3660
J. Phys. Chem. 1981, 85,3660-3667
mol dm-3. At low ionic strengths (p C 0.04 mol d r n 9 the rate constant of eq 3 was independent of p(kobsd= 0.258 f 0.018 dm3/2mol-1/2s-l, the average of 19 determinations at 25 "C in aqueous HC104-LiC104 media). This is consistent with Scheme A. At p > 0.04 mol dm-3 the value of k increased gradually, to 0.49 f 0.06 dm3l2mol-l s-l at p = 1.00 mol dm-3. Even here, however, the increases were well below those expected from Scheme B, and must be attributed to deviations from the BDH equation at higher ionic strengths. The results are depicted in Figure 1,which shows a plot of log kobsdvs. 0.509~'/~(1 + P'/~). It should be pointed out that the decision in favor of Scheme A and against Scheme B was also supported by quantitative studies of the chain-inhibiting effect of Cu2+,as discussed elsewhere.' The magnitude of the ionic strength effect associated with the different mechanisms given for reaction 4 is also expected to depend on which one applies, as well as on the ionic charge on substrate S. The expected variations are summarized in Table I, and illustrated schematically in Figure 2. Why is there a difference with regards the relationship between the detailed mechanism and salt effect for some chain mechanisms but not for nonchain processes? In the latter cases, where the algebraic form of the rate equation gives the chemical composition of the activated complex,
the composite rate constant is the product of an elementary rate constant and one or more equilibrium constants. In such cases the concept of a net activation process4 is applicable. Such is not the case for many chain reactions, most notably those for which initiation and termination are not the reverse of one another. It is in just those cases, where the rate depends upon the partition function of more than one transition state, that the more common interdependence of a rate law and its salt effect breaks down. In complex enzymatic reactions there occasionally arise limiting forms of rate laws deemed unusual in that the activated complex is not in equilibrium with the predominant form of the enzyme and the composition of the activated complex is not necessarily given by the concentration dependence of the rateag In such cases also, the magnitude of the primary kinetic salt effect will be different for kinetically equivalent forms.1° Acknowledgment. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division, Budget Code KC-03-02-01 under Contract W-7405-ENG-82. ~
~~
(9) King, E.L.J. Am. Chem. SOC.1956, 60, 1378. (10) This was pointed out to use by E. L. King, private communication.
Kinetic Study of Carbon Dioxide Reaction with Tertiary Amines in Aqueous Solutions D. Barth, C. Tondre," G. Lappai, and J.-J. Delpuech" Laboratoire de Chimie Physique Organique, ERA CNRS 222, Universit6 de Nancy I, C.O. 140, 54037 Nancy Cedex, France (Received: February 5, 198 1; In Final Form: July 24, 1981)
Reaction kinetics of C 0 2 with triethanolamine (TEA) and methyldiethanolamine (MDEA) in aqueous solution have been studied by using a stopped-flow technique with pH detection. Rate constants are obtained from the comparison of experimental and theoretical curves giving the optical density as a function of time. At concentrations of COz well below the saturation limit, the results are consistent with the hydration reactions of the COz molecules either with neutral water molecules or with hydroxide ions, depending upon the pH, itself governed by the ionization equilibrium of the dissolved amine. Moreover, a specific ("catalytic") reaction, first order with respect to both carbon dioxide and amine (rate constant, 2.85 M-'s-l at 25 "C), has been shown to contribute significantlyto the reaction rate in the case of the first amine (TEA) only.
Introduction Reactions of carbon dioxide with amines have been extensively studied during the last few years because of their industrial importance, particularly for natural-gas purificati0n.l In these processes the most widely used amines are mono- (MEA),di- (DEA),and triethanolamine (TEA), whose physical properties like viscosity, corrosiveness, water solubility, etc., are convenient for industrial use. Washing natural gas with ethanolamines allows one to remove not only the carbon dioxide but also the hydrogen sulfide contained. In order to improve the processes of selective desulfurization, it is necessary to know the kinetic scheme of the reactions involved, which can influence the absorption ability. Different kinetic methods have been used by previous workers in order to study the reaction of carbon dioxide (1) (a) P. V. Danckwerts and M. M. Sharma, Chem. Eng., 44, 244 (1966); (b) P.V. Danckwerts, Chem. Eng. Sci., 34,443 (1979). 0022-3654/81/2085-3660$01.25/0
with amines, for instance, the fast mixing method of Hartridge and Roughton,2 the wetted-wall column met h ~ dand , ~ the 14Cdiffusion m e t h ~ d . ~ In this paper we have limited our effort to the study of two tertiary amines, methyldiethanolamine (MDEA) and triethanolamine (TEA), by observing for the first time the fast pH change following the instantaneous mixture of an aqueous solution of C02 with an aqueous solution of the above amines. Although the kinetic mechanisms for tertiary amines are expected to be simpler than for primary or secondary amines, for which carbamate formation also has to be considered, discrepancies have appeared in the literature concerning the proposed mechanisms. The (2) H. Hikita, S. Asai, H. Ishikawa, and M. Honda, Chem. Eng. J. (Lausanne),13, 7 (1977). (3) E.Sada, H.Kumazawa, and M. A. Butt, Can.J. Chem. Eng., 54, 421 (1976). (4) Y. N. Nguyen, Ph. D. Dissertation, University of Rochester, Rochester, NY, 1978; T. L. Donaldson and Y. N. Nguyen, Ind. Eng. Chem. Fundam., 19,260 (1980).
