1253
J . Phys. Chem. 1984,88, 1253-1257
Kinetic Behavior of L-Arginine in the Interlamellar Layer of Montmorillonite in Aqueous Suspension Tetsuya Ikeda and Tatsuya Yasunaga* Department of Chemistry, Faculty of Science, Hiroshima University, Hiroshima 730, Japan (Received: May 26, 1983: In Final Form: August 1, 1983)
Two relaxations were found in aqueous suspensions of montmorillonite containing L-arginine by using the pressure-jump relaxation method with electric conductivity detection. It was found that L-arginine intercalates into the interlamellar layer and is hydrolyzed slighlty into ornithine and urea. Some plausible mechanisms were examined by using kinetic and static experimentalresults, and fast and slow relaxationsobserved were attributed to the intercalation of L-arginine into the interlamellar layer and the hydrolysis of the intercalated L-arginine in the interlamellar layer of the montmorillonite, respectively. The forward and backward rate constants of the former process were determined to be 8.5 X lo4 mol-' dm3 s-' and 5.8 X lo2 s-I, and the forward and backward rate constants of the latter process 2.0 X lo2 and 2.2 X lo2 s-', respectively, at 25 O C . The experimental results showed that the equilibrium constant of the overall reaction obtained kinetically was in good agreement with that obtained from the adsorption isotherm, and that the ornithine- or urea-releasingreaction in the proposed mechanism was the rate-determing step, i.e.
HrO
Argi-
fast
3 r n or urea
slow
very slow
Introduction One of the interesting properties of a layered compound such as montmorillonite is an intercalation of adsorbing molecules into the interlamellar layer,' in which the regular spacing of a clay sheet plays an important role as a shape-selective catalyst.2 Exchangeable sodium ions are bound on the two-dimensional host lattice in the interlamellar layer of the montmorillonite and are exchanged with various guest cations. Ion-exchange equilibrium has been studied in order to understand intercalation and shape selectivity for exchanging molecules. However, the mechanisms of such phenomena have not been clarified because of a lack of kinetic information. In previous papers, similar intercalation kinetics has been established in the ion exchange with organic cations in zeolites by using the pressure-jump relaxation m e t h ~ d . ~ - ~ An application of the chemical relaxation method contributes to the success of the kinetic approach to a rapid adsorption-desorption of ions at the solid-liquid i n t e r f a ~ e . ~ - ~ The hydrolysis of L-arginine catalyzed by arginase is well-known as the ornithine cycle, in which L-arginine is decomposed into L-ornithine and urea. Although this is a specific enzyme reaction in vivo, it is hoped that the use of a clay mineral instead of an enzyme will give a significant clue for the clarification of functionality of a clay mineral in catalysis. Montmorillonite is a suitable material for such an application because it exhibits various catalytic properties which originate from a unique layered structure. In this paper, we present the results of pressure-jump relaxation experiments on the intercalation of L-arginine in aqueous suspensions of montmorillonite and discuss the plausibility of the hydrolysis of L-arginine catalyzed by the montmorillonite particles.
Experimental Section The details of the pressure-jump apparatus have been described previo~sly.~The time constant of the pressure jump is 80 ws. The sodium montmorillonite, Kunipia-G, used was supplied from the Kunimine Industries Co. The diameter of the montmorillonite particles was determined to be 0.2-1 ~m by using a membrane filter. The cation-exchange capacity was determined to be 100 mequiv/lOO g from the adsorption isotherm of L-arginine. The montmorillonite particles were dispersed in aqueous solution by ultrasonication and formed very stable suspensions under the present experimental conditions. All reagents were reagent-grade chemicals and were used without further purification. The equilibrium concentrations in the bulk phase were determined by means of colorimetric analysis with ninhydrin at a wavelength of 570 nm for L-arginine'O and with 2,3-butanedione-2-oxime and semicarbazide at a wavelength of 440 nm for urea." The amount of L-ornithine released by the hydrolysis of L-arginine was measured with a Hitachi amino acid analyzer (type KLA-5). Prior to the measurements, samples of the montmorillonite suspensions were centrifuged for 30 min at lOOOOg to settle completely the particles. The amount of L-arginine adsorbed was determined from the concentration change in the supernatant solution. The concentrations of urea and ornithine in the stock solution of L-arginine were determined by means of the above analysis but were found to be negligibly small under the present experimental conditions. pH values of the montmoril1onite-Larginine system were adjusted with HC1. All preparations and experimentation were done in a nitrogen atmosphere, and the temperature was controlled at 25.0 & 0.1 OC.
