326
Anal. Chem. 1986, 58,326-330
(13) Wade, A. P. Anal. Proc. (London) 1983, 2 0 , 108-111, 523-527. (14) Betteridge, D.;Sly, T. J.; Wade, A. P.; Tillman, J. E. W. Anal. Chem.
1292-1299. (15), Betterldge, D.; Taylor, A. F.; Wade, A. P. Anal. Proc. (London) 1984, 21 373-375. (16)Bourke, G.C. M.;Stedman, G.; Wade, A. P. Anal. Chlm. Act8 1983, 1983, 55,
(18) (19)
Deming, S. N.; Parker, L. R. CRC Crit. Rev. Anal. 187-202. Leggett, D. J. J. Chem. Educ. 1983, 60, 707-710.
Chem. 1978, 7 ,
I
153, 277-280.
(17)
Nelder, J. A.; Mead, R.
ComputerJ. 1965, 7 , 308-313.
RECEIVED for review June 21,1985. Accepted September 24, 1985.
Quantitative Study of Chemical Equilibria by Flow Injection Analysis with Diode Array Detection Rathnapala S. Vithanage and Purnendu K. Dasgupta*
Department of Chemistry, Texas Tech University, Lubbock, Texas 79409-4260
Controlled dispersion as generated in flow InJectIonanalysis permits essentially infinite known composltionai varlatlons. I f carrier-sample composltlons are appropriately chosen, reasonably accurate values of equliibrlum constants are easily obtained in proton-ligand and metal-ligand systems with muitidlmensionai spectral detection. Choice of an appropriate carrier-sample buffer system Is crltlcal In proton-ilgand studies and Is dlscussed in detali. Metal-ligand association constants are reliably obtained with both high and low conditional stability constants.
In recent years, flow injection analysis (FIA) has emerged into an analytical technique of considerable utility (I). However, for the large majority of applications, FIA merely serves as the unsegmented analogue of segmented continuous flow analysis (SCFA), i.e., as a tool to automate batch mode analysis. Reproducible controlled dispersion is an aspect unique to FIA. This aspect has been considerably less exploited and critically appreciated, according to the original inventors of FIA (2). In the present paper, we wish to report the utility of FIA in conjunction with a photodiode array (PDA) UV-vis spectrophotometer, which can acquire spectral information over a large wavelength range relatively rapidly, as a detector for the quantitative study of chemical equilibria. It is the controlled dispersion aspect of FIA that is exploited for this work. Proton-ligand and metal-ligand equilibria have been investigated.
EXPERIMENTAL SECTION A Pharmacia P-1 peristaltic pump was used to pump the carrier solution at a flow rate of 0.20-0.50 mL/min. The sample solution was introduced into the carrier stream by a rotary loop injection valve (Rhecdynetype 50, Cotati, CA). A single-bead string reactor (3) was fabricated by filling a 0.8 mm i.d., 70 cm long polytetrafluoroethylene tube with 0.5 mm diameter glass beads and used as the dispersing device. The injection volume used was 150 pL. A Hewlett-Packard 8451A photodiode array spectrophotometer, equipped with a 40-pL flow-through cell was used as a detector. All data files were stored on magnetic media and data manipulations were carried out on the HP-85 microcomputer associated with the instrument, using HP-BASIC. For the study of proton-ligand equilibria, the following combinations of carrier/sample media were found suitable for limited pH ranges: (1) 0.1 M NaOAc/O.l M HOAc, (2) 0.4 M NaH2P04/0.1M H3P04,and (3) 0.1 M Na3P04/0.1M Na2HP04 + 0.1 M NaH2P0,. The dispersion coefficient of the injected sample was determined by the following steps: (a) determine the isosbestic
wavelength (Ais,,) by superimposing spectra of the indicator of identical concentration in strongly basic and strongly acidic solution and noting the crossover wavelength@; (b) determine the absorbance of the original sample (A&, at Ab; and (c) divide (Ab)o by the observed absorbance at time t at this wavelength, (Ai&, to obtain the dispersion coefficient (D)of the injected sample at time t. The pH corresponding to this temporal slice of the bolus was then computed, as a first approximation, from the HendersonHasselbalch equation ( 4 ) , for the systems mentioned earlier, respectively pH = PKHOAC + log (D- 1) pH = PK3H3p04+ log (D- 2)/3