0 1981 American Chemical Society
Carbon Dioxide Reaction with Tertiary Amines
The Journal of Physical Chemistty, Vol. 85, No. 24, 1981 3661
major question is to know whether the carbon dioxide hydration involves the intermediate formation of an alkyl carbonate or, at least, a specific ("catalytic") effect on the reaction rate. Experimental Section Technique. The technique used in this work was the stopped-flowmethod with light-absorption detection using the color change of a pH indicator to follow the proceeding of the reaction. The apparatus was essentially a Durrum DllO model except that the optical part was a Unicam SP500 UV-visible spectrometer, which replaced the original monochromator and lamp assemblies. The gastightness of the syringes was improved by using Teflon plungers with seal rings. A Texas 980A on-line computer allowed us to collect the kinetic data through a Biomation 805 analog-digital transient recorder. The data could either be stored on magnetic tape or displayed on a Hewlett-Packard 7210 A digital plotter. In a typical run, before mixing, one syringe contained the amine solution and the pH indicator, the other syringe containing the COz solution. The amine solution was always degassed in order to reduce the possibility of cavitation effects during mixing. The temperature range used was between 20 and 40 "C. Chemicals. The chemicals used were of the following origins; MDEA and TEA from Merck-Schuchardt (p.a.); COz (99.998%) from Air Liquid. In order to prepare COz solutions with varying concentrations, we proceeded by degassing the distilled water under vacuum and then bubbling the COzthrough a glass frit until a desired partial presswe was read on a manometer. Several hours (we used to wait overnight) are then needed to reach the equilibrium pressure. Then the concentration was determined by Van Slyke's m e t h ~ d . ~The concentration ranges used were between 2 X and 2 X lo-' M for amines, and between 3X and 3 X M for COP Note that concentrations given are always the concentrations of solutions before mixing in equal volumes. The choice of the pH indicator has to fulfill some requirements: (i) the equilibrium between the acid and base forms must be established instantaneously compared to the reaction studied, which is always the case on the time scale of the stopped flow; (ii) the pKI of the indicator must be close enough to the pKA of the amine, and the extinction coefficient must be high enough to ensure a good sensitivity; (iii) only one form must contribute to the absorption at the wavelength chosen for detection if a simple relation between light transmission and pH is wished. Thymol blue and m-cresol purple (both from Merck) have been used at a concentration of M and at wavelengths of 596 and 578 nm, respectively. Treatment of Data. The variation of absorption during the course of the reaction is in no case exponential, and special treatment of the experimental curves is required to test the kinetic models giving the best fit. As an analytical integration of the rate equations is not possible, we have built a Fortran IV program in order to integrate numerically the rate equations postulated, allowing us to simulate the kinetics on a digital plotter (see Figure 1for details of the program). The best kinetic parameters are obtained from the simulation giving the smallest value of the sum of squared deviations. Theoretical Part In order to make comparisons with the experimental curves, we need to establish theoretically the time-de(5) D. D. Van Slyke and J. M. Neil, J. Biol. Chern., 61, 523 (1924).
ISPUT VALUES OF PARAMETERS USED
COMPUTATION OF FINAL pH (equilibrium] CHOICE O F INTEGRATION METHOD CALCULATED "Runge- Kurt a method" j. U'"
I
I
I activity
I
/
I I
coefficients]
1-
I
1
'v I COMPUTATION OF CONCENTPATIONS H2C03, HCO;, Cog-, C02, Am, AmH', OH-
+
JCOMPUTATION OF L I G H T G Z Z 'd ' 1
1
CURVE PLOTTILG Transmission versus time versus t i m e Concentrations versus time
J Figure 1. Organization of program used for theoretical curve simulation. For the computation of activity coefficients, y is first taken to unity, and then the following are computed: the concentrations of different species, the ionic strength, and a first value of the activity coefficient according to eq 14 and 15. Then the concentrations are calculated again with the new value of y and so on until convergence of the iteration. In the Runge-Kutta method, parameters X, are calx, = hF(u,,), x, = hF(u, culated according to the following: X0/2), X , = hF(u,, i- X1/2),and X3 = hF(u,, X,), with h =,,t - tn-l (time interval between nth and ( n - 1)th points), giving the reciprocal of H+ concentration in the form u,,+~= u,, l/6(X0 2X1 2X2
+
+
+
+ X3).
