Anal. Chem. 1989, 6 1 , 991-994
991
Quantitation of Interferences under Equilibrium Conditions with Application to Free Chlorine Analysis in the Presence of Organic Chloramines James N. Jensen' and J. Donald Johnson* Department of Environmental Sciences and Engineering, School of Public Health CB-7400, University of North Carolina, Chapel Hill, North Carolina 27599-7400
The measurement of free chlorlne In chlorinated natural waters Is subject to Interference by organlc chloramlnes. Ouantltatlon of thls Interference Is problematlc, slnce organlc chloramines can hydrolyze to free chlorine. This work describes a general model for the slrnultaneous determlnatlon of degrees of Interference and analyte-lnterferent equilibrium constants, wlth applicatlon to the organlc chloramine-free chlorine system. Amperometrlc membrane electrode responses ranged from 1 (N-chlorocyanurate) to 5 2 (N-chloro-5,5-dlmethyIhydantoln) tlmes the true equlllbrlum [HOCI]. The model allowed for the evaluation of the hydrolysk constants of N-chlorosucclnlmlde (pK = 6.46), N-chlorocyanurate (pK = 4.80), and N-chloro-5,5-dlmethylhydantoln (pK = 8.24).
INTRODUCTION
Free chlorine (HOC1 + OC1-) is commonly used in the United States for the disinfection of public water supplies. Accurate measurement of free chlorine residuals is essential, because U.S. Environmental Protection Agency regulations consider the presence of such a residual to be an indication of microbiologically safe drinking water (I). Interferences in the analysis of free chlorine by less effective disinfectants result in inaccurate assessment of treated water disinfection quality. Organic chloramines, formed by the reaction of free chlorine and nitrogen organic compounds such as amines and amides, are likely suspects for such interferents. First, organic chloramines are poor disinfectants ( 2 4 ) . Second, interferences in the measurement of free chlorine by organic chloramines have been suspected in chlorinated groundwater (5) and chlorinated wastewater (6). Quantitation of interferences from organic chloramines is problematic because the chloramines hydrolyze to some extent to form equilibrium concentrations of free chlorine. Free chlorine methods such as the NJV-diethyl-p-phenylenediamine (DPD) methods measure increasing quantities of apparent free chlorine with time. The equilibrium shifts as HOC1 reacts with DPD. The chloramine hydrolyzes further and interferes during the measurement. The amount of interference varies with time in these methods. Equilibrium free chlorine methods (e.g. the amperometric membrane electrode, linear sweep voltammetry, and direct spectrophotometry) measure the equilibrium free chlorine concentration without consuming it. In these methods, interferences are some fraction of the equilibrium chloramine concentration. The present work is limited to equilibrium measurements, where the interference is calculated by comparing the instrumental response and the true equilibrium free chlorine concentration. Calculation of the true equilibrium free Current address: Department of Civil Engineering, State University of New York at Buffalo, 212 Ketter Hall, Buffalo, NY 14260. 0003-2700/89/0361-0991$01.50/0
chlorine concentration requires knowledge of the chloramine hydrolysis constant. Thus, determinations of interferences and hydrolysis constants are closely intertwined. Previous attempts a t quantitation of free chlorine interferences due to organic chloramines have ignored the free chlorine in equilibrium with the chloramine (7). On the other hand, determination of the chloramine hydrolysis constant has sometimes involved measuring free chlorine without regard to possible interference from the chloramine (8). The degree of interference and the hydrolysis constant must be determined simultaneously. A regression-based model has been developed for the simultaneous evaluation of the analyte-interferent equilibrium constant and the degree of interference. The model is generally applicable where the interferent is in equilibrium with the analyte. This model has been applied to the amperometric membrane electrode and the chloramine hydrolysis problem. Hypochlorous acid was measured in the presence of several organic chloramines by an amperometric membrane electrode (9). The model was used to simultaneously measure the organic chloramine hydrolysis constants and quantitate the chloramine interferences in the free chlorine measurements by the electrode.
