Computer Controlled Stopped-Flow Studies-Application to Simultaneous Kinetic Analyses Donald Sanderson, John A. Bittikofer, and Harry L. Pardue’ Department of Chemistry, Purdue University, Lafayette, Ind. 47907 The design and construction of a fully automatic stopped-flow instrument featuring a computer controlled sample preparation unit, a newly designed sampling system, and real time data collection and treatment are presented. The instrument is used for a kinetic study of the exchange reaction between a Ni(ll)-citrate complex and thiol acids. Information obtained from this study is used to develop an analytical procedure for the simultaneous determination of two thiol acids, cysteine and thiolactic acid in mixtures. Samples of thiol acids were determined quantitatively in the concentration range of 5 x l o - S M to 5 x 10-4M. Results for the two-component systems are presented.
IN CERTAIN SITUATIONS, the kinetic approach to chemical analysis may have one o r more of several potential advantages when compared to the thermodynamic approach for the same species. These advantages include greater speed ( I ) , greater sensitivity (2, 3), a higher degree of selectivity (4-6), and the possibility of performing types of analyses which are not otherwise possible (7-9). The power of stopped-flow spectrophotometry as a tool for fundamental kinetic studies is well established (10). Recently, it has been demonstrated that the stopped-flow method also is useful for very fast kinetic analyses (1, 5, 11). Recent work has been directed a t the improvement of this technique via the use of on-line computers for collecting and processing data (12, 13) and via the use of a highly stabilized spectrophotometer (13). To date, however, little effort has been directed a t the automation of the sample handling step. This report describes the integration of computer controlled sample preparation and sampling systems with a stopped-flow mixing system to provide a highly automated stopped-flow spectrophotometer. I n practice, the investigator need only 1
Correspondence should be addressed to this author.
(1) A. C. Javier, S . R. Crouch, and H. V. Malmstadt, ANAL.CHEM.,
41, 239 (1969). (2) R. L. Habig, H. L. Pardue, and J. B. Worthington, ibid., 39, 600 (1967). (3) J. B. Worthington and H. L. Pardue, ibid., 42, 1157 (1970). (4) S . Siggia, “Quantitative Organic Analysis via Functional Groups,” John Wiley & Sons, New York, N.Y., 1966, pp 655-83. (5) J. B. Pausch and D. W. Margerum, ANAL.CHEM.,41, 266 (1969). (6) D. W. Margerum, J. B. Pausch, G. A. Nyssen, and G. F. Smith, ibid., p 233. (7) B. Hess, “Enzymes in Blood Plasma,” Academic Press, New York, N.Y., 1963. (8) 0. Bodansky, Amtr. J. Clin. Pathol., 38, 343 (1962). (9) J. H. Wilkinson, “An Introduction to Diagnostic Enzymology,” Williams and Wilkins, Baltimore, Md., 1962. (10) H. B. Mark, Jr., and G. A. Rechnitz, “Kinetics in Analytical Chemistry,” Interscience, New York, N.Y., 1968. (11) B. G. Willis, W. H. Woodruff, J. R. Frysinger, D. W. Margerum, and H. L. Pardue, ANAL.CHEM.,42, 1350 (1970). (12) R. J. Desa and Q. H. Gibson, Comput. Biomtd. Res., 2 , 494 (1969). (13) B. G. Willis, J. A. Bittikofer, H. L. Pardue, and D. W. Margerum, ANAL.CHEM., 42, 1340 (1970). 1934
ANALYTICAL CHEMISTRY, VOL. 44,
supply the instrument with stock reagents required for the study or analysis to be carried out and initiate the experiment; after this, all operations are carried out automatically to provide the specified data or results. Specific capabilities of the stopped-flow instrument include the ability to prepare and mix samples and reagents automatically, to acquire kinetic data on the mixed solutions, to process these data to provide the desired information, and to report these data in one or more of several formats. All of these operations are under computer control; and each can be performed repeatedly o n the same sample or separately on different samples as desired. During a set-up phase, instructions are given to the computer as to what samples are to be prepared, in what order they are to be prepared, the rate and amount of data to be collected, and what mathematical operations are to be performed o n the data. Once this is done, the system prepares the first sample by delivering the desired amounts of selected reagents to a receiving vial. The sample is then transferred to the stopped-flow instrument for mixing with a final reagent to start the reaction. The reaction is initiated in the mixing jet and is followed photometrically. Data are collected and processed by the computer. The processed data are displayed graphically on a display oscilloscope and/or printed in numerical format on a Teletype. The sample preparation and run cycles are then repeated until all experiments have been carried out. The automated stopped-flow system is applied to a study of the kinetics of the exchange reaction between Ni(I1)-citrate and the thiol acids cysteine and thiolactic acid and to the simultaneous kinetic determination of the two acids in mixtures. Thiol acids react with Ni(I1) to form stable complexes that have absorption maxima in the ultraviolet region of the spectrum (14, 15). The reactions can be forced into pseudofirst-order behavior with different rate constants for different acids, and therefore are useful for simultaneous kinetic analyses (11). This report includes kinetic data which have been used to develop analytical methodology for the simultaneous determination of cysteine and thiolactic acid in mixtures of the two. INSTRUMENTATION