+
+
pendent change of the transmitted light corresponding to well-defined experimental conditions for the different possible kinetic mechanisms. The following equilibria have to be considered in any case: HzO
@
H+ + OH-
(1)
HzC03e H+ + HCOc
(2)
HC03- ~1 H+ + CO2-
(3)
AmH+ @ H+ + Am
(4)
which are described respectively by the following equilibrium constants (the parentheses standing for activities)
Kw = (H+)(OH-)
(5)
Ki = (H+)(HCO~-)/(HZCOJ
(6)
Kz = (H+)(C0S2-)/(HCO3-)
(7)
KA = (H+)(Am)/ (AmH+)
(8)
All of these reactions are considered to be fast so that the equilibria are instantaneously established. We have found it necessary to introduce the activity coefficients, which
3682
The Journal of Physical chemistry, Vol. 85, No. 24, 1981
Barth et al.
k4/kZ = KdKWf/Klf
(19)
Kd being the dehydration equilibrium constant (Kd = [C02]/[H2C03]). Note that eq 17 is the total balance of eq 1, 2, and 16. If y designates the instantaneous concentration of COz, the rate equation for the consumption of COz is given by -dy/dt = (k1 + kz[OH-])y - k3[H2C03] - k4[HC03-] = (20)
x
Mechanism II. The amine is assumed to associate with the reacting species H20before the reactions of mechanism I occur, the result being a catalytic action of amines. This scheme corresponds to the general base-catalyzed hydration4J0 Figure 2. MDEA-CO, system; transmitted light T (left scale) and corresponding calculated instantaneous CO, concentration(right scale) vs. time at 24 OC. The smooth lines correspond to the theoretical simulations according to mechanism I with values given in Table I. Stoichiometric concentrations of solutions before mixing: [MDEA] = 5 X lo-, M, [CO,] = 2.88 X M.
have the advantage of giving a general model suitable for any ionic strength and allowing the treatment of experiments in the presence of added salt. If one takes to unity the activity coefficients, yi, of neutral species and uses a Debye-Huckel law6 for charged species in the form
+
+
log yi = - A ~ t [ 1 ' / ~ / ( 1 11/2) BY]
(9)
with zi the number of elementary charges, I the ionic strength, and A and B" empirical constants at a given temperature, it follows that
KWf = f K w
(10)
Kl, = f K 1
RR'R"N:
n t H-o
HI cII" 1-
t
c
I
= RR~R~~N+-H ks
t HCO;
0
In this case the reaction rate is described by the equation
in which the rate constant for the reverse reaction has been introduced as the product of the forward rate constant and a combination of equilibrium constants. The last term being comparatively very small in the basic range of pH, it will be neglected in the following (the validity of this approximation in our experiments has been verified by computation of the different terms). Mechanism III. In parallel with reactions 16 and 17, the amine and COz associate to form a hypothetical zwitterionic intermediary (by analogy with the carbamate formation occuring with primary and secondary amines), which would be rapidly destroyed because of its instability:
with
Three different possible mechanisms have been postulated to account for the observed pH changes with time. Mechanism I. The amine is assumed to contribute to the reaction only through the neutralization of the species formed by the COz hydration: 7-9 C02
+ H20
kl
HzC03
Applying the steady-state approximation to the zwitterionic species gives as the new rate equation
with very likely two limiting cases depending on whether the term ( k , k,[OH-]) is much smaller or greater than k7. In the former situation the rate equation will reduce to -dy/dt = X k,'[Am]y in the acid range (26)
+
+
and to (6) P. A. H. Wyatt, "Energy and Entropy in Chemistry", Macmillan, London, 1967, p 115. (7) J. T. Edsall and J. Wyman, "Biophysical Chemistry", Vol. 1, Academic Press, New York, 1958. (8) D. M. Kern, J. Chem. Educ., 37, 14 (1960). (9) B. R. W. Pinsent, L. Pearson, and F. S. W. Roughton, Trans. Faraday SOC.,52, 1512 (1956).
(10) J. P. Guthrie, J . Am. Chem. SOC., 102, 5286 (1980). (11) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolyte Solutions", Reinhold, New York, 1958. (12) "Handbook of Chemistry and Physics", 55th ed., CRC Press, Cleveland, OH, 1974-75. (13) K. Schwabe, W. Graighen, and D. Zpiethoff, Z. Phys. Chem. (FrankfurtlMain), 20, 68 (1959). (14) J. Bjerrum and E. J. Nielsen, Acta Chem. Scand., 2,318 (1948).
