1794
Anal. Chem. 1905, 57, 7794-7798
Reaction Rate Measurement by Flow Injection Analysis Using the Gradient Stopped-Flow Method James M. Hungerford, Gary D. Christian,* Jaromir Ruzicka,' and J. Calvin Giddings2 Center for Process Analytical Chemistry, Department of Chemistry, University of Washington, Seattle, Washington 98195
Prlnclples and mantfold dedgns of stopped-flow FIA are compared for wrlal assay and phydochemkal rate appllcatlons. An FIA microcondutl system b adapted for rate measuruineni Wtth wdccklkred Mlal r e m condltkns selected from a concentratlon gradient obtalned by controlled dlsperdon. The system descrlbed k applled to the measuremnt of rate constants and reactlon orders In the permanganate oxldatkms of benzaldehyde and crotonk actd. Both pseudofirstorder and eecof&wder solutlon condttlonr are used, abng the petmanganate concentration gadlent, to determhe rate constants In exceknt agreement wlth ltlerature values. The system has a 0.6-8 dead thm. Umnatkns ol the present system and possible deslgn Improvements are discussed.
It is well recognized that flow injection analysis (FIA) yields a response curve which is the result of two processes, both kinetic in nature: the physical process of dispersion and the chemical process of formation of various compounds ( I ) . The kinetics of physical dispersion have been described in a number of papers, while attempts to describe the results and interactions of both processes as they occur simultaneously are fewer (2-6). Most recently, the computer simulation by Betteridge et al. based on a random walk model (31,the work of Painton and Mottola (4), and a paper dealing with single bead string reactors by Reijn, Poppe, and Van der Linden (5) have provided detailed and instructive treatments of kinetic effects in FIA. If FIA is to be used for the purpose of determining reaction rates and rate laws, an experimental approach is needed which allows resolving the individual contributions of physical dispersion and chemical kinetics. The method should not compromise the convenience of FIA by requiring extensive calculations or a large number of experiments. Precision should not be jeopardized by dependence on change and measurement of flow rate or channel dimensions. Ideally, reaction orders higher than f i t - or pseudo-first-order should be directly accessible. Finally, the initial reaction conditions should be well defined, to allow meaningful comparison with the results of batch experiments. A straightforward approach to resolve dispersion and kinetics is to record the FIA response curve in the absence of a chemical reaction and compare it with the one recorded while chemical reaction occurs. This has been done on a continuous flow basis by measuring peak heights (2,5-7) and peak areas (2,6).Thus, in the recent work of Vanderslice et al. (6) the rate of oxidation of benzaldehyde by permanganate ion was measured spectrophotometrically. From the comparison of peak heights (or areas) recorded in the presence and absence of benzaldehyde, pseudo-first-order rate constants were measured. With the exception of multiple detection schemes 'Present address: Chemistry Department A, The Technical University of Denmark, Building 207, DK-2800 Lyngby, Denmark. 2Present address: Department of Chemistry, University of Utah, Salt Lake City, UT 84112. 0003-2700/85/0357-1794$01.50/0
(7), it is a common feature of all FIA kinetics experiments using continuous pumping that changes in reaction times require changes in pumping rates, channel volumes, or geometry. None of the methods allow easy measurement of infinite time absorbances. Of all the currently available forms of FIA, stopped-flow FIA has many advantages in the measurement of reaction rates. In addition to providing a continuous recording of reaction rate during a selected stopped-flow time interval (t,, Figure l),various concentration ratios of the reacting species, as found in a zone dispersed within a carrier stream of reagent, can be selected electronically. This is easily accomplished by choosing the length of a delay time, td, allowed to elapse between sample injection and a stopped-flow period. The analytical value of this technique has been demonstrated in a number of enzymatic assays (I, 8,9) as well as other analytical applications (1, 10). Reaction rate parameters have been correlated with data from stopped-flow FIA (11). Kagenow and Jensen demonstrated the potential of the technique for the calculation of a pseudo-first-order rate coefficient (IO). Since their work did not addres rate measurement in the physiochemical sense, certain initial reaction conditions were undefined and a detailed treatment was not given. It is the purpose of the present work to show how gradient FIA can be used