for D >2
(1)
(3a)
pH = p K ~ ~ +p log 0 ~( 2 0 - 1)/(2 - D) for D < 2 (3b) The linear buffer was made up after Astrom (5)and composed of HCl (1.0 M), HCOOH (0.1 M), CH3COOH (0.1 M), piperazine (0.1 M), bis(tris(hydroxymethy1)aminomethane) (0.015 M), Nmethylmorpholine (0.025 M), methyldiethanolamine (0.025 M), and malonic acid (0.015 M). For the linear buffer system, the linear buffer itself was used as the carrier and the sample was put in 0.65 M NaOH. Unlike the other buffering systems, the agreement between the measured pH and the pH calculated by iterative numerical methods was poor, possibly due both to complexity of the buffering system and lack of ionic strength corrections. The pH of the NaOH linear buffer system was therefore measured at different mixing ratios (Figure 1A) and combined with the measured temporal dispersion of the experimental system (a portion of this is shown in Figure 1B) to produce the temporal pH profile (Figure IC). Overlay spectra, such as that in Figure 2, were generated by overlaying any desired number of data arrays ( A vs. A), after multiplying the absorbance values of the array by the dispersion coefficientcorresponding to the particular scan so that all scans represent the same normalized concentration, namely that of the original sample. For metal-ligand complexation studies, the metal asd ligand solutions were buffered at the desired pH by an acetate (0.1 M HOAc 0.1 M NaOAC) or ammonia (0.01 M NH, + 0.01 M NH,Cl) based buffering system. The ligand solution was used as the carrier into which the metal ion solution was injected. In much the same fashion as proton-ligand equilibria, free ligand and metal ligand complexes display isosbestic wavelengths. The dispersion coefficient was determined based on the isosbestic absorbance (vide infra).
+
RESULTS AND DISCUSSION Consider the pH-dependent spectra of bromocresol green (Figure 2). Beyond its esthetic appeal, the frequent ap-
0003-2700/86/0358-0326$01.50/00 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
I
300
500
327
1
700
Wavelength, n m Flgure 2. pHdependent overlay spectra of bromocresol green obtained by a single injection in a FIA system. The 615-nm absorption band increases with increasing pH as the indicator turns from yellow
to blue.
20
30
40
50
ilYE(SEC1
12
..
I1
..
**** * * *
. .. n .. 10
D
C
Figure 1. pH of the linear buffer system: (A) pH as a function of the dispersion coefficlent as 0.65 M NaOH is diluted by the linear buffer; (B) typical temporal dispersion profile in the experimental system: (C) pH as a function of time from injection, compounded from A and B. The arrows Indicate the portlon of the data used for actual domputation (see text). In this and in part B the times shown are the times from the commencement of spectral data acquisition, which starts 60 s after injection. The dispersion profile utilized is that of the trailing edge of the sample pulse.
pearance of similar figures in promotional literature underlies the fact that for conventional spectrophotomers, generation of such figures requires good reproducibility in monochromator and recorder chart drive systems. Normally, the figure is produced by overlay recording a number of spectra of the same concentration of the indicator at various pH levels around its pK value. In the present case however, Figure 2 was generated from data obtained from a single injection of the indicator sample into a flowing stream and recording the spectra of the dispersed sample as it passed through the detector.