Carbon Dioxide Reaction with Tertiary Amines
-dy/dt = X
+ k6'[Am][OH-]y
The Journal of Physical Chemistry, Vol. 85, No. 24, 198 1 3663
in the basic range (27)
with
kg/ = k 6 k ~ / k 7 k{ = k&g/k7
+
In the latter situation (when k8 k,[OH-] -dy/dt = X k6[Am]y
+
>> 4) (30)
which gives a kinetic law undistinguishable from mechanism I1 (eq 21) and also from eq 26. Some of the values from the literature which have been used in the calculations have been collected in Table I, where are also given some values determined in this work. The experimentally directly accessible variable is not y but the light transmission, T, from which the pH can be calculated and then the corresponding value of y. (The reverse procedure is actually used as explained in the Figure 1.) The ionization equilibrium of the pH indicator HI P I-
+ H+
(31)
is characterized by the equilibrium constant KI KI = (I-)(H+)/(W
(32)
Taking the general case of a pH indicator whose acid form bears a charge zI, and the basic one a charge zI- 1, one can put eq 32 into the more general form KI = yW-zdK I f
(33)
Kv being the equilibrium constant written with concentrations in place of activities in KI. In the case where the basic form I- is the only one absorbing at the wavelength used, the optical density d is such that d = -log T = 4[I-]
(34)
(eI being the extinction coefficient and 1 the optical path
length). From the preceding equations the following expression can be deduced for the pH:
with d, = tICJ (36) CI being the total concentration of indicator. For the sake of simplification in the following, we introduce the change of variable u = l/[H+]
(37)
so that eq 35 can be rearranged as 1 u=-- d (38) dmax - d K , We have to integrate a rate equation of the general form dY --
du - f(u,y) = --dY (39) dt du dt At the very initial stage of the reaction, the value of y is just half its value before mixing the solutions, i.e., yo. u can be determined by solving eq 40, -
Klfu + 2KljKZfU2 1 + Klfu + KlfKzp2
b + K W f U - -1 - 1+KAu ZA[A]- ZC[C]= 0 (40)
obtained from mass-conservation and charge-conservation laws applied to eq 1-4, where everything has already been defined except a and b, respectively the stoichiometric concentrations of COz and amine, and [A], [C], ZA, and ZC, respectively the concentrations and charges of eventually added anions and cations (for experiments at varying ionic strength). In the evolution with time, yo just has to be replaced by y, the time-dependent variable, in eq 40. Equation 39 can be rearranged into the form du/dt = -(dy/dt)/[d(a - y ) / d ~ ] (41) where dy/dt is known from eq 20 or 25 to 30, depending on the postulated mechanism, and d(a - y)/du from the expression of a - y as a function of u in eq 40. Numerical integrations of such equations resulting in eq 41 were done with two different methods: (1)the trapezoidal rule and (2) the Runge-Kutta method of fourth order. In the first case, one sets du/dt = 1/H(u)
(42)
and H(u) is integrated by using a series of ui values of the variable corresponding to constant pHi intervals. The result of the integration gives the corresponding time ti. In the second case, one sets du/dt = F(u) (43) and the integration of F(u) allows one to calculate u at constant time intervals, which can be chosen to be the same as for the digitalized experimental curve. For this reason this method is more convenient for direct comparison with the experimental curves and for the calculation of the sum of squared deviations. It takes, nevertheless, a much longer computation time, although giving the same simulation as the previous one. For more details on the calculation procedure and programming, the reader should refer to Figure 1.
Results Experiments have been performed at different concentrations of amine and C02,at different temperatures and ionic strengths for MDEA and TEA, and also with two different pH indicators (thymol blue and rn-cresol purple). MDEA-C02 System. Figure 2 shows a typical experimental result for the transmission vs. time change as well as a theoretical simulation of the curve according to mechanism I with values in Table I. The corresponding calculated y change has also been represented. The theoretical fit is not always as nice as it is in Figure 2, and the quality of the fit, which has been characterized by a standardized sum of squared deviations RO,lSis very much dependent on the C02concentration, as is shown in Figure 3 and Table 11. In fact, the more concentrated the COz solution, the less good is the theoretical simulation in the hypothesis of mechanism I and the literature values of Table I. The fitting can be improved by adjusting kp. The best fits are then obtained with k2 values ranging between 8 X lo3 and 1.6 X lo4 s-l M-l depending on the concentrations of amine and C02,which is not satisfactory. The fitting can also be improved by introducing a catalytic effect as postulated in mechanisms I1 and 111. In the first case, values of k5 ranging between 2 and 8 s-l M-l are obtained, whereas in the later k{ values range between 5 X lo4 and lo6 s-l M-l. Thus, there is no satisfactory way to improve the quality of the fit. The possible drawback of cavitation effects when large COz concentrations are (15)R = EiSl"(Tjexptl - Tj,)2/[T(1) - T(n)I2, where T is the value of transmitted light, the indexes standing respectively for experimental, theoretical, first, and nth point.