for the measurement of rate coefficients and orders, to examine differences between the design of FIA systems for serial sampling and for physiochemical measurement, and, f d y , to outline the limitations of the present system and to visualize possible design improvements. Principles and Designs of Manifolds. Reviewing the principles of stopped-flow FIA for chemical analysis reveals details of manifold design important in adopting the technique for physiochemicalrate study. The simplest so-called one-line FIA system (Figure la) has been used for enzymatic assays based on reaction rate measurements ( I , 8,9). By injection of a sample (A) into a reagent stream (B)by means of an injection valve (SA), a well-defined zone is formed, which disperses on its way through a reaction coil a, forming a mutual concentration gradient with reagent B. When the forward movement of the carrier stream is stopped, a small section of the dispersed zone is arrested in the flow cell. Since dispersion is then stopped, the changing signal during the stopped flow period (t,) reflects the rate of chemical reaction. Highly reproducible injection, movement of the dispersed zone, and the use of a time (T) allow precise selection of a zone element. Specifically, the timer is used to choose a delay time (td) which is t o elapse from the point of injection of the sample to the moment the pump is stopped. After the conclusion of a stop interval (tJ, pumping is resumed to wash out the system prior to the next sampling cycle. The system is calibrated by injecting a series of analyte standards to yield calibration graphs at each delay time. As a eradient technioue. l o wuses the precision . ~ t o..~ ~ e d - f FIA and variety of dispersed elements of the sample zone to advantage. This is best understood by considering the dispersion in each solution element. Sample zone dispersion (I) is defined 0 1985 American Chemlcal Soclety
ANALYTICAL CHEMISTRY, VOL. 57, NO. 9, AUGUST 1985
B
m
where X and Yare the pumping rates of the C and B lines, respectively. Thus the advantage of designing flow channels as shown in Figure l b is that CB,~can be related to an initial reaction time ti, shown in Figure lb. The following treatment will show that there is also advantage in decreasing the volume of coil a as in Figure IC. The initial concentrations of sample C4 for each delay time are obtained by dispersion experiments in which the horizontal portions of the stopped flow curves correspond to C A in eq 1. Since in coil a (Figure lb,c) both dispersion and chemical reaction take place simultaneously, it is necessary to consider the error caused by the reaction of A with B during the time t, allowed for mixing (see timing segments, Figure lb,c). If C, is defiied as the concentration of A consumed by reaction in coil a, the apparent initial concentration of A detected in the flow cell is
W
SA
C
W
B
rn
Sa
C
8,
W
q ti
Figure 1. Three types of flow channel designs for stopped-flow injection analysis. SAis the injection valve. FC Is the flow cell, and W is the waste. For explanation of tlming sequences and other symbols, see text.
as the ratio of the sample (A) concentration before injection CAoto the gradient concentration CA of the zone element held within the flow cell during measurement
DA = CA'/CA and for peak maximum DAmru= CAO/ CAmax (1) Thus DA is the dispersion coefficient describing the concentration of CAwithin the sample zone gradient element at delay time t d . In a single line FIA system (Figure la) the dispersion of reagent (B) will consequently be given by
-') -'
DB = CBo/CB = (1- DA
1795
where D is the dispersion calculated a t a given delay time, t d , and CA,c is the concentration of A consumed by reaction in coil a. As long as t, , ,C the above expression simplifies to a familiar pseudo-first-order expression
In CAo/DA - In CAt = C&,t
= k;t
(10)
where k; is the pseudo-first-order rate mnstant at a given C, An expression similar to eq 9 can be derived for the benzaldehyde stoichiometry with a pseudcArst-order expression identical with eq 10. While kf1 can be calculated without knowledge of CAo/D, it has little value if CB,iis unknown.
zL3
0 'Scan
Ftpm4. Abswbance-tlme respo~e cuvos for reaction rate meastu~mentof ox!daHon of crotonic acld by KMnO,. D , values w a obtained by dispersion experiments. All c w a s h each set of experiments(&and Figwe &)were remded amecuKvei~tmm hsame starting polnt (SA),with an increasing d&y time (td = 7 , 8. 9, and 10 s,a to d and a' to d') with stopped Row period 1. = 20 s. Cuves wllhout desdpaOn had 1. = 0. (a)K M , (C,' = 5.54 X lo-' M) in phosphate buffer in absence of crotonic acld. (b) KMnO, (CAo = 8.54 X IO-' M) in phosphate buffer, crotonic acld (CsJ= 2.10 X IO-' M) in phosphate buffer. stream B.