(1) Whittingham, M. S., Jacobson, A. J., Eds. "Intercalation Chemistry"; Academic Press: New York, 1982. (2) Solomon, D. H.; Ross, M. J. J. Appl. Polym. Sei. 1965, 9, 1261. (3) Ikeda, T.; Sasaki, M.; Mikami, N.; Yasunaga, T. J. Phys. Chem. 1981, 85, 3896. (4) Ikeda, T.; Sasaki, M.; Yasunaga, T. J. Phys. Chem. 1982,86, 1680. ( 5 ) Ikeda, T.; Sasaki, M.; Yasunaga, T. J. Phys. Chem. 1983, 87, 745. (6) Ikeda, T.; Sasaki, M.; Astumian, R. D.; Yasunaga, T. Bull. Chem. SOC. Jpn. 1981, 54, 1885. (7) Ikeda, T.; Sasaki, M.; Yasunaga, T. J . Phys. Chem. 1982, 86, 1678. (8) Ikeda, T.; Sasaki, M.; Hachiya, K.; Astumian, R. D.; Yasunaga, T.; Schelly, Z. A. J. Phys. Chem. 1982,86, 3861.
Results and Discussion Figure l a shows a typical relaxation curve observed in aqueous suspensions of the montmorillonite-L-arginine system in the pH range 10-1 1 by using the pressure-jump relaxation method with electric conductivity detection, where the direction of the relaxation
0022-3654/84/2088-1253.$01.50/0
(9) Hachiya, K.; Ashida, M.; Sasaki, M.; Kan, H.; Inoue, T.; Yasunaga,
T.J . Phys. Chem. 1979, 83, 1866. (10) Troll, W.; Cannan, R. K. J . Biol. Chem. 1953, ZOO, 803. (11) Newell, B. S.; Morgen, B.; Cundy, J. J. Mar. Res. 1967, 25, 201.
0 1984 American Chemical Society
1254
The Journal of Physical Chemistry, Vol. 88, No. 6,1984 6
I
I
1
3
I
(a) 6 -
Ikeda and Yasunaga
-
I
I
0
0.5
I
1.o
.
I
I
I
1.5
2.0
2.5
ADDED L-ARGININE 1 0-2mol dm-3 Figure 3. Dependence of the fast reciprocal relaxation time on the added L-arginine concentration in aqueous suspensions of the montmorillonite at a particle concentration of 5 g dm-3 and 25 OC.
T I M E , ms
-.