The automated stopped-flow system consists of a sample preparation unit, a sampling unit, a Sturtevant-type mixing system, a highly stabilized photometer, and a small generalpurpose computer (Hewlett-Packard 21 15A) which controls the operation of the remainder of the system. All parts of the system except the sampling unit have been described earlier (13, 16) and these will not be discussed further here. Figure 1 is a schematic representation of the sampling system. It consists of two lines connected to pneumatically driven syringes at one end and connected to the two inlet
(14) D. L. Leussing, J . Amer. Chem. Soc., 81, 4208 (1959). (15) R. A. Libby and D. W. Margerum, Biochemistry, 4, 619 (1965). (16) S. W. Deming and H. L. Pardue, ANAL.CHEM., 42,1466(1970).
NO. 12, OCTOBER 1972
tubes of the mixing cell at the other end. The line on the left side is assumed to carry some “standard” reagent of constant composition while that on the right carries the test reagent (or sample) whose composition is being varied and a “push” liquid used to force the test reagent to the mixing cell. All valves can assume one of two positions, one for filling syringes and sample loop, and one for mixing. All valves are shown in the filling configuration in the diagram. In this configuration, the backward motion of the syringe plungers draws the standard reagent into one syringe and a push liquid into the other syringe. The test reagent is drawn into the sample loop (coiled representation) by a mild vacuum. In the mixing configuration, all valves are rotated 90 degrees clockwise and the forward motion of the syringe plungers forces the standard and test reagents through the mixing chamber and into the observation cell. The interface between the test reagent and the push liquid is stopped just before valve No. 3 to ensure that the sample being observed is not diluted by the push liquid. Data acquisition is initiated automatically by closure of a micro-switch at the end of the mixing cycle. A potential problem with this system is cross contamination between sequential samples. Titrimetric experiments were used to evaluate the magnitude of this problem. For a section of tubing containing 1.2 ml of sodium hydroxide solution, a 1.4-ml displacement with distilled water is sufficient to displace more than 99.5 of the base from the tubing. The timing of the filling cycle is adjusted so that the volume of the new test reagent drawn through the sample loop represents two full displacements of the loop. The lines from the sampling system to the mixing chamber and observation cell are short so that each injection causes multiple displacements of the solutions in these lines and the cell. Thus, the potential problem of cross contamination between samples is reduced to an insignificant level, so that each cycle includes its own rinse step and no separate rinse cycle is required between samples. For illustrative purposes, it was convenient to represent the valve motion as rotational in Figure 1. The actual valves used (type CAV, Chromotronics, Inc., Berkeley, Calif.) employ a sliding motion. Thus, they are easily operated by electrical solenoids. The valves can be combined by twos so that the four valves represented in this system required only two solenoids (Modernair, Angola, Ind.). These valves were selected because they are chemically inert, they have zero dead volume, they are rated at 500 psi of pressure; and their operation can be controlled electrically. The tubing used for the reagent lines is 0.125411. 0.d. X 0.063-in. i.d. Teflon tubing (Chromotronics, Inc., Berkeley, Calif.). The approximate lengths of the various sections are represented in the caption of Figure 1. The filling, mixing, and data acquisition steps are repeated under computer control until the preset number of experiments have been performed. EXPERIMENTAL
Reagents. Distilled, deionized (Amberlite MB-3 column) water was used for preparing all solutions. All glassware was cleaned with a 50-50 mixture of concentrated sulfuric and nitric acids. BUFFERS.Borate buffers used were prepared according to Perlman (17). For a pH of 9.0, exactly 20.8 ml of 0.1M NaOH was added to 50 ml of a 0.1M boric acid-0.1M KC1 solution. Additional amounts of KCI were added to adjust the ionic strength of the buffer solutions to the desired level. The volume was then adjusted to 100 ml with distilled, deionized water. The final pH was checked with a Sargent-
(17) P. Perlman, “Reagents and Solutions in Analytical Chemistry,” Franklin Co. Inc., Englewood, N.J., 1966.