EXPERIMENTAL SECTION Reagents and Solutions. All chemicals usad were Analytical Reagent grade. Benzaldehyde and crotonic acid were checked for purity by '€ NMR I and IR spectrometry and used without furtber purification. Phosphate buffer solutions were prepared as described by Wiberg (12, 13). Filtration of stock KMnO, solutions following the experimentsgave no residue, and their absorbance readings were stable and reproducible for 1week. Crotonic acid and ascorbic acid solutions were prepared immediately before use. Apparatus. All pumping, sample injection, and timing operations were controlled by a Tecator 5020 FIA analyzer, while a Radiometer Servograph recorder gave analog readouts. Both were connected through a logarithmic converter to a B a d and Lomb Mini 20 spectrophotometer. T h e flow cell was connected to the spectrophotometer and a tungsten light source via fiber optics entering at the top and bottom (see insert Figure 2) and had an 1EpL volume and 10-nunpath length. Both the flowcell and flow channels were integrated into one unit as shown in detail in Figure 2, which corresponds to design Figure IC.All micromnduit cbannels were semicircular (d = 1.0 mm) in mo88 section, with volumes a = 19 pL and b = 75 pL. A PTFEtube connecting the injector and channel b had a volume of 10 p L (d = 0.5 mm). The sample volume injected in all experimentswas 20 pL. All experiments were conducted at 25 0.1 "C. Calibration Procedure. Relative pumping rates were calibrated by continuously pumping bromothymol blue (BTB) through the reagent (B) line and borate buffer through the carrier (C) line and then pumping BTB through both lines. The steady-state absorbance ratios thus obtained at 620 nm provided
*
I
*scan
I
Figwe 5. Absorbsncbtime response awes for reaction rate meas u r e m of oxldafbn of aoMnk acld (CEl = 1.05 X 10 IO9 M. stream B) by KMnO, (CAo= 8.54X IO-' M) Injected InM Sbeam C. For detalh me Figure 4 and text.
a dilution value of Y/(X+ Y) = 0.400 at the pumping rates of the benzaldehyde experiments. In the m h i c acid experiments, this dilution value was 0.434. The individual flow rates were volumetridy measured to be X = 1.15 mL/min and Y = 0.88 mL/min. The initial mncentrations of KMnO,, ie., C, were established by calibrating the FL4 system depicted by Figure ICwith bro. mothymol blue that wan injected into the colorlesscarrier stream which, after passing mils b and a, carried the dispersed ulne into the detector. Again, by monitoring the absorbance of BTB at 620 nm and from knowledge of the absorbance of the original dye concentration C", the dispersion values were computed for the peak maximum Dmu = 5.21 (Figures 3-5), as well as for delay times td,which were increased in 1-8 intervals thus yielding the f0llOwiUg DAVdlles: 6.56 ( t d = 10 S), 8.95 ( t d = 11 S), 12.3 ( t d =
ANALYTICAL CHEMISTRY, VOL. 57, NO. 9, AUGUST 1985
Table I. Rate Constants for Permanganate Oxidation of Benzaldehydeavb td, 8
cB,i/cA,i
10 11 12 13 14
5.02 6.85 9.42 13.1 19.3
lo‘k’l,
S-l
5.16 5.00 5.31 5.59 5.74 5.36 f 0.30
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Table 11. Rate Constants for Permanganate Oxidation of Crotonic Acida
k2, M-I s-l
cB,i
td, S
CB,~/CA,~
1O2k‘1, S-‘
kp: M-‘ s - ~
0.316 0.307 0.326 0.343 0.352 0.329 f 0.018‘
2.10 x 10“‘
7 8 9 10
1.48 2.10 3.25 5.19
b b 4.58 4.62 4.60 f 0.03
222 222 219 220 221 f 2
1.05 x 10-3
7 8 9 10
7.39 10.5 16.2 25.9
= 2.13 x 10-3M, cB0= 4.08 x 10-3 M, cBj= 1.63 x 10-3 M. *Rate plots had coefficients of correlation >0.998. Wiberg and Stewart (12) found ks = 0.324 Me’s-’. acA0
12 s), 17.3 ( t d = 13 s), and 25.2 ( t d = 14 s) (Figure 3). Since the dye was nonreactive and since no dispersion took place during the stopped flow period (t, = 15 min), the absorbance did not change in time and the recorded BTB curve was parallel to the base line for all delay times. For clarity, only one of these BTB curves is indicated by the dotted line in Figure 3a. Having thus established performance of the flow system in the absence of chemical reaction, a reference or “base line” had to be established for KMn04 since this strong oxidant is known to self-decompose in the presence of organic materials-of which the microconduit is made, Therefore, the dispersion experiment was repeated by injecting KMn04 into the phosphate buffer (which was pumped in both lines C and B) and by recording the absorbance at 525 nm. During the long stopped flow period (Figure 3a), to be used later for benzaldehyde experiments, the absorbance of KMn04 slowly decreased and this “base line” allowed for subsequent reaction rate measurements (see below). For a shorter stopped flow period (to be used later for crotonic acid experiments) the same experiment was repeated and it was found that no appreciable reduction of KMn04took place (Figure 4a), as indicated by the horizontal “base line”. In this manner two objectives were established. The manifold in Figure ICwas calibrated by BTB experiments to establish Cki by means of DA and CB,i by dilution ratio experiments. And the above “base lines” and initial permanganate absorbances (A) were obtained for subsequent reaction rate measurement (Figure 3a).