2 t T T
I N
Figure 1. (a) Typical relaxation curve in the montmorillonite-L-arginine system observed by using the pressure-jump relaxation method with
electric conductivity detection at a particle concentration of 5 g d ~ n and -~ 25 O C . (b) Semilogarithmic plot of the relaxation curve. I
1
0
05
1.a
I
I
1
1.5
2.0
2.5
ADDED L-ARGININE, l o 2 mol dm-3
Figure 4. Dependence of the slow reciprocal relaxation time on the added L-arginine concentration in aqueous suspensions of the montmorillonite at a particle concentration of 5 g d r f 3 and 25 "C. *I
0
E 5 TIME , h
Figure 2. Time profile of urea-releasing reaction. Each sample of the montmorillonite suspension was centrifuged for 10 min at 20000g to settle
completely the particles. signal indicates a decrease during the relaxation. No relaxation was observed in a montmorillonite suspension of the same pH and in the supernatant solutions ,of the montmorillonite-L-arginine system. The amplitude of the relaxation curve for a constant concentration of L-arginine (1.0 X mol dm-3) was diminished with decreasing pH by addition of HC1. On the other hand, no relaxation was observed in the montmorillonite-L-ornithine system, in which the structure of L-ornithine is nearly the same as that of L-arginine. These facts indicate that positively charged b a r ginine does not relate to the observed relaxation and that the relaxation may reflect the difference of the molecular structure between L-arginine and L-ornithine. Furthermore, it was found from colorimetric analysis that the L-arginine added was hydrolyzed slightly by adsorption-desorption onto the particles. The reaction profile of urea release after mixture of the L-arginine solution and the montmorillonite suspension is shown in Figure 2. It can be seen from this figure that the hydrolysis of L-arginine accompanied by the urea-releasing reaction requires nearly 2-3 h for equilibration. The semilogarithmic plot of the typical relaxation curve in Figure l b shows that the relaxation curve consists of two relaxation
I a I
-
1
0
0.5
I
1.o
I
I
1.5
2.0
J
BULK CONCN. OF L-ARGININE, lO-*mol dm-3
Figure 5. Adsorption isotherm of L-arginine (0) and amounts of Na' and 25 O C . The bulk released ( 0 )at a particle concentration of 5 g concentration of L-arginine determined by means of colorimetric analysis indicates [Arg'] and [Arg'-].
processes. The dependences of the fast and slow reciprocal relaxation times T ~ and - ~ T ~ on - the ~ concentration of added L-arginine in aqueous suspensions of montmorillonite are shown in Figures 3 and 4, respectively. As can be seen from these figures, - ~ T ~ increase - ~ with increasing concentration the values of T ~ and bf added L-arginine. Taking into account the two relaxations and the urea release, it appears that the hydrolysis of L-arginine may consist of at least three elementary processes. Now, in order to clarify the mechanism which involves the above elementary processes, the equilibrium properties of the montmorillonite-Larginine system must be investigated. Figure 5 shows the adsorption isotherm of L-arginine onto the montmorillonite particles in aqueous suspensions, where the bulk concentration of L-arginine is the sum of cationic and zwitterionic L-arginine concentrations. In the present suspensions, ion-exchange
The Journal of Physical Chemistry, Vol. 88, No. 6,1984 1255
Kinetic Behavior of L-Arginine in Montmorillonite
and the released state of Na+ induced by the Arg+ adsorption, respectively, and k+.1,2are the rate constants of steps 1 and 2. Under the two assumptions that the hydrolysis of the zwitterion of L-arginine, Arg+-, in the bulk phase is a very fast reaction with a hydrolysis constant of KBand that (i) step 1 is much faster than step 2 or (ii) step 2 is much faster than step 1, the fast reciprocal relaxation time, T ~ - is~ ,given by
I 1
I
' Ol I
0
0.5
I
1.0
I
I
1.5
2.0
BULK CONCN. OF L-ARGININE, 1 O-*mol dm3 Figure 6. Dependence of pH on the bulk concentration of L-arginine in aqueous suspensions of the montmorillonite at a particle concentration of 5 g dm-3 and 25 OC.
E k 0
9p:
'O1
I
1
I
I
5-
3 LL
0
0
0.5
1.0
1.5
(i) step 1 is much faster than step 2
(ii) step 2 is much faster than step 1
= k2 + k-,([S(Arg)]
T ~ - ~
+ [Na'])
(2)
In order to plot eq 1 and 2 , one must obtain the equilibrium concentrations of Arg', S(Na), and S(Arg). The concentrations of Arg+ were determined from the adsorption isotherm in Figure 5 and the pH values in Figure 6 by using the dissociation constants of a- and eamino groups. The amount of S(Na) was estimated from the adsorption isotherm, in which the total site number was determined to be 5.0 X mol dm-3 from a Langmuir plot. The concentration of S(Arg) equals the amount of Na+ released in Figure 5. However, the plots of eq 1 and 2 yield negative values of the rate constants k , and k2, which is physically meaningless. Thus, mechanism I must be eliminated. Next, the mechanism of ion exchange of Arg+ for Na+ accompanying adsorption-desorption of Arg+- into the interlamellar layer was considered:
2.0
BULK CONCN. OF L-ARGININE, 1 O-' mol drn-3 Figure 7. Amounts of urea released by the hydrolysis of the adsorbed L-arginine in aqueous suspensions of the montmorillonite at a particle concentration of 5 g dm-' and 25 OC.