U Injection Syringe #I
Push Reagent
Valve #I
E
Loop Sample
I
b
To Cell
Figure 1. Schematic representation of the sampling and injection system Valves: Type CAV, Chromotronics,Inc., Berkeley, Calif. Tubing: Teflon, 0.125-in. o.d., 0.063-in. i.d.
Welch pH meter (Model LS) and if necessary was adjusted to a pH 9.00 i 0.02 with either concentrated solution of HC1 or NaOH. Other buffer solutions at other pH values were prepared in the same manner using different amounts of 0.10M NaOH. NICKELSOLUTION.Nickel solutions were prepared by dissolving reagent grade nickel sulfate hexahydrate (Mallinckrodt Chemical Works) in distilled, deionized water. SODIUMCITRATESOLUTION. Sodium citrate solutions were prepared by dissolving reagent grade sodium citrate dihydrate (Mallinckrodt Chemical Works) in distilled, deionized water, adjusting the pH to 9.00 by adding concentrated NaOH, and diluting the solution to the desired volume with water. NICKEL-CITRATE SOLUTION.Nickel-citrate solutions were prepared by dissolving the appropriate amount of both nickel sulfate hexahydrate and sodium citrate dihydrate in the appropriate buffer and readjusting the pH to the proper level with NaOH before diluting to a final volume with buffer. All the nickel solutions were standardized using a n EDTA titration as outlined by Welcher (18). CYSTEINESOLUTION.Highest purity cysteine hydrogen chloride hydrate (Calbiochem, Los Angeles, Calf.) was desiccated at 4°C. Appropriate amounts of the dry salt were dissolved in the appropriate buffer and diluted to 100 ml with that buffer. Oxygen was removed from the cysteine solutions by bubbling nitrogen through them. This reduced the rate of oxidation of cysteine to cystine. The nitrogen was freed of oxygen by passage through a chromic-zinc amalgam scrubber (19). The cysteine solutions were prepared immediately before use and showed no decomposition over a period of three to five hours in the absence of oxygen. (18) F. J. Welcher, “The Analytical Uses of Ethylenediamine
Tetraacetic Acid,” Van Nostrand Co., Princeton, N.J., 1958. (19) L. Meites, A i m / . Cliim., Acta, 18, 364 (1958).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
1935
Table I. Kinetic Determination of Iron Using Automated Stopped-Flow Apparatus“ Fe (moles/liter) X lo4 Concn Error, % Taken Found Re1 std dev, % 1 .o 1.007 1 .oo +O .70 2.0 1’.99 0.83 -0.45 3.0 2.987 0.97 -0.43 4.0 3.995 0.62 -0.12 5.0 4.981 0.75 -0.40 a h = 450 nm; cell path length = 3 mm.