RESULTS AND DISCUSSION Response Curves and Rate Constants. The rate of oxidation of benzaldehyde with permanganate was measured by using manifold Figure ICand by pumping 4.08 X M KMnO, (dissolved in phosphate buffer) through line B. The recorded curves a’ to e’ (Figure 3b) reflect reaction rates for different permanganate/ benzaldehyde ratios since dispersion of KMnO, gives C4 values decreasing with increasing DA and delay times ( t d ) . By use of corresponding “base line” values from Figure 3a (i.e., by correcting reaction rate curve a’ with “base line” a, curve b’ with “base line” b, etc.), reaction rate constants were computed from CA,~, CA,~, and C B , ~in the usual manner. As shown in Table I, the average value of k2 is in excellent agreement with that obtained by Wiberg and Stewart (12). A small increase in k2 values with decreasing initial concentration of KMnO, was also observed when the conventional reaction rate method was used (12). The same approach was adopted for measurement of the oxidation rate of crotonic acid by permanganate using the manifold in Figure IC(CA’ = 8.54 X lo4 M KMn04) with crotonic acid concentrations of 4.84 X lo4 M (Figure 4b) and 2.42 X loe3M (Figure 5 ) in phosphate buffer. Since the “base line” for KMn04 alone for a shorter stopped flow period (20 s) was horizontal (Figure 4a), no correction was necessary, and reaction rate curves a’ to d’ (Figures 4b and 5b) could be used directly using A, t, t d , and DA values to compute pseudo-firstand second-order rate coefficients, kl and k2, respectively (Table 11). Some features of the response curves require comment. First, stopped flow curves in Figure 3 show an increase of
22.8 22.4 23.1 22.4 22.7 f 0.3
217 213 220 213 216 f 3
Rate plots all had coefficients of correlation >0.999. CAo= 8.54 lo4 M. bRate constants determined from second-order plot. “Grand average, k2 = 218 f 3 M-’ s-l. Wiberg and Geer (13)found k, = 232 f 11 M-’ 8-l. X
absorbance at the very beginning of the stopped flow period. This upward drift is strictly reproducible and is due to diffusion of permanganate within the flow cell. Each stopped flow curve attained a maximum absorbance within a few minutes and this was used to determine Cw Rate data points were used only at times later than this steady-state point. At the lower permanganate concentrations and short stop times used in the crotonic acid experimeats, the above diffusion effect was insignificant. The next feature, the appearance of a second peak in Figures 4 and 5, is an artifact of the stop-go pumping mode. During the stopped flow period, only the section of the sample zone held within the flow cell and the small adjacent coil a has been mixed with reductant so that permanganate was reduced in this section of the dispersed zone during the stopped flow period. When pumping is resumed, a larger section of unreacted zone, which has been accommodated in coil b during the stopped flow interval, is recorded as a second peak when passing through the flow cell. The orderly decreasing magnitude of the artifact peaks is the result of the progression of delay times t d as different sections of the KMn04 are stopped in front of channel a. This observation leads to the question of how short channel a could possibly be to allow even faster reaction rates to be measured and yet allowing A to be sufficiently well mixed with B (in the radial direction) before reaching the flow cell. To obtain some indication of the minimum achievable mixing time of the system, 2.42 X M ascorbic acid was used as reductant while 8.54 X 10“‘ M KMnO, was injected using manifold Figure IC. No peaks were recorded since all permanganate was reduced within 0.6 s, during which the mixture of A and B passed from the confluence point into the flow cell through the short coil a. This confirms that time tmmin must be shorter than mixing time t,(0.57 s from Va/Qa, eq 5). The value of the minimum mixing time (tmmin) was estimated using eq 5 (see below). Finally, a comment has to be made