3664
The Journal of Physical Chemistry, Vol. 85, No. 24, 198 1
Barth et al.
TABLE I : Rate Constants and Equilibrium Constants Used in the Calculations with Their Temperature Dependence constant
system or reaction studied CO, + H,O CO, + OHeq 6 eq 7 eq 5 eq 18 thymol blue rn-cresol purple MDEA TEA
temp coeffa value at 25 "C
A
B
lo-*
329.85 13.635 14.843 6.492 -22.759 1523.9 -14.01 -28.31 -14.01 -13.526
-17265.4 -2895 -3404.7 -2902.4 0 0 3 67 2474.5 0 0
2.58 8.32 4.43 4.57
X
x 103 8-1 M-1 x 10-7M X
lo-"
M
M2 3.861 X 10' 6.27 2.08 2.26 1.68
lo-'' M x 10-9 M x 10-9 M X
X
lo-* M
C -110.54b 0 -0.03279 -0.0238 0.0294 -3.825 0.012 0.038 0.018 0.0193
Law of the general form log K = A + B / T + CT except for b and c. Log k , = A t BIT t C log T . K , = K l ' ( l t K d ) where K,' is the apparent association constant [H+][HCO,-]/([CO,] t [H,CO,]). a
ref 9 9 11 11 12 11 this work this work 13 14 Kd = A t
CT.
TABLE 11: Influence of Amine and CO, Concentrations on the Kinetics Determined at 25 "C for the MDEA-CO, System
85 73 75 80 86 76 81 96 87 74 77 82 88 79 84
2.0 2.0 2.0 2.0 5.0 5.0 5.0 5 .O 10.0 10.0 10.0 10.0 20.0 20.0 20.0
3.03 1.28 1.04 0.58 3.03 1.04 0.58 3.03 1.28 1.04 0.58 3.03 1.04 0.58
3.00 1.28 1.05 0.56 2.40 0.98 0.52 0.29 2.80 1.28 1.01 0.52 2.90 1.00 0.55
10.13 10.19 10.21 10.23 10.40 10.44 10.45 10.44 10.56 10.59 10.60 10.61 10.73 10.76 10.77
6.59 8.36 8.56 8.98 8.69 9.18 9.47 9.67 9.00 9.39 9.49 9.76 9.39 9.78 10.00
1.5 2.0 2.0 1.4 1.4 0.9 0.75 0.78 0.9 0.55 0.50 0.24 0.44 0.30 0.28
6.1 4.1 1.3 0.4 3.7 0.7 0.7 0.2 10.1 2.5 2.8 4.8 14.7 4.2 8.2
R o is the standa VS = Van Slyke; as. = asymptote. ardized sum of squared deviations when assuming mechanism I with values of Table I. employed will be discussed in the next section. For this reason C 0 2 concentrations always smaller than 0.7 X M will be used in the following. In Table I1 are also compared the C 0 2 concentration measured by Van Slyke's method and determined from the calculated asymptote. In most cases a very good agreement is obtained. The calculated pHs a t the initial (pHi) and final (pHJ stage of the reaction are also given, as well as a half-reaction time, tlI2, which gives an idea of the time scale on which the reaction takes place. Similar information is given in Table 111, which relates the influence of temperature a t two different ionic strengths. Only low concentrations of COz (around onetenth of the saturation concentration) have been used, giving excellent agreement between experimental and calculated curves (as indicated by the value of R,) when assuming the occurrence of mechanism I and using rate
time(s)
10
2511
J
20
Figure 3. MDEA-CO, system; Influence of stoichiometric COP concentration on the transmitted light Tvs. time curves: [MDEA] = 5 X lo-' M, (a) [CO,] = 2.40 X lo-' M, (b) [CO,] = 0.98 X IO-* M, (c) [CO,] = 0.52 X lo-' M, (d) [CO,] = 0.29 X lo-' M (-) experlmental results, (- - -) theoretical simulation according to mechanism I and values in Table I (both curves are coincident in d).