Figure 2. Response curves for Ni(I1)-cysteine tion
reac-
A. Singlerun B. Seven runs superimposed
Abscissae: 50 pointslrun, 5 msec/point Ordinates: Arbitrary scales
THIOLACTIC ACID SOLUTION.Thiolactic acid (Pierce Chemical Co., Rockford, Ill.) used was 95 % pure. The acid was purified by a vacuum distillation procedure. The purified thiolactic acid was then standardized by back titrating an excess of silver nitrate solution with ammonium thiocyanate using ferric alum as indicator (20). The thiolactic acid obtained from this procedure was found to be 99.6% pure. Appropriate amounts of thiolactic acid were dissolved in buffer solutions and diluted to the desired volume. I t was noted that thiolactic acid was not susceptible to oxidation by atmospheric oxygen, and showed no decomposition of the solution after a 24-hour period. Working solutions of cysteine and thiolactic acid were prepared by diluting stock solutions with appropriate buffers. Procedure. System control and data processing operations are handled by two main programs written in BASIC language. These programs make use of Subroutines written in assembly language. These programs are referred to as the “set up” and “operational” programs. The purpose of the set up program is to permit the operator to enter the necessary parameters concerned with the preparation of the individual samples. The program functions in the following manner. Stock concentrations of individual constituents along with the volume of the receiving vial are entered as parameters via the Teletype. The computer then asks for the concentrations (20) J. H.Karcher, “The Analytical Chemistry of Sulfur and Its Compounds,” Wiley-Interscience, New York, N.Y., 1970. 1936
of the individual constituents which make up each sample for the individual runs. The computer then calculates the feasibility of making the desired runs at the desired concentrations. These calculations are based upon the total volume of the receiving vial and the stock concentrations of the individual constituents. If the total volume required to prepare any one sample exceeds the capacity of the vial, the computer will indicate this to the operator. The program is written so that it is possible to make 25 different runs without introducing new concentration parameters. The operational program utilizes the information entered during the set-up step to carry out the stopped-flow experiments. This program works in the following manner. Parameters which control the number of data points to be taken, the time interval between points, and the number of conversions to be made per point are entered via the Teletype. These parameters will remam constant throughout any particular set of runs. After these data are entered, two subroutines are called which switch the solenoids of the injection and sampling systems into a predetermined initial state. The computer halts at this point. This provides the operator with an opportunity to check all systems before initiating the running of the samples. The operator initiates the experiments by pressing the “RUN” switch on the computer. After that, all further operations are carried out automatically and independently of the operator. The volume to be added for each constituent is printed out along with the corresponding run number. Then the correct amount of each constituent is added to the receiving vial. The sampling system sequence is then initiated and the experiment is run. After the run is complete and all data are processed, the results are displayed on the oscilloscope and/or printed on the Teletype in the specified formats. RESULTS AND DISCUSSION
System Performance. The iron(II1)-thiocyanate reaction was used to carry out a preliminary evaluation of the performance of the automated stopped-flow system. Previous work with this reaction has established conditions under which it follows pseudo-first-order kinetics (13). Also, quantitative data were supplied which can be used for comparison purposes. Kinetic data obtained using the system described here were completely consistent with those obtained earlier using the more conventional mixing system. Table I presents data for the quantitative determination of Fe(II1) using the computerized stopped-flow system. These data compare favorably with those reported earlier using more conventional manual sampling methods (13). Neither these nor any of many other experiments showed any signs of systematic errors resulting from carry-over between samples of different concentrations. These data established the level of reliability to be expected from the system under near ideal conditions. Ni(I1)-Thiol Acid Reactions. Methods currently available for the selective determination of thiol groups required a
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
85
80
90
95
no
PH
Figure 4. Effect of pH upon initial rates 0 Cysteine A Thiolactic acid CN,(II)= 1.25 X 10-2M. Ccrstelne= 2.0 X lO-'M. 0.83/X 10-'hf. CThiolaetio acid = 1.5 x iO-'M
Cc,t=
Wavelength (nm)
Figure 3. Absorption spectra of the thiol acids and their Ni(I1) complexes
-Cystein -.-.
--- Thiolactic acid
Ni(I1)-cysteine pH
=
-. .-.