on the fact that the absorbance signal will be nonzero when reaction is complete (cf. Figure 4b). The response curves obtained with the most concentrated crotonate solution showed that, throughout the concentration gradient, the final absorbance values at each delay time were 11% of the initial values of corresponding curves 4b (a’*’). They were also independent of the crotonate concentration, so the absorbing product obeys Beer’s law and is proportional to the permanganate concentration. The above results support the proposal by Geer and Wiberg of a rapid reaction between the product Mn02and the phosphate buffer. The data were corrected for this absorbance as previously described (13). In Table 11, the values of k’, and k2 obtained from response curves at the two crotonic acid concentrations shown in Fig-
1798
ANALYTICAL CHEMISTRY, VOL. 57, NO. 9, AUGUST 1985
i
a
‘:i
Table 111. Initial Reaction Times
9.9
td,
(ti - td),
7a
-0.44 -0.45 -0.43 -0.44
7b 8 9
-1nCA 250:.7
t (s)+
Figure 6. Rate plots for oxidation of 2 X lo-‘ M crotonic acid by KMnO, at t, = 8 s (cf. curve b’ Figure 4b). Black dots are -In CAvs.
while white squares are a vs. t . Respective linear regression coefficients were 0.987 and 0.999. t
ures 4b and 5 are presented. When CB,iis sufficiently higher than CA,~, pseudo-first-order conditions prevail, and k 1’ and k2 may be calculated from logarithmic plots and eq 10. This condition is satisfied at the 9- and 10-s delay times yielding curves 4c’ and d’ as well as at all delay times given in Figure 5, where crotonic acid is always in sufficient excess. However, a t the higher permanganate concentrations of curves 4a’ and b’, and the lower initial crotonate concentration of the Figure 4 data, the chosen ratio of crotonate/permanganate is small enough to yield second-order kinetics in the first half-life. As shown in Figure 6, significant deviations from pseudo-first-order behavior are observed in the first half-life, where time curve 4b‘ is transformed and plotted according to both pseudo-first- (-ln C) and second-order (a, see eq 9) kinetics. When the second-order parameter is plotted vs. time, a straight line is obtained. Values of kz obtained in this way from both the 4a’ and 4b’ curves are in excellent agreement with the other results. Average k’l values obtained at the two crotonate concentrationations shown indicate that the reaction is 0.99 order in crotonic acid. At a given CB,i,k2 values determined along the permanganate concentration gradient differ from each other by only 2%. Furthermore, the grand average value of k2 of 218 M-’ s-l is in excellent agreement (-5%) with the literature value (13). Initial Reaction and Radial Mixing Times. Estimates of (ti - t d ) and minimum times tmminneeded for mixing in a radial direction are essential to testing the approximations of eq 3-5 and evaluating the limits of the present system. Values of (ti - t d ) estimated by extrapolation of one second-order and four pseudo-first-order rate curves are shown in Table 111. Also shown are values estimated from the natural logarithms of corrected reaction and no reaction peak maxima and average values of kl and k p All (ti - t d ) times are remarkably similar over a wide range of solution conditions, for both stopped and continuously pumped streams. (Note that this would not be the case for a one-line channel, Figure la). By use of an average value of (ti - td) and eq 5, the minimum radial mixing time tmmin can be estimated to be on the order of 150 ms. Assuming that the stream inlet could be moved closer to the flow cell, the above estimates indicate that the mixing time could be further reduced from the 0.6 s required to traverse coil a in the system depicted in Figures ICand 2 to about 150 ms; thus, reactions with half-lives on the order of 1s could easily be accommodated. Further reductions in mixing time might be achieved by increasing the flow rate. The present work demonstrates the feasibility of performing precise and accurate measurements of reaction rate parameters by stopped-flow FIA of reactions with k’, on the order of 1
td, 8
10 C
d e
(ti
- td)t 8
-0.40 -0.39 -0.43 -0.37
aFrom rate curve extrapolation to 1y = 0 using Figure 4b data. *From rate curve extrapolation of -In CA,, using Figure 5 data. Calculated from peak maxima of Figure 4, parts a and b, assuming kl = 4.60 X s-l. dAs in footnote c, from Figure 4a,b peaks, assuming k’l = 2.27 X lo-’ s-l. eAs in footnote c, from Figure 4a M croand peaks obtained by injecting same C A O into 5.25 X tonic acid, and assuming k’, = 1.14 s-*, Based on k, = 218 M-’s-l.