constants and temperature coefficients given in Table I. For experiments in 0.3 M ionic strength, the dependence of the k2 value with ionic strength has been taken into account (there is no charged species involved in the reaction governed by k,) in the form: log kZ(Z,T) = log k,(Z=O,T) + 0.261 (44) The fits are far from being as good as those found when the ionic-strength dependence of k 2 is not taken into account. Note that the results given in the tables have been obtained by using thymol blue as pH indicator. Similar results have been obtained with m-cresol purple for the calculated curves. TEA-C02 System. Figure 4 shows an example of experimental results and calculated curves assuming mechanism I or I1 (or 111). For mechanism I, the parameters of Table I have been used. The theoretical fit can be improved a lot by searching for the value of parameter k5
TABLE 111: Influence of Temperature (T) on the Kinetics of the Reaction at Ionic Strength Z for the MDEA-CO, System expt no. 95 96 97 98 99 110 111 112 113 114
10, x
10' x
[amine], M 5.0 5.0 5.0
[CO,], M 0.29 0.28 0.28 0.28 0.29 0.51 0.57 0.57 0.57 0.57
5.0 5.0 2.0 2.0 2.0 2 .o 2.0
I, M 0 0 0 0 0
0.3 0.3 0.3 0.3 0.3
T,"C 20.6 24.4 29.8 34.8 39.6 20.1 24.9 29.8 34.7 40.5
PHi 10.53 10.44 10.31 10.20 10.08 10.31 10.19 10.08 9.96 9.81
PHf 9.74 9.67 9.58 9.50 9.40 9.13 8.99 8.91 8.82 8.72
t,,,, s
RO
0.30 0.78 0.30 0.34 0.20 2.4 1.5 1.0 0.5 0.38
0.10 0.16 0.13 0.36 0.70 0.32 0.11 0.04 0.18 0.13
The Journal of Physical Chemistry, Vol. 85,No. 24, 198 1 3665
Carbon Dioxide Reaction with Tertiary Amines
60rT,.,,
Figure 4. TEA-COP system; transmitted light T vs. time at 25 'C: [TEA] = 8 X lo-' and [CO,] = 4.95 X M before mixing; (-) experimental results, (- - -) theoretical simulation according to (a) mechanism I or (b) mechanism I1 with k5 = 2.7 M-' s-'.
Figure 5. TEA-Cop system; the standardized sum of squared devlations R5 vs. the value of the catalytic rate constant k5: (0)[TEA] = 8 X lo-, M, [CO,] = 5 X M; (+) [TEA] = 5 X I O - * M, [CO,] M. =4X M; (X) [TEA] = 2 X lo-' M, [CO,] = 4 X
TABLE IV: Influence of Amine Concentration on the Kinetics at 25 "C for the TEA-CO, System
k 5, (or 1 0 - 5 ~ expt no. 129 130 131
102x [amine],
102x
ks 5- l' L ks -6l ' ,
M
[CO,], M
pHi
pHf
M"
M-'
ti,,, s
8.0 5.0 2.0
0.49 0.40 0.40
10.12 10.01 9.78
8.95 8.83 8.39
2.7 2.7 3.0
1.3 1.5 4.0
0.85 1.15 1.20
(or k5/) which gives the minimum standardized sum of deviations squared, referred to as R5in the following. When the amine concentration is changed, a catalytic effect according t o mechanism I1 or I11 has to be introduced into the theoretical predictions if a good fit with the experimental curve is to be obtained. Either k5 (or k;) or kg/ has been introduced in addition to the parameters of Table I. Table IV shows the value of k5 (or k5/) or kg/ giving the best theoretical fits. Whereas with k5 (or k5/)as the adjustable parameter approximately the same value gives the smaller standardized sum of deviations squared, R5, as shown in Figure 5, the situation is less good when taking k l as the adjustable parameter. Figure 6 shows the comparison of experimental results and theoretical predictions when k5 (or k;) is used as the adjustable parameter for the three different amine concentrations. The temperature dependence of k5 (or k;) has been studied, and the results are shown in Table V. An activation enthalpy of 7.7 kcal/mol for the catalytic reaction has been deduced from the Arrhenius plot shown in Figure 7. Note finally that the same value of k5 (or k5/) was obtained for both thymol blue and m-cresol purple as the pH indicator. This shows the reliability and generality of our theoretical treatment.
Discussion According to the results presented in the preceding section, it appears that the MDEA-C02 reaction is in
time(s1
i
10
30b
Figure 6. TEA-CO, system; influence of TEA concentration on the transmitted light Tvs. time curves at 25 'C: (a) [TEA] = 2 X lo-' M, lC02] = 0.4 X lo-' M; (b) [TEA] = 5 X lo-' M, [COP = 0.4 X 10- M; (c) [TEA] = 8 X lo-' M, [CO,] = 0.49 X 10' M; (-) experimental results, (- - -) theoretical simulationassuming mechanism I1 with k, = 2.7 M-'s-'.
Figure 7. TEA-Cop system; Arrhenius plot obtained from the temperature dependence of k,. Error bars have been shown, which indicate the accuracy of values obtained from theoretical simulation.
