlikely since in strongly acidic solutions even one side of the diamine would not be likely to be completely deprotonated for very long. However, ring formation could take place incorporating a water molecule. At any rate these possibilities could not be ruled out without further investigation. We reasoned that if reaction 5 were important, a significant drop in the rate would occur upon quaternization of one side of I. An investigation of the monoquanternary salt (11) showed the protolysis rate actually increased slightly. This ruled out any sort of intramolecular exchange mechanism. Thus reaction 1 is found to be the mechanism which significantly contributes to the total rate observed. Reaction 1represents the net process of proton exchange with water, but several workers have found it more meaningful to divide this total process into a two-step
where [ +HBBH+J represents the total concentration of the diprotonated species. This equation together with a second term in cases where reaction 4 is important have been successfully used to describe the protolysis kinetics of a wide variety of amine^.^^^^^^ Depending upon the relative magnitudes of k~ and k-,[H30+], one may be able to simplify the denominator in the preceding rate expression by neglecting one or the other term. A plot of 1,'' us. l/aH t (or l/ho) at several concentrations of amine gave a straight line with an intercept of zero within experimental error for I, 11, and 111. Assuming k-,[H30'] >> k ~ the , first term in the denominator of eq 9 can be neglected and we can calculate k~ from the slope and known K,. However, IV gave a curve as shown in Figure 1. This curve may he divided into three regions; the first is at high acidity where k-,[H30+] >> k H . After neglecting k H in the denominator we may estimate k H from the slope and K,. I n the curved central region k-,[HlO+] = k~ and both are important. I n the limit of low acidity, k-a[H,O+]