EQUILIBRIUM MODEL Theory. Consider an analyte, A, and an interferent, I, in equilibrium with the equilibrium constant K = [A]/[I]. If the instrument responds proportionally to the analyte concentration in the absence of the interferent and also responds proportionally to the interferent, then one can model the response as follows: In eq 1, p is the response factor for the interferent relative to the analyte. For many types of analyses (e.g. voltammetry, spectrophotometry), p is constant. For example, if the instrumental response obeys the Beer-Lambert law, then absorbance = eAl[A]
+ eIl[l]
For this system, R = absorbance/(eA1)and @ = One can use other equilibria and mass balance equations to express the proportional response R in eq 1 as a function of K , p, and known quantities. The response is measured a t various [A] + [I] values, and K and /3 are estimated by nonlinear regression techniques. The chloramine-free chlorine system follows this general model. The pertinent equations are summarized in Table I. Note that the response in eq 2 (Table I) is expressed as a function of K , p, and the known or measurable quantities: total chlorine, total nitrogen, Kcl,KN,and pH. This method is most useful for the evaluation of moderate to large hydrolysis constants ( K > M), where the free chlorine concentration is large enough to be measurable by the membrane electrode. Even smaller hydrolysis constants can be estimated for very sensitive methods of analysis. 0 1989 American Chemical Society
992
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989
Table I. Example of the Equilibrium Model-Hydrolysis of an Organic Chloramine
’”
I
Analyte-Interferent Equilibrium: K RR’NCl+ H20 = RR’NH + HOCl Other Equilibria: RR’NH + HZO = RR’N- + H@+ KN” HOCl + HzO = OCl- + H30’ Kcl Mass Balances: total chlorine = C ~ T = [HOCl] + [OCl-] + [RR’NCI] total nitrogen = NT = [RR’NH] + [RR’N-] + [RR’NCI] Response Equation: R = [HOCl] + P[RR’NCl] = (HOC11 + P(clT - [HOCl]/aci) (2) where: [HOCl] = 0.5~tcl(-b+ [b2 4 C 1 ~ K / ( f f c p ~ ) ] ~ ’ ~ ) ~ and: b = K/(acpN) + NT - c1T ~ C =I 1/(1 + Kci/[H+I) f f = ~ 1/(1+ KN/[H+I) aFor amines: RR’NH2+ + H20 = RR’NH + H30+ KN’; (YN = 1/(1 + [Ht]/KN’). *This expression for [HOCl] is derived by solving the system of five equations (three equilibria expressions and two mass balance equations listed above) in five unknowns ([RR’NCI], [RR’NH], [RR’N-J,[HOCl],and [OCl-1). Model Validation. Evidence for model validation comes from four sources. First, a numerical example will be presented which demonstrates the reliability of the computer code and the relative insensitivity of the model to random error. Second, a chemical example from the literature will demonstrate the general applicability of model. Third, the ability of the model to predict measured responses in the chloramine system will be evaluated. Fourth, the appropriateness of the model will be evaluated by examination of residuals calculated with and without the interference term in eq 1. EXPERIMENTAL SECTION Materials. Sodium hypochlorite solutions (Fisher Scientific Co., Pittsburgh, PA) were rendered chloride-free by a modification of the procedure of Reinhard and Stumm (10). Hypochlorous acid solutions were rejected if the chloride molarity (as C1-) of a reduced aliquot was more than 10% greater than the total chlorine concentration (as C1-) of the HOCl solution. All other chemicals were used as received. Organic nitrogen sources were free acids or bases, obtained from Sigma Chemicals (St. Louis, MO). Ammonium chloride was used as the ammonia source. Reagent grade chemicals were used as available. Experimental Design. All experiments were conducted in 0.1 M NaC104 to ensure constant ionic strength. The pH was buffered with a 5 X M KHzPOl solution which had been adjusted to pH 7 with NaOH. Temperature was controlled to 25.0 (k0.2) “C with a Model D1-G constant temperature bath (Haake Buchler Instruments, Inc., Saddle Brook, NJ). Ten total chlorine values were employed for each compound, with the total chlorine to totalsubstrate ratio constant. Experimental conditions are listed in Table 11. Solutions were equilibrated for a given amount of time before temperature, electrode, total chlorine, and pH readings were recorded. Electrode readings were obtained with a Model 924 chlorine analyzer (Delta Analytical/Xertex, Hauppauge, NY), operated at +200 mV applied voltage. Total chlorine was measured by forward amperometric titration, using a rotating platinum electrode at an applied voltage of +200 mV
Q
0
A
Q 0 Response
A Pred.
resDanse
A
0
04 0
10
20
30
50
40
TOTAL CHLORINE (gtJ Cl2)
Flgure 1. Measured and predicted electrode responses for N-chlorocyanurate.