Ni(II)-thiolactic acid
9.0
cxI(II) = 2.5 x CCitrate
=
1 0 - 4 ~ . cCgstelne = 2.0 x 1 0 - 4 ~ . 5.0 x i0-4M. CThiolactlo A c i d = 2.0 x 10-4~
Inset:
cNI(II) = 1.5 x 1 0 - 4 ~ . cCitrdte = 3.0 x 1 0 - 4 ~
separation prior t o the measurement step. Preliminary work with certain thiol acids indicated that the rates of formation of Ni(I1)-thiol acid complexes are dependent upon the structure of the acid. This observation suggested the possibility of simultaneous determinations based upon kinetic measurements. Results o f a study reactions of cysteine (CYS) and thiclactic acid (TLA) are presented below. All results reDorted are for a temDerature of 25 "C and an ionic strength of 0.3. RESPONSE CURVES. Figure 2 shows typical time dependent data for the formation of the Ni(I1)-CYS complex. Figure 2a represents data for a single run while Figure 2b represents the superimposition of seven separate runs o n a storage oscilloscope. It is observed that with the possible exception of the derivative curve, there is no discernible difference between line widths of comparable curves in the two plots. The most significant feature of these plots is the fact that the reaction exhibits a n induction period which extends through the first ten to fifteen milliseconds of the reaction time. Analytical applications of this reaction are based upon data collected after the induction pel'iod has elapsed. Response data for the formation of the Ni(1I)-TLA complex exhibit the same general behavior. ABSORPTIONSPECTRA. Figure 3 represents the absorption spectra for the free acids in solution as well as the Ni(I1) complexes of the acids. Each complex exhibits an absorption maximum in the near ultraviolet region where neither free acid exhibits significant absorption. Consequently, these maxima can be used to monitor the course of the reactions. Since the ultimate goal was to monitor both reactions simultaneously, and since it is convenient to use a
1
10
15
20
I
%it"N,
Figure 5. Effect of citrate to NiW) concentration ratio upon initial rates 0 Cysteine A Thiolactic acid
cslcII, = 1.25 x 1 0 - 4 ~ . cCkstelne = 1.5 x 1 0 - 4 ~ . C T h i o l i c t i c acid =
2.0 x iO-'M
common wavelength for both species, a wavelength of 275 nm was selected for monitoring. This wavelength provides near maximum sensitivity for both species and involves minimal interference from the free acids. Complexes of both acids were shown to obey the Lambert-Beer law at 275 nm in reaction media to be described below. However, the molar absorptivity for each complex is dependent upon the Ni(I1) concentration. In each case, the molar absorptivity decreases by about 25z when the Ni(1I) to thiol acid concentration ratio increases from about 1 :1 to 50:l. Thus, it is necessary to evaluate the molar absorptivity for the specific conditions of the experiments to be performed. Equilibrium studies indicate that both reactions form 1 :1 complexes under the reaction conditions finally selected for analyses. Under the analysis conditions described below and assuming a cell length of 3.00 mm, the molar absorptivities at 275 nm were evaluated to be 3.18 X lo3 and 4.43 X l o 3literimole-cm for CYS and TLA, respectively.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
1937
"
Figure 6. Effect of Ni(I1) concentration upon initial rates 0 Cysteine A Thiolactic acid C,,t/Cv,cII, = 0.65 C L \ . t r > n e = 1.5 x w 4 M .CTh
o I w t l C o c ~ d=
2.0
x iw4M
-7
I
pears that the dependency is approaching zero order at a ratio of about 0.6. However, a t this ratio, the Ni(I1) solutions are only transiently stable while at ratios of 0.65 and above, solutions showed no signs of hydroxide precipitates after several days. Thus, the criteria of maximal sensitivity, long reagent lifetime, and minimal dependency upon changes in citrate concentration suggest a citrate to Ni(I1) concentration ratio of 0.65 as the optimal value for analytical purposes. This is the concentration ratio used for other studies reported in this paper. NICKEL(II)DEPENDENCY. Figure 6 represents the Ni(I1) dependency of the reactions at a citrate to Ni(I1) concentration ratio of 0.65 and constant thiol acid concentrations. The reactions approach maximal sensitivity and minimal dependency upon Ni(I1) concentrations above a value of about 1.25 X 10-2M. This is the value selected for this work. It may be reasoned that lesser dependency on changes in Ni(I1) concentration for higher thiol acid concentrations could be achieved by working at