reaction may occur as described above. The Na+ release from the interlamellar layer was found by using a N a electrode and the amounts of Na+ released are also shown in Figure 5. These results confirm that L-arginine adsorption takes place in the interlamellar layer of the montmorillonite. When one compares the amounts of L-arginine adsorbed and of Na+ released by the adsorption, it can be seen in Figure 5 that the amount of Na+ released from the interlamellar layer by the ion exchange is less than that of L-arginine adsorbed. The dependence of pH on the bulk concentration of L-arginine is shown in Figure 6. To obtain information about the hydrolysis of L-arginine in aqueous suspensions of the montmorillonite, the concentration of urea in the bulk phase was measured. The amount of urea decomposed by the hydrolysis of intercalated L-arginine is shown in Figure 7. If one compares Figures 5 and 7, one can see t,hat the amount of L-arginine hydrolyzed by the adsorption in the interlamellar layer of the montmorillonite is markedly less than that of L-arginine adsorbed. First, taking into account the kinetic and static results obtained, the mechanism of ion exchange of positively charged L-arginine Argt for Na+ in the interlamellar layer of montmorillonite, which is schematically the same as that reported previously: was considered:
step a
step b
K3
S(Na)
+ Arg+ 2 S(Arg) + Na+ k-3
(IV)
step c
with Kl = [S(Na.Arg+-)]/([S(Na)l[Arg+-l) = k,/k-,
(3)
K2 = [S*]/[S(Na.Arg+-)] = k 2 / k - z
(4)
K3 = [S(Arg)l[Na+l/([S(Na)l[Arg+l) = k3/k-3
(5)
The symbols S(Na.Arg+-) and S* stand for the bound state of Arg+- which diffused into the interlamellar layer of the montmorillonite by the intercalation and the second bound state followed by the intercalation process, respectively. For the coupled mechanism 11-111, the fast and slow reciprocal relaxation times are given by 71.2-1
= Mal,
+ a22
* ((all + a22)2- 4(a11a22 - a12a21)11'21 (6)
with [Arg+-]
+ [OH-] + [S(Na)]KB[Arg+] + [Arg+] + [OH-]
)
+ k-1 (7)
step 1
step 2
where the symbols S(Na), S(Na.Arg+), and S(Arg) denote the adsorbed state of Na+, the coexistent state of both Na+ and Arg+,
a12 = k-1
(8)
a21 = k2 a22 = k2 + k-2
(9) (10)
In general, if a l l and aZ2are separated by at least 1 order of magnitude, two relaxations approximately correspond to two separate reactions. However, since the relaxation times in the present study are the same order of magnitude, two consecutive
1256 The Journal of Physical Chemistry, Vol. 88, No. 6,1984
0
C Figure 8. Plot of
T]-I
I
I
1
2
I
/ i
'm
6
4
(CNa+lCOH-l)-l. 1 O6 mo?dm6 Figure 10. Plot of r*,/([S(Na)l[Arg+-]) vs. ([Na+][OH-])-' in eq 14.
+ ~ 2 - lvs. C in eq 11.