vs SCE (11). The amperometric chlorine membrane electrode response was calibrated against amperometric titration before each experiment. Free chlorine concentrations were calculated from electrode responses corrected for pH (at 25 “C, HOCl pKa = 7.54) (12). The pH corrections were necessary since the membrane electrode responds to HOC1, not OC1- (9). Linear calibration c w e s exhibited correlation coefficients greater than 0.99 (relative standard error of the estimate of the slope ranged from 3.8 to 9.1%). Nonlinear regression analysis was performed by use of the Gauss-Newton algorithm (13). RESULTS Interferences a n d Hydrolysis Constants. The electrode free chlorine response versus total chlorine curve for chlorinated cyanuric acid is plotted in Figure 1. Predicted response values shown in Figure 1 were calculated from the measured hydrolysis constants and j3 values. Predicted responses must be calculated discretely in order to incorporate the measured total chlorine values. The average unsigned error for the predicted responses was 8.3% for this experiment. The lack of linearity in Figure 1indicates that hydrolysis plays a role. Hydrolysis constants and j3 values for the model compounds in this study are listed in Table 111. Model Validation. Synthetic data were generated to simulate experimental conditions (see Table IV). Normally distributed random errors (14) were imposed on the synthetic data. The results of the simulation are given in Table IV. Note that accurate K and j3 predictions are obtained, even with 10% imposed random error. In addition, the method is able to predict the true response (that is, the response in the absence of imposed error) in spite of the imposed error. This exercise demonstrates the value of a regression-based technique. The general suitability of the model will be shown by applying it to data from the literature. Albert and Serjeant (15) evaluated the pKa of the conjugate acid of p-nitroaniline spectrophotometrically. The base and conjugate acid both absorb at the analytical wavelength, and thus the equilibrium interference model can be used to evaluate the equilibrium constant (K,) and relative interference (ratio of molar absorptivities). The model predicted the acid dissociation constant within 1.7% and the molar absorptivitiy of the conjugate acid within 4.4%.
Table 11. Experimental Conditions” equilibrasubstrate succinimide HzCy- (Cy = cyanuric acid) 5,5-dimethylhydant~in~ ammoniad
chlorine concn, M (as Cl,) 3.03 X to 2.85 X 5.94 x IO4 to 4.75 X 1.04 X to 8.98 X 8.47 X to 6.74 X
(2.15-20.21 mg/L)
(0.42-3.37 mg/L) (0.74-6.37 mg/L) (4.21-31.62 mg/L)
ratiob (range) 0.475 (0.467-0.487) 0.0959 (0.089-0.100) 0.935 (0.8604.979) 0.136 (0.123-0.149)
mean pH (range) tion time, h 6.93 (6.92-6.94) 6.89 (6.85-6.93) 7.19 (7.12-7.23) 6.78 (6.70-6.89)
0.5 0.5
2.0 0.5
“0.1 M NaC104, 25 O C . *Mean molar total chlorine-to-totalsubstrate ratio. ‘Eight data points, 0.005 M phosphate, room temperature. dFour data Doints.
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989
Table 111. Experimental Results-Predicted Constants and B Values
Hydrolysis
I
--
substrate
401
succinimide
3.5 X
(6.1X HzCy- (Cy = cyanuric acid) 1.6 X (3.8X lo4) 5,5-dimethylhydant~in~ 5.7 X (1.9 X low8)
ammonia
C
..
0 (std dev)
14.3
fO f5 f10
predicted 0 (std dev)
1.01 x 10-7 (5.2 X 1.11 x 10-7 (2.6X 1.10 x 10-7 (6.2x 10-8)
9.88 x 10-3 (8.4X 7.02 x 10-3 (4.0X 7.80 x 10-3 (9.7 x 10-3)
e
e./
-
e 0-
6.3
0
0
0
0
0
0
0
0
0
-104
0
10
20
30
TOTAL CHLORINE (@A
Data Set
predicted K , M (std dev)
v
8.3
M
%
error
W Vl
Model Amide: 0 = 1.0 X M hydrolysis constant = K = 1.0 X pKN= 9.0 (KN= amide acid dissociation constant)
imposed
e
with @
ep=o
errora
0.046 (0.038) 0.11 (0.020) 0.072 (0.0062) 0.064 (0.024)
Data Set: 10 data points total chlorine = 1 X lo4 to 1 X total nitrogen = total chlorine pH 7.0 for all data points
0 Model
mean
%
aError = lresponse - predicted responsel/response. * K is not corrected for ionic strength. ‘ K is too small for a precise prediction. We estimated K = 7 X M (lit. 5 X M (19)).
Table IV. Model Validation-Synthetic
I
I”
(v
chloramine hydrolysis constant K , M (std dev)
993
% re1 errora
0.1
2.5 1.1
a Mean of unsigned error with respect to response in the absence of imposed error.