TABLE V : Influence of Temperature on the Kinetics of the Reaction for the TEA-CO, System expt no. 143 131 145 146 154
102 x [amine], M 2.0 2.0 2.0 2.0 2.0
102 x [CO,], M
T,"C
0.33 0.53 0.33 0.33 0.54
20.4 25.2 29.8 35.2 39.8
k , (or
PHi 9.92 9.79 9.69 9.57 9.44
pHf 8.65 8.39 8.50 8.42 8.17
k 5 ' ) ,S-' M-' 2.2 2.7 3.2 4.0 5.0
tl,,,
s
2.2 1.2
0.8 0.45 0.3
R, 0.24 0.23 0.25 0.25 0.20
3666
Barth et al.
The Journal of Physical Chemistry, Vol. 85,No. 24, 1981
agreement with mechanism I (except at high C02 concentration) whereas the introduction of a catalytic effect is necessary to explain the results obtained for the TEAC 0 2 system. In this last case a rate constant k5 (mechanism 11) or kgl (mechanism 111) of 2.85 f 0.15 M-l s-l a t 25 "C has been obtained, in very good agreement with the value of 3 M-I s-l given in ref 4, in which a totally different experimental approach has been used. Unfortunately, a distinction between mechanisms I1 and I11 (limiting case, eq 26) is not possible on kinetic grounds. When a catalytic effect exists, mechanism I1 has, however, our preference because the following reasons are playing against mechanism I11 (i) The opening of one double bond of the carbon dioxide molecule to yield a zwitterionic species similar to that postulated in eq 22 is strongly favored in the case of primary and secondary amines because the loss of one proton from the nitrogen atom allows the formation of a partial N-C double bond, which cannot occur with tertiary amines. For this reason the formation of a zwitterion is much less likely than in the case of primary or secondary amines. (ii) The lifetime of carbamic acid zwitterions has been shown to be very short,16J7so that, if it was existing in the present case, the zwitterionic species would regenerate free C02extremely rapidly. The postulated transfer of carbon dioxide directly from amine to water (eq 23 and 24) appears thus very unlikely.18 One may wonder whether a catalytic effect does not actually exist with MDEA or whether it is too small to be detected under the conditions used. In fact, the replacement of one -CH2CH20H group of TEA by a -CH3 group, which is a stronger electron donor, is expected to result in a strengthening of the nitrogen electron pair (indicated by a higher pKA)and consequently in a greater catalytic efficiency of MDEA compared to TEA. However, the greater basicity of MDEA simultaneously contributes to raise the pH range of the reaction, thus increasing the contribution of the basic hydration of carbon dioxide (mechanism I, eq 17). In order to try to understand this contradictory situation, we have evaluated the contribution of each term in eq 21 by assuming that a catalytic effect occurs with MDEA with the same value of k5 as found for TEA. The concentrations of species involved in the kiterms can be calculated by our program (see Figure 1) at any stage of the reaction. In Table VI, the contributions of the different terms have been given as percentages of the total rate at the initial stage of the reaction for MDEA and TEA (the terms in k3 and k4 for the back-reactions are negligible at this stage). The contribution of the terms in k5 ranges between 1.92% and 5.93% for MDEA, and between 4.5% and 8.1% for TEA. This contribution increases with the amine concentration, as expected from eq 21, but is not much dependent on the C02concentration. Consequently, the large discrepancies between theoretical simulation and experiment, observed in Figure 3 only when the C02 concentration is large, do not seem to arise from the fact that we have not introduced a catalytic effect. As previously shown,lgcavitation is very likely to occur when the C02concentration is larger than a quarter of its saturation value. Any kind of artifact may then happen which can
rl
m
rl
0
m
rl
Q,
N
rl
*W Q,
t-
(13
W
N 00
tt-
*t* 00 (0
Q,
,
(16) S. L. Johnson and D. L. Morrison, J. Am. Chem. SOC.,94, 1323 (1972). ,--- -,-
(17) S. P. Ewing, D. Lockshon,and W. P. Jencks, J.Am. Chem. S O ~ . , 102, 3072 (1980). (18)We would like to acknowledge the referees for their constructive remarks on this point. (19) J. A. Sirs, Trans. Faraday SOC.,54, 201 (1958).