higher Ni(I1) concentrations. One reason for working at the lowest feasible value of Ni(I1) concentration is the fact that the Ni(I1)-citrate complex absorbs energy at 275 nm, as is shown in the insert in the corner of Figure 3. Thus, the lower Ni(I1) concentration minimizes the magnitude of a blank absorbance which must be compensated for. The extinction coefficient for the Ni(I1)citrate complex is about 7.4 literlmole-cm compared to values of 3.18 X l o 3 and 4.43 X lo3 liter/mole-cm for the CYS and TLA complexes at this wavelength. Thus, although there will be a significant equilibrium absorption blank contributed by the Ni(IJ)-citrate complex, the kinetic blank will be less than about 0.3 2 for both acids. THIOL ACIDDEPENDENCY. Having established near optimal conditions for the analysis (p = 0.3, pH = 9.0, CsicII) = 1.25 X 10-*M and Cclt/Cs;c~~) = 0.65) it was necessary to establish the dependency upon both CYS and TLA. Extensive studies showed that for reaction times between about fifteen and two hundred milliseconds, both reactions follow pseudo-first-order kinetics depending only on the thiol acid concentration. Pseudo-first-order rate constants evaluated were 21.5 =k 0.23 sec-I for CYS and 11.0 h 0.13 sec-I for TLA . Figure 7 illustrates the degree to which pseudo-first-order kinetics are obeyed. The curves represent experimental data for mixtures of the two acids plotted along with computed values of the response curves using the values of extinction coefficients cited above. All computed data for reaction times above fifteen milliseconds involved the assumption of two non-interfering first-order reactions proceeding simultaneously and the use of the pseudo-first-order rate constants given above. Good agreement between experimental and predicted data is observed throughout most of the time period reported. Similar plots for single components for samples exhibited similar behavior. These data combine t o demonstrate that there is little if any interference of either reaction on the other. The data below fifteen milliseconds involve the assumption of two consecutive first-order reactions for each thiol acid and are discussed in more detail below. Quantitative Anal!,ses. Observations reported above were used to develop methodology for single- and two-component mixtures of' the two acids. Analyses were based upon fifty data points taken at equal time intervals throughout the first 250 nisec of the reaction time. A nonlinear regression pr&ram was used to evaluate concentrations of CYS and TLA
9 i = A
N
B C
L cIO
40
70
103
160
Ix)
190
I
220
Time (rnsec )
Figure 7. Absorbance cs. time plots for mixtures of cysteine and thiolactic acid - -Observed A B C
D
--
Predicted [Cysteine]
2.0 x 10-4M 2.0 x 1 0 - 4 ~ 2.0 X 10-4M
1.0 x 1 0 - 4 ~
CN,([I)= 1.25 X 10-2M, Cc,t,,t,
[Thiolactic Acid]
2.0 x 10-4.44 1.5 x 1 0 - 4 ~ 1.0 x 1 0 - 4 ~ 1.0 x 10-4M
= 0.83 X 10-2M.
Celllength
=
b=3mm
p H DEPENDENCY. Initial work with the reactions indicated that p H values well above the neutral point were required for maximum rates. Since Ni(I1) forms an insoluble hydroxide under these conditions, it was necessary to devise some means of keeping Ni(I1) in solution at the elevated p H if maximal sensitivity was to be achieved. This is accomplished by adding citrate which forms a complex with Ni(I1) which is sufficiently strong to keep the former in solution but sufficiently weak to permit the thiol acid reaction to proceed at analytically useful rates. Thus, all data reported from this point on are for citrate medium. Figure 4 represents the p H profile for CYS and TLA. Both reactions exhibit a broad maximum near p H 9.2. A value of 9.0 was selected as the pH for this work. This p H represents a near minimal value for maximal sensitivity for both acids. CITRATE DEPENDENCY. Figure 5 represents the dependency of both reactions on the ratio of the citrate and Ni(I1) concentrations. It is clear from this plot that maximum sensitivity is obtained at concentration ratios below 1 : l . It ap1938
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
Q
Table 11. Analysis of Mixtures of Cysteine and Thiolactic Acid‘ Concentration (molesil. X 104) Error, CYS TLA ~Found CYS TLA Taken Found Taken 1.519 -0.7 +1.3 1.490 1.500 1,500 2.624 0.870 2.500 +5.0 -13.0 1 ,000 +10.3 -7.3 2.317 2.206 2.500 2.000 1.025 0.969 1,000 -3.1 $2.5 1 .ooo $4.1 -4.8 1 ,000 0.952 2.000 2.081 +6.7 -6.3 1.406 2.133 1.500 2.000 +6.3 2.000 -5.6 1.889 2.000 2.125 See text for conditions.