As the indicator sample disperses in the carrier, the pH along various points in the sample bolus can be varied in a controlled gradual fashion (without sharp changes) if the carrier solution and the sample medium are the constituents of a buffer system. For example, the sample may be contained in the solution of a weak acid (HA) while the carrier stream is the solution of NaA or vice versa where both HA and NaA are optically transparent in the wavelength domain of interest. In an analogous fashion, a weak base and its strong acid salt may be used as components of the buffering system. As HA in the sample bolus is diluted by the NaA in the carrier in varying proportions, varying pH levels are produced at different points along the sample zone with the minimum pH occurring essentially near the sample peak maximum, the zone containing the peak HA as well. (This is an approximation, differences in diffusivities of HA and the sample indicator may lead to nonidentical patterns of overall dispersion, ref 6.) Note that the necessity of using a buffering system arises from the requirement of producing a gradual, rather than abrupt, change in pH. This requirement in turn is due to the finite time necessary for the acquisition of the spectra data. For a 600 nm wide spectral range with a wavelength resolution of 2 nm, instrumentation used in this study can perform the measurement in a minimum period of 100 ms; however, transfer of the resulting data to retrievable memory locations requires a minimum cycle time of 800 ms before the next measurement can be made. (This refers to internal RAM storage; transfer to magnetic storage requires significantly longer.) Consequently, it is necessary that the pH change be gradual relative to this temporal resolution. Secondly, for the simple HA-NaA sample-carrier stream t o successfully produce Figure 2, pK, of the buffering system must be reasonably close to pKI, because the pH along the sample zone varies in the vicinity of pK,. In Figure 2, the sample was contained in 0.1 M CH,COOH (pK, 4.75), which is very close in acid strength to the bromocresol geen indicator (pKh 4.791,with 0.1 M CH&OONa being used as the carrier. Phosphate buffering systems, as described in the Experimental Section, can be similarly used. Unfortunately, such an approach requires prior knowledge of pKI,. Choice of a Wide-Range Buffer System for Studying Proton-Ligand Equilibria. The ideal buffer system of choice should produce a gradual change in pH over a large pH range. Parts A-D of Figure 3 show the pH profiles as a function of the dispersion coefficient, D, as the sample is diluted by the carrier. Ionic strength effects have not been
328
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986 1
3 5 0
7
I 1
I 9 11 13 1
2
3
4
5
6
7
8
9
io D isp. r s ion Coefficient
Dirperlion Coefficient
r
I
4
i
1
Dispersion
Coefficient
1
1
3
3
5
5
7 ;
7
9
9
11
11
3i i
0
1
13
b
4 0
j
.A
9
10
Dispersion C o e f f i c i e d
Flgure 3. pH as a function of the dispersion coefficient as various concentrationsof HBPO, (0.10, 0.15, 0.20, 0.25,0.30,0.35,0.40, 0.45, 0.50 M) are injected into carrier solutions of (A) 0.2 M NaOH, (8)0.2 M NH3, (C) 0.2 M NH, 0.04 M NaOH, and (D) 0.05 M ethylenediamine.