- 1.01
2
0
3
10-'moI dm-3
,
Ikeda and Yasunaga
I
'0
I
I
I
c
0
1
C Figure 9. Plot of
T~-IT~-'
I
I
1
2 ,
I 3
I O - *m o l dm-3
vs. C in eq 12.
reactions must be treated as a coupled reaction. For the evaluation of the four rate constants with good precision, the sum and product of the two relaxation times are expressed as follows: 3*5 ~1-l
+ k-l + k2 + k-2 = kl(k2 + k 4 ) C + k-lk-2
+ 71'
71-172-1
= klC
(11) (12)
with C = [Arg+-]
[Arg'] + [OH-] + [S(Na)] KB + [Arg'] + [OH-]
PH Figure 11. pH dependence of the amount of ornithine released for the mol dm-' at a particle concentration of added L-arginine 1.0 X concentration of 15 g dm-) and 25 O C .
line and are listed in Table 11, showing fairly good agreement between K' obtained kinetically and statically. This agreement of the equilibrium constants obtained from different sources leads to the conclusion that the two relaxations can be attributed to steps a and b in mechanism 111. Next, the possibilities of the remaining mechanism must be examined. In the case in which reaction IV is much faster than steps a and b, the concentration term C in eq 13 is rewritten
(13)
+
The plots of T ~ - ~72-l vs. C and T ~ - ~ Tvs.~ -Care ~ shown in Figures 8 and 9 and yield straight lines. These straight lines lead to the conclusion that the two relaxations observed can be attributed to steps a and b in mechanism 111. The four rate constants were evaluated from the slope and the intercept of the obtained straight lines. The values of the four rate constants obtained are listed in Table I. The static equilibrium constants K1, K,, and K3 of mechanisms I11 and IV can be evaluated from the following relation:
[S(Na)l [A%+] KB
+ [Arg'] + [OH-]
KB + IArg+] KB + [Arg+] + [OH-]
+
where FArg is the amount of L-arginine adsorbed. The amounts of urea and ornithine released are negligibly small compared to that of L-arginine adsorbed under the present experimental conditions. The plot of eq 14 shown in Figure 10 yields a straight line, which indicates that the proposed mechanism is statically plausible. The values of the equilibrium constants K1, K2, and K3 were obtained from the slope and the intercept of the straight
+
I
+ [S(Arg)] + [Na+] +
However, the plots of T,-' r2-' vs. C'and 71-'72-' vs. C'yield a negative k , , where the value of K3 in eq 17 was statically obtained. This fact indicates that the ion exchange of Arg' for Na+ does not contribute to the observed relaxation. Considering that the mechanism which accompanies the ion exchange of Arg' for Na+ was eliminated from the plausible mechanisms and that the equilibrium constant obtained kinetically is in good agreement with that obtained statically, one may conclude that reaction IV
J. Phys. Chem. 1984,88, 1257-1261 .LULL
TABLE I: Rate Constants of Steps a and b at 25 “C
m
1257
ULUL ‘G luLLL 7//////// 0/7:/; 7 ‘ 77im
k , , mol-’ dm3 s-’
k., , s-’
k,, s-’
k.,, s-’
A rg*-
HzO
Orn orurea
8.5 X l o 4
5.8 X 10’
2.0 X 10’
2.2 X 10’
step a intercalaction
step b
step b’ (very slow)
TABLE 11: Kinetic and Static Equilibrium Constants of Reactions Ill and IV at 25 “C K’, mol-’ dm3
K,,
mol-’ dm3 150
___-
K, 0.91
kinetie
static
K3
290
200
5.5
a This value was calculated by using the kinetic equilibrium constants K , and K,.
does not relate to the observed relaxations. The intercalation of L-arginine into the interlamellar layer of the montmorillonite accompanies the release of urea from the hydrolyzed L-arginine. Taking into account a lack of relaxation in the montmorillonite-L-ornithine system, the relaxations observed must be due to the hydrolysis of L-arginine in the interlamellar space. Thus, reaction I11 may be rewritten as
hydrolysis
(VI
Figure 11 shows the dependence of the released ornithine on the pH at a constant concentration of L-arginine, 1.O X mol dm-3, and a particle concentration of 15 g dm-3. It can be seen from this figure that the amount of ornithine released decreases with a decreasing pH. This variation profile is nearly the same as that of Arg+- in the bulk phase. This fact leads to the conclusion that the hydrolysis of L-arginine may be induced by the intercalation of Arg+- into the interlamellar layer. Similar kinetic studies on the catalysis in the interlamellar layer of various layered compounds are now in progress. The results will be reported in due course.