rl
00
W t-
W 30
3 XJ
in
c-
rn c-
in x)
0
E +a
a x
J. Phys. Chem. 1981, 85,3667-3673
affect the shape or amplitude of the transmitted light vs. time curve. The values given in Table VI indicate that the contribution of the k5 term would be about twice as large for TEA as compared to MDEA at similar amine concentrations. The difference may come from the decrease of the iZ2 term in the case of TEA, because the reaction takes place in a slightly less basic region. A way of checking the validity of these assumptions would have been to carry out the MDEA reaction in a slightly more acidic range, so as to decrease the contribution of reaction 17 relative to the catalytic term, due to the fact that the more basic hydroxide ion is neutralized before MDEA by a small addition of a strong acid. We thus tried to decrease the pH at the initial stage of the reaction by adding a small amount of HC1 to the amine solution before mixing. Unfortunately, we could not simulate the experimental curve obtained with our program. A possible explanation could be the occurrence of an esterification reaction on the -OH groups of ethanolamine changing the pH prediction. This part of our investigations will be further developed by using tertiary alkylamines (see below). We have not examined in this paper the eventuality of C 0 2 reaction with the -OH groups of ethanolamines postulated by others.2>20Such a situation is in fact very unlikely because we found in preliminary experiments that qualitatively the same behavior is obtained when using triethylamine in place of triethanolamine, as also demonstrated by Nguyen and D ~ n a l d s o n On . ~ the other hand, this assumption would result in a kinetic law formally analogous to eq 27; indeed, the formation of monoalkyl carbonate from C02and triethanolamine20 can be represented by the following reaction scheme: (20) E. Jsrgensen and C. Faurholt, Acta Chem. Scand., 8,1141(1954). (21)J. Legras, “MBthodes et Techniques de YAnalyse NumBrique”, Dunod, Paris, 1971.
Absolute Rate Constant of the Reaction OH
N(R)&H&H20H
3667
+ COZ + OH- e N(R)2CH&H&O3-
+ HzO
The corresponding rate equation (analogous to eq 27) has been rejected because of the poor quality of the curve fitting then obtained (see above). In addition, as pointed out by one referee, the kinetics observed in ref 20 took place on a much slower time scale than observed here. In conclusion, these investigations greatly clarify the mechanism of the reaction of tertiary amines with carbon dioxide in aqueous solution. Previous investigations using solutions of tertiary ethanolamines generally assumed the formation of an alkyl carbonate as a first step. In fact, the present results show that the main contributions to the reaction rate simply arise from the hydration of the C 0 2 molecules either by the water molecules or by the hydroxide ions, depending upon the pH, itself governed by the ionization equilibrium of the dissolved amine. Moreover, a specific (“catalytic”) effect has been shown to occur with TEA on the basis of mechanism I1 or 111, with a preference for mechanism 11. The program which has been developed to calculate the theoretical curve gives the best simulation with a value of 2.85 M-l s-l for the catalytic rate constant k5 a t 25 “C, in very good agreement with ref 4, which, however, used a completely different experimental approach. A catalytic effect is also very likely to occur with MDEA, but it is much more difficult to ascertain owing to its relatively weak contribution to the overall reaction rate. In fact, mechanism I, which is the simplest possible, gives an excellent description of the experimental results when the C02 concentration is kept well below the saturation limit.
Acknowledgment. We (particularly D.B.) thank the Soci6t6 Nationale Elf Aquitaine S.N.E.A.(P)for financial support during the work. We also acknowledge MM. C. Blanc, G. Guyot, and C. Thibaut from S.N.E.A.(P) for stimulating discussions and helpful suggestions.
+ HOP
-+
H20
+ O2
Leon F. Keyser Molecular Physics and Chemistry Section, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 9 1 109 (Received: May 15, 1981; In Final Form: July 17, 1981)
-
The absolute rate constant of the reaction OH + HOz HzO + 02 was determined by using the discharge-flow resonance fluorescence technique at 299 K and 1-torr total pressure. Pseudo-first-order conditions were used with HOz concentrations in large excess over OH. Secondary reactions of atomic oxygen and atomic hydrogen were shown not to interfere under the conditions used. The result is (6.4 f 1.5) X 10-l’ cm3molecule-l s-l where the error limits are twice the standard deviation. The overall experimental error is estimated to be &30%.
Introduction Reactions of odd-hydrogen radicals, HO, (H, OH, H02), play a major role in atmospheric chemistry and combustion In the stratosphere HO, species enter into several catalytic cycles which destroy odd oxygen (0,03). They also interact with other radical species such as NO, and C10,. The recombination of OH and H 0 2 (eq 1)is an (1)Nicolet, M. Reu. Geophys. Space Phys. 1975,13, 593: (2)Kaufman, F.Annu. Reu. Phys. Chem. 1979,30, 411. (3)Chang, J. S.; Duewer, W . H. Annu. Reu. Phys. Chem. 1979,30,443.
-
+
OH + HO2 H2O 02 (1) important loss of odd-hydrogen species in the upper atmosphere and limits the efficiency with which they destroy odd oxygen. There have been several previous measurements of the rate constant, kl, using various experimental techniques.”’l (4) Hochanadel, C. J.; Sworski, T. J.;Ogren, P. T. J. Phys. Chem. 1980, 84,3214. ( 5 ) Lii, R.R.; Gorse, R. A,, Jr.; Sauer, M. C., Jr.; Gordon, S. J.Phys. Chem. 1980,84,819.
0022-365418112085-3667$01.2510 0 1981 American Chemical Society