+
taken into account in generating these figures (necessary algorithms in Applesoft BASIC are available from the authors on request), and as such, the information shown should be regarded as semiquantitative. Figure 3A shows the results for a 0.2 M NaOH carrier into which various concentrations of H3P04are injected. In the vicinity of the two equivalence points for the neutralization of H3P04, pH changes are too abrupt for the system to be useful. Consequently only pH ranges of 2-3 and 6-8 are usable. With substitution of NH3 for NaOH, pH change in the vicinity of the second neutralization point becomes more gradual (Figure 3B). However, pH values greater than 10 cannot be attained. If a small amount of NaOH is incorporated in this system, the upper pH limit is extended (Figure 3C). If ethylenediamine is used as carrier (Figure 3D), the sharpness of pH change for the first neutralization point of is reduced, but not eliminated. Ideally, an appropriate buffer system may be comprised of a strong base reacting with a n-protic acid where n is very large and K , through K, are equally spaced and span a large range. The closest approximation to such a system is the ”linear” buffer system developed by Astrom (5). The merit of this system lies not only in a wide buffer range but also in the 220-900 nm spectral range where the components are all essentially noncomplexing and optically transparent. However, agreement of calculated vs. measured pH was relatively poor, so that actual pH as a function of time from injection for a 0.65 M injected NaOH sample was determined as described in the Experimental Section. As Figure 1C shows, the usable pH range is very large (2-13) and no prior knowledge of pKIn is therefore required. Computation of pKInfrom Spectral Data. The results from the experiments include complete spectral information over the chosen wavelength domain, typically consisting of 10-100 usable A vs. A data arrays. The time domain used for
computations with the linear buffer system is indicated by arrows in Figure 1C. The sample concentrationfor each array is known from Ah, and the dispersion factor determined from Aisoenables the pH corresponding to this particular array to be calculated. Obviously, given such information, a large number of approaches are possible to compute pKI,. The specific method we have utilized involves the following: (a) Limit attention to data representing D 5 10, to assure the presence of a significant sample concentration in the data considered; further, consideration is limited to those data arrays that show significant presence of both the acid and the base forms. (b) Normalize the absorbance values in each data array by multiplyingwith the corresponding dispersion factor. ab(c) Compute EIn(h],,), EHIn(Xln)’ €In(AHIn), and %n(AHln) sorptivities of In- at ,A, for In-, of HIn at ,A, for In-, of Inat A,, for HIn, and of HIn at A,, for HIn, respectively), which are available from the spectral measurements made for the indicator in strongly acid and strongly basic solutions (knowledge of exact concentration of the indicator is not actually necessary; E values can be left in arbitrary units). (d) Consider the values of AI, and AHInfor each normalized data array under consideration, recognizing AIn
= %(XI,) [In-] + EHIn(X1,) [HIn]
(4)
(5) + tHIn(X~~n)[H1n] and solve for [In-] and [HIn] from the simultaneousequations (4 and 5). (e) Compute pKIn from the pH for this data array as
AHIn =
tIn(X~l,)[ln-l
for each array, and calculate the mean pKI, and the resulting standard deviation.
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
Table I. pKImMeasured in This Work Compared to Literature Data
compd
PKIll measd f lit. value” std dev
quinaldine red methyl orange bromocresol green methyl red (thiazolyl) azoresorcinol
2.63 3.74 4.79
5.12 10.76
buffer system used (carrier/sample)
2.75 f 0.28 Na2HP04/H3P04 3.78 0.03 NaOH/linear buffer 4.78 f 0.10 CH,COONa/ CH3COOH 4.81 f 0.10 NaOH/linear buffer 10.31 f 0.10 Na3P04/NaH2P04 + Na2HP04
*
Taken from ref 7.
ficient of the sample at any time t, Dt, is then calculated from
(7) Consequently, this temporal slice represents a totalhetal concentration of cM/D, and a total ligand concentration of CL(Dt - l)/Dt. A plot of AXMLn ks. C M / ( C M + CL(Df- 1)) is made; the maximum AXmn,A,,, corresponds to the optimal formation of ML, (the correspondingD, is designated Dt,,,), thence (8) n = CM/(CL(Dt,max - 1)) [ML,] for this temporal slice is computed from
[MLnI = Arnax/€ML,