Acknowledgment. We thank Professor Oka and Dr. Shigeta of Hiroshima University for the amino acid analysis. Registry No. Montmorillonite, 1318-93-0;L-arginine, 74-79-3; Lornithine, 70-26-8; urea, 57-13-6.
General Thermodynamic Analysis of the Contributions of Temperature-Dependent Chemical Equilibria to Heat Capacities of Ideal Gases and Ideal Associated Solutions Gilbert J. Mains,*+ John W. Larson,** and Loren G. Hepler*o Department of Chemistry, University of Lethbridge, Lethbridge, Alberta, Canada TI K 3M4 (Received: July 7, 1983; In Final Form: August 3, 1983)
Considerations of heat capacities of mixtures of ideal gases and of ideal associated solutions in chemical equilibrium have shown that there are both “compositional”and “chemical relaxation” contributions to the equilibrium heat capacities. These relaxation contributions, which are due to temperature-dependent equilibria and related enthalpies of reaction, are in some cases (such as ortho-para hydrogen) quite large in comparison with the long-recognized compositional contributions. We have derived general thermodynamic equations for these two kinds of contributions to the total heat capacity and have applied these general equations to three systems: ortho-para hydrogen ideal gas, ideal associated solutions with a single equilibrium of type A + B = AB, and ideal associated solutions with coupled equilibria of types A + B = AB and A 2B = AB2.
+
Introduction It has long been recognized that the heat capacities of some mixtures can be represented as appropriate sums of the heat capacities of the constituents of the mixtures. Specific heat capacities of Athabasca oil sands and defined components provide a recent example.’ In this case it has been shown that the specific heat capacities of various samples of oil sands are accurately expressed as appropriate sums of terms of type fC, in which f and Cp represent mass fractions and specific heat capacities of components. The situation is more complicated, however, for mixtures in which there is a temperature-dependent equilibrium between components of the mixtures. During the course of a calorimetric measurement of the heat capacity of such a mixture, the temperature is intentionally changed, which leads to a shift in the equilibrium between components and thence to a “relaxation” contribution to the heat capacity. These relaxation contributions are in some cases quite large in comparison with the long-recognized “composition“ contribution. TVisiting scientist from the Department of Chemistry, Oklahoma State University, Stillwater, OK 74078. *Visitingscientist from the Department of Chemistry, Marshall University, Huntington, WV 25701. *Present address: Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2.
0022-3654/84/2088-1257$01,50/0
Long ago McCollumZmeasured heat capacities of the N204(g) = 2N02(g) equilibrium system and correctly recognized that his
measured heat capacities contained contributions from the chemical species (N204and NOz) and from the shift of equilibrium with changing temperature. His treatment of what we are calling the relaxation contribution to the heat capacity was both correct and straightforward. More recently, McCollum’s procedure has been extended (only for ideal gas equilibria) in textbooks3s4of physics. It has also been recognized (only qualitatively) for a long time that relaxation contributions might be important in connection with certain liquid solutions. For example, in 1941 Randall and TaylorS wrote the following: “If a reaction-for example, the dissociation of bisulfate ion into hydrogen and sulfate ions-is more complete at a higher temperature than at a lower, then the heat corresponding to the additional fraction of bisulfate ion dissociated at the higher temperature will be measured as though (1) D. Smith-Magowan, A. Skauge, and L. G. Hepler, J . Can. Pet. Technol., 21, 28 (May-June 1982). (2) E. D. McCollum, J . Am. Chem. SOC.,49, 28 (1927). (3) P. S . Epstein, “Textbook of Thermodynamics”, Wiley, New York, 1937. (4) M. W. Zemansky, ”Heat and Thermodynamics”, 5th ed., McGrawHill, New York, 1968. ( 5 ) M. Randall and M. D. Taylor, J . Phys. Chem., 45, 959 (1941).
0 1984 American Chemical Society