Preliminary chlorination experiments were conducted with four amines. The average unsigned error (Iresponse - predicted responsel/response) over the 38 data points in these experiments was 7.6%. Average unsigned errors for the final experiments reported here are listed in Table 111. The model is thus reasonably successful in predicting the measured responses. The inclusion of the interference term in the model is justified by the residuals analysis. Residuals are without apparent trends if the model in eq 1 is used to analyze the data. If the interference term is ignored (that is, if one assumes /3 = 0), then a strong trend in the residuals is observed (see Figure 2).
DISCUSSION The data in Table I11 indicate that the amperometric membrane electrode responds to some organic chloramines as well as hypochlorous acid. The instrument response factors for the chloramines examined here relative to HOCl range from 0.046 to 0.11. From these values and the chloramine hydrolysis constants, one can calculate the true hypochlorous acid concentrations (eq 2 in Table I and ref 16). These calculations show that the electrode response is l to 52 times the true hypochlorous acid concentrations. This suggests that the electrode can significantly overpredict HOCl concentrations. The potential for overestimation of the disinfection ability of chlorinated water exists. Interference affects the evaluation of the hydrolysis constants. Hydrolysis equilibrium constants were calculated by
40
00 1
50
C12)
Residuals analysis of the electrode response data for N-chlorocyanurate.
Figure 2.
using the model in eq 1 and also assuming no interference (/3 = 0). If one presumes no interference, as previous workers have assumed (8), the measured [HOCl] will appear to be larger since all of the response is attributed to hypochlorous acid. Since K = [RR’NH][HOCl]/[RR’NCl], the predicted K will also be larger if one assumed /3 equals zero. Under that assumption, the predicted hydrolysis constant increases by a factor of 2.3 for N-chlorocyanurate, 22.7 for N-chlorosuccinimide, and 132 for N-chloro-5,5-dimethylhydantoin. The presence of interference does indeed have an effect on the calculated hydrolysis equilibrium constants. It should be noted that the calculated hydrolysis constants listed in Table I11 have large relative standard deviations. In spite of this low precision, the calculated hydrolysis constants and p values predict the measured responses quite well. Although this method shows low precision in the estimates of the hydrolysis constants, approaches which ignore interferences will inherently contain systematic errors. A detailed comparison of the calculated hydrolysis constants with literature values may be found elsewhere (16). Two investigators have calculated the N-chlorocyanurate hydrolysis constant by measuring the equilibrium free chlorine and assuming no interference from the chloramine. In one case ( l a , the observed hydrolysis constant was larger than that determined in the present work. This suggests that interferences were present, since interferences would increase the apparent free chlorine concentrations and thus increase the apparent value of the hydrolysis constant. In the other case (8), the observed hydrolysis constant is slightly smaller than that determined in the present work. However, evidence for interferences exists. If one analyzes their data with this model, one finds that the estimated hydrolysis constant decreases by about 35%. These observations are consistent with the hypothesis that previous investigators did not account for interferences in their free chlorine measurements. The model described here is also useful for evaluation of analytical procedures where equilibrium interference is unquantified. For example, Pinsky and Hu (8)claim that linear sweep voltammetry is not interfered with by chlorocyanurates. This claim can be quantified by the use of the equilibrium model. Analyzing their data with this model, one finds p = 0.073 (standard deviation = 0.022). This /3 value is smaller than, but within one standard deviation of, that observed with the amperometric membrane electrode (see Table 111). The physical/chemical mechanism of interference in the membrane electrode is not fully understood. In order for interferences to occur, the chloramine must cross the macroporous membrane and be detected at the gold cathode. It is interesting to note that the amperometric membrane electrode (gold cathode, +200 mv) p values for monochloramine, N-chlorosuccinimide, and N-chloro-5,5-dimethylhydantoin are very similar to the amperometric titration (platinum electrode, +200 mV) values (18). This suggests
994
Anal. Chem. 1989, 61, 994-998
that the partitioning process may not be the limiting step in the interference.