If overlaid spectra are not necessary, measurement can be made with a dual wavelength spectrometer at Xi,, and XI, or XHIn, instead of a PDA instrument. Simultaneous consideration of any two data arrays then enables the computation of pKh Results for a number of indicators spanning a large pH range are shown in Table I, along with literature values (7). Within the limitation of the lack of activity corrections, the agreement is generally good. Metal-Ligand Systems. The parameters of general interest in metal-ligand equilibria are the values of n in ML, and the corresponding association constant, KML,. The value of n is commonly determined by a continuous variation plot or a mole ratio plot, whereas Km, is assessed by spectrometric determination of the actual concentration of ML, in a solution of that stoichiometry (for a recent example, see ref 8; the general topic is covered in the classic treatise by Rossotti and Rossotti (9)). If the carrier ligand concentration is CL and the sample metal ion concentration is CM, a plot of Ahmn(Xmnbeing the wavelength of maximum absorption by ML,) vs. CM/(CM+ CL(D - 1)) is the continuous variation plot because the latter quantity is the mole fraction of the metal; it reduces to 1 / D for the special case of CM = CL. The value of n in ML, may be obtained from such a plot in the usual manner. (The dispersion coefficient, D, used here is that of the sample, DM; this is related to the dispersion coefficient of the carrier ligand, DL, by the relationship l/DM 1/DL = 1, which is valid throughout the t domain.) The following steps are generally necessary: (a) Obtain the spectrum of the free ligand (concentration CL) in an appropriately buffered solution and store in memory. (b) Add to the ligand solution an aliquot (few microliters, dilution of ligand solution should be negligible) of a relatively concentrated metal ion solution buffered in the same fashion as the ligand; not only must the total ligand concentration be much higher than the total metal concentration but also the conditional value of KML, must be sufficiently high so that near-quantitative formation of ML, can be assumed without significant error. (c) Obtain the spectrum of the solution in (b); subtract the entire data array of (a) from the current array; the difference spectrum yields (1) the isosbestic wavelength, Xiso (where absorptivities of L and ML, are equal), at which a zero residual (or closest thereto) is observed; (2) the wavelength of maximal absorption for ML,, Am,, where the largest residual is observed; and (3) the molar absorptivity of ML, at AML,, ~ML,. (In a strict sense, the subtracted array should represent the free ligand concentrationand not the total ligand concentration to obtain accurate values of XML, and EML,,. However, if either EL = 0 a t XML, or CL >> CML,, the error is negligible). (d) Perform the FIA experiment; unless overlay plots are desired, it is sufficient to store only A,,, and AXMLn, The isosbestic absorbance of the ligand in the carrier ( A d o is available from data representing times prior to the entry of the sample bolus into the detector. The dispersion coef-
+
329
(9)
and KML, is then computed from
KML,=
Results for two different complexation equilibria are given below as examples. These examples are chosen to illustrate the quality of results obtained under two different experimental situations: high conditional formation constant and low conditional formation constant. The first example involves 1,lO-phenanthroline M) in 0.1 M HOAc 0.1 M NaOAc as carrier and Fez+(“4 X lo4 M, in same buffer, small amount of NH,OH-HCl added to prevent oxidation) as sample. The isosbestic wavelength for this system is 360 nm, XML, is 506 nm, and CML, is 1.1X lo4. A, maximum was observed at CM/(C, + CL(D,- 1)) = 0.248 (no data were specifically available for 0.25))corresponding to the formation of FeL,. The conditional formation constant was computed from eq 10 to be 5.2 X 1017;this is in reasonable agreement with the value of 1.2 X lozothat may be computed for the conditional formation constant of Fe(o-phen)32+in 0.1 M acetate medium from literature data (IO). The second example involves methylthymol blue (MTB, =IO4 M) in 0.01 M NH3 + 0.01 M NH4C1as carrier and Mg2+ M, in same buffer) as the sample. Since maximum absorption of the complex was observed at CM/(CM+ CL(D, - 1)) = 0.67, corresponding to the formation of Mg2L, t M g z ~ was determined under high Mg:MTB ratio. The overlay spectra, normalized with respect to the amount of ligand present in the particular slice (rather than with respect to the metal, since the complex is of the type M,L rather than ML,), is shown in Figure 4. There are a number of isosbestic points in this system; the present experiment utilized the 506 nm value. Maximum absorption by MgzL occurs at 595 nm with eMg2L being 1.5 X lo4. The datum corresponding to CM/(CM + CL(Dt - 1))= 0.67 yielded a value for the conditional formation constant 3.5 X lo9. The pH of the experimental system is 9. The successive pK values for MTB, a hexaprotic acid, are 1.8, 2.0, 3.04, 6.85, 11.14, and 12.94 (IO). The true complexation constant ([Mg2L]/([Mg2+I2[L])) is 4.68 X and the formation constant for Mg(NHJ2+is 1.70 (IO). From these values, a conditional formation constant for our system is computed to be 3.7 X lo9, in excellent agreement with the observed result.