t o provide the best fit of the experimental data to a predicted response using first-order equations for the two acids. Results for single-component samples of each of the acids in the concentration range between 5 X 10-5 and 5 X 10-4M exhibited average relative errors for CYS and TLA of 0.35% and 0.43 %, respectively, and relative standard deviations were less than 2% in all cases. Results for two component samples are shown in Table 11. Average error for these results is 5.5 % and relative standard deviations are less than 2%. These results are comparable to those reported previously for other chemical systems using conventional ( I , 5) and computerized (ZI) stopped-flow instrumentation. Kinetic Considerations. The kinetic data presented above are not sufficiently complete t o establish unequivocally the mechanism or complete kinetic expression for the reaction system. However, some observations and conclusions drawn from these data are in order. All reaction conditions examined yielded response curves with a n induction period during the first few milliseconds lifter mixing the Ni(I1)citrate solution with the thiol acids. This observation suggests the formation of a n intermediate which subsequently reacts to produce the final product. It is observed from Figure 5 that for citrate-to-nickel concentration ratios less than unity, the reaction approaches zero-order dependency in citrate concentration, while at higher ratios, citrate inhibits the reaction. These observations suggest that two paralle! reactions may be involved, one involving the reaction between an aquo complex of Ni(I1) and the thiol acid and one involving a citrate complex of Ni(I1) reacting with the thiol acid, with the former reaction proceeding more rapidly than the latter. In each case, the thiol acid likely forms a mixed complex intermediate with Ni(I1) and another ligand (H,O o r citrate). Figure 6 shows that the dependency on Ni(I1) eventually reaches zero order suggesting that at high Ni(I1) concentrations, all of the thiol acid is tied up as the mixed complex and that the reaction rate should be dependent only on the analytical concentration of the thiol acid. Equilibrium studies showed that Ni(I1) forms a 1 :1 complex with both cysteine and thiolactic acid, suggesting that the order with respect to each acid should be unity. N o attempt was made to develop a rate expression which would satisfy all observations. However, an expression explicit only in the thiol acids has been developed for the conditions established for the quantitative analyses. The expression is based upon a pathway of the form: Ni(I1)
+ TA & Intermediate
-
NiTA
(1)
Re1 std dev, CYS TLA 1.3 1.3 1.7 1.7 1.1 1.1 1.3 1.3 0.9 0.9 0.5 0.5 1.3 1.3
The rate expression satisfying this type pathway for the situation when Ni(I1) is present in large excess is (21) 1
where [TA], represents the initial or analytical concentration of the thiol acid. The data in Figure 2 show that the induction period is much shorter than the remainder of the reaction. I t follows that kl can be assumed to be significantly larger than k z and that Equation 2 should reduce to a simple first-order form after the induction period has passed and the quantity e-’it approaches zero. Thus the constant, k?, was evaluated from kinetic data which followed the induction period. Then kl was evaluated using the resulting value for k? and a nonlinear regression program to fit all of the data. Resulting values of the constants were kl = 783 sec-l and kl = 21.5 sec-l for cysteine and kl = 156 sec-’ and k2 = 11.0 sec-’ for thiolactic acid. The predicted curves in Figure 7 were computed using these constants substituted into Equation 2 for both acids. The fit is observed to be quite good throughout the reaction time examined. Only those data below about fifteen milliseconds reflect any change due to the inclusion of the preequilibrium step. It is reemphasized at this point that Equation 2 applies only for the conditions specified for the analytical procedure, and that the rate constants are apparent constants depending upon experimental conditions. Work is continuing with this system in an attempt to characterize more completely the reaction mechanism and provide a rate expression including all variables. Also, the system is being extended to include other thiol acids. ACKNOWLEDGMENT
Appreciation is expressed to J. W. Amy and John Vasiliades for their helpful suggestions during the course of this work.
RECEIVED for review March 24, 1972. Accepted June 15, 1972. Research sponsored by AFOSR Grant No. 71-1988.
(21) A. Frost and R. G. Pearson, “Kinetics and Mechanism,” John Wiley and Sons, New York, N.Y., 1961, pp 166-8.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 12, OCTOBER 1972
1939