s-l. Second-order kinetics may be studied as accurately as pseudo-first-orderrates, since both reagent and sample initial concentrations are well defined. Caution should be exercised, however, in the choice of manifold as well as sample volume. In experiments where either large sample volumes or low dispersion reactors yield limited dispersion, steep concentration gradients are present. In addition to encouraging diffusion during the stop interval, these steep gradienta could, in principle, distort rate data since the nonlinear response curves are averaged by the detector over the flow cell volume. We have found that this effect is made minimal by using medium or large dispersion conditions. The effectiveness of the mixing of streams B and C within 150 ms at the confluence point has a practical consequence for microconduit design since additional mixing devices were not needed for the present experiment. Yet it should be emphasized that streams B and sample A had the same viscosities, while solutions with widely different viscositieswould not mix so readily. Micromixing in flow injection channels remains an interesting subject which warrants further studies. As a FIA gradient method, the technique described here proved to be a novel and flexible tool and could certainly find application in the study of chemical and biochemical reactions of moderate speed. It is anticipated that the present study will inspire others to use the flow injection method for purposes other than automated analyses. While in such serial analyses high sampling frequency is essential, the present work shows the importance of an exact knowledge of solution conditions for accurate measurement of rate coefficients, stability constanta, and other data of fundamental nature. The versatility of the FIA concept allows appropriate changes of FIA designs to be made to suit these new requirements, often without additional complexity or extensive calculation.
ACKNOWLEDGMENT The authors express their gratitude to Radiometer America Inc. and to Tecator Inc. (Virginia) for the loan of equipment. LITERATURE CITED (1) Ruzlcka, J.; Hansen, E. H. “Flow Injectlon Analysis”; Wlley: New
York, 1981. (2) Haagensen, P., ref 1, p 26. (3) Betterldge. D.; Marczewskl, C. 2.;Wade, A. P. Anal. Chim. Acta 1984, 165, 227. (4) Palnton, C. C.; Mottola, H. C. Anal. Chim. Acta 1984, 158, 67. (5) Reljn, J. M.; Poppe, H.; Van der Llnden, W. E. Anal. Chem. 1984, 56. 943. (6) Vanderslice, J. T.; Beecher, G. R.; Rosenfeld, A. G. Anal. Chem. 1984, 56. 268. ( 7 ) Hooky, D. J.; Dessey, R. E. Anal. Chem. 1983, 55, 313. (8) Ruzlcka, J.; Hansen, E. H. Anal. Chlm. Acta 1979, 106, 207. (9) Ruzicka, J. Anal. Chem. 1983, 55, 1040A. (10) Kagenow. H.; Jensen. A. Anal. Chim. Acta 1083, 145, 125. (11) Yoza. N.; Miyaji, Ti; Hlrai, Y. J . Chromatogr. 1984. 283,89. (12) Wiberg, K. B.; Stewart, R. J . Am. Chem. SOC. 1954, 7 7 , 1786. (13) Wlberg. K. B.; Geer, R. D. J . Am. Chem. SOC. 1968. 88, 5827.
RECENEDfor review January 2,1985. Accepted April 26,1985.