+
CONCLUSIONS We have, at best, carried out a very modest exploration of the manifold studies of chemical systems that can benefit from the controlled dispersion generated in FIA. One rather unique aspect of the present work is that because the use of multidimensional detection permits the calculation of the dispersion
330
ANALYTICAL CHEMISTRY, VOL. 58, NO. 2, FEBRUARY 1986
ponent(s1 of interest (6). The important point however is that any experiment involving studies of the effects of compositional variation of different components can benefit from FIA adaptation because it is possible to generate essentially infinite compositional variations in such a system. This may indeed be particularly useful in kinetic studies, which have not been addressed here. For reactions slow in a FIA time scale, the possibility of air segmentation after achieving the desired dispersion, rather than, or in addition to, stopped-flow FIA, is especially intriguing to us, particularly since porous membrane tubes have rendered air desegmentation an entirely trivial task. L 300
100
wavelengt h , e s
Figure 4. Normalized overlay spectra of the Mg*+-methyRhymol blue system at pH 9 (NH,-"&I), obtained by a single injection in a FIA system. The increasing absorption In the 5C5-nm band reflects lncreasing amounts of Mg'.' coefficient corresponding to any data array by virtue of existence of the isosbestic point(s), the reproducibility of the dispersion profile in successive injections is irrelevant. If the dispersion profile is sufficiently reproducible for the needs of these types of investigations, dispersion profiles that relate the dispersion coefficient to a given temporal slice may be obtained first, followed by single wavelength monitoring of the continuously variable equilibrium composition generated by the FIA system. For equilibrium systems that lack a suitable isosbestic point or for nonequilibrium systems (e.g., kinetic studies), we have had a modest degree of success in incorporating in the sample some indifferent marker that neither influences nor is influenced by the reacting components, and that spectrally absorbs at a region removed from the absorption of the components of interest. Clearly, availability of such a marker for many systems poses a serious limitation, aside from any differences involved in the exact dispersion characteristics of the marker and the sample com-
ACKNOWLEDGMENT The authors thank S. Gluck, The Dow Chemical Co., for information on the linear buffer system. LITERATURE CITED (1) Ruiieka, J.; Hansen, E. H. "Flow InJectlon Analysis"; Wiley: New York, 1981. (2) Ruiieka, J.; Hansen, E. H. Anal. Chim. Acta 1983, 145, 1-15. (3) Reijn, J. M.; Poppe, H.; Van der Linden, W. E. Anal. Chim. Acta 1983, 145, 59-70. (4) Day, R. A,, Jr.; Underwood, A. L. "Quantitative Analysis", 4th ed.; Prentice-Hall: Engiewood Cliffs, NJ, 1980, p 114. (5) Astrom, 0. Anal. Chlm. Acta 1977, 88, 17-23. (6) Vanderslice, J. T.; Rosenfeld, G.; Beecher, G. R. 36th Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, New Orleans, LA, Feb 26, 1985; Abstr. 417. (7) Bishop, E., Ed. "Indicators"; Pergamon: New York, 1972. (8) Garcia Alonso, J. I.; Diaz Garcia, M. E., Sanz Medel, A. Talanta 1984, 31, 361-366. (9) Rossotti, F. J. C.; Rossotti, H. "The Determination of Stability Constants"; McGraw-Hill: New York, 1961. (10) Martell, A. E.; Smith, R. M. "Critical Stability Constants"; Plenum: New York, 1977.
RECEIVED for review July 22,1985. Accepted September 16, 1985. This research was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, of the U.S. Department of Energy (DOE), through Grant DEFG0584ER-13281. However, this report has not been subjected to review by the DOE and no endorsements by the DOE should be inferred.