CONCLUSIONS A model has been developed for the simultaneous determination of analyte-interferent equilibrium constants and degrees of interference. This model is applicable to any system where the measurement of one component of the equilibrium is interfered with by another component of the equilibrium. The model has been applied to the measurement of HOCl by an amperometric membrane electrode in the presence of an organic chloramine. Hydrolysis constants for the N-chloro derivatives of succinimide, cyanuric acid, and 5,5-dimethyl1.6 X and 5.7 x hydantoin were found to be 3.5 x lo4 M, respectively. Interference is also significant with these chloramines. Although response factors for these chloramines relative to HOCl are small, the electrode responses are 1 to 52 times the true HOCl concentrations. Since organic chloramines are generally poor disinfectants, the electrode response is not a good measure of disinfection ability in these model systems. The model has also been used to compare analytical methods for the measurement of free chlorine in the presence of interfering organic chloramines. Registry No. H,O, 7732-18-5; C12, 7782-50-5; N-chloro85424succinimide, 128-09-6;N-chloro-5,5-dimethylhydantoin, 98-2. LITERATURE CITED (1) U.S. Environmental Protection Agency Fed. Regist. 1975, 40(248), 5956649588.
Marks, H.C.; Strandskov, F. B. Ann. NY Acad. Scl. 1950, 53(1), 163-171. Kruse, C. W., Olivieri, V. P.; Kawata, K. Water Sewage Works 1971, 118(6), 187-193. Wolfe. R. L.; Ward, N. R.; Olson, B. H. Environ. Sci. Technol. 1985, 79,1192-1195. Cooper, W. J.; Mehran, M. F.; Slifker, R. A,; Smith, D. A,; Villate, J. T.; Gibbs, P. H. J. Am. Water Works Assoc. 1982, 74(10), 546-552. Isaac, R. A. J.-Water Pollut. Controlfed. 1983, 55(11), 1316. Wajon, J. E.; Morris, J. C. Envlron. I n t . 1980, 3, 41-47. Plnsky, M. L.; Hu, H. C. Envlron. Sci. Technol. 1981, 75(4), 423-430. Johnson, J. D.; Edwards, J. W.; Keeslar. F. J. Am. Water Works AssOC. 1978, 70(6), 341-348. Reinhard, M.; Stumm, W. I n Water Chbrination: Envlronmental Impact and Health Effects; Jolley, R. L., Ed.; Ann Arbor Science: Ann Arbor, MI, 1980; Vol. 3, Chapter 20. Standard Methods for the Examinatbn of Water and Wastewater, 16th ed.;American Public Health Association, American Water Works Association, Water Pollution Control Federation: Washington, DC, 1965; pp 294-315. Morris, J. C. J. Phys. Chem. 1966, 70, 3798-3802. Constantinides, A. Applied Numerical Methods with Personal Computers. McGraw-Hill: New York, 1987; Chapter 7. Box, G. E. P.; Muller, M. E. Ann. Math. Stat. 1958, 29, 610-611. Albert, A.; Serjeant, E. P. The Determination of Ionization Constants; 3rd ed.: Chapman and Hall: New York, 1984; p 82. Jensen, J. N.; LeCloirec, C.; Johnson, J. D. I n Water Chlorination: Environmental Impact and Health Effects; Jolley, R. L., Ed.; Lewis Publishers: Chelsea, MI; Vol. 6, in press. Brashear, G., University of North Carolina at Chapel Hill, unpublished results, 1982. Jensen. J. N.; Johnson, J. D., submitted to Environ. Sci. Technol. Morris, J. C.; Isaac, R. A. I n Water Chlorination: Environmental I m pact and HeaRh Effects; Jolley, R. L., Ed.; Ann Arbor Science: Ann Arbor, MI, 1983; Vol. 4, Chapter 2.
RECEIVED for review August 12, 1988. Accepted January 23, 1989. This work was sipported by the Electric Po& Re' search Institute (EPRI Grant No. RP2300-7).
High-Sensitivity Electronic Raman Spectroscopy for Acceptor Determination in Gallium Arsenide T. D. Harris,* M. Lamont Schnoes, and L. Seibles
AT&T Bell Laboratories, Room 7C-223, 600 Mountain Avenue, Murray Hill, New Jersey 07974
A new method for acceptor determlnatlon by electronic Raman scatterlng in bulk semi-insulating GaAs Is reported. Separate laser wavelengths for photoneutrallzation of acceptors and probing neutral acceptor populations are employed. Sensltlvity is hproved by I O 4 over previous methods. The added sensttlvlty permits a more complete understandlng of charge balance, allows spatial mapping, and Illuminates the varlatlon of shallow donor concentratlon.
INTRODUCTION The determination of trace impurities is central to understanding the growth and processing of semiconductors and devices. Many modern electronic materials have purity levels that place the concentration of unintentional dopants far beyond the detection limit of any currently available analytical method. This condition is particularly true of undoped semi-insulating (SI) GaAs, in that the desired electrical behavior is achieved by a careful balance of the shallow impurities and deep intrinsic defects. Changes in impurity concentrations at the part-per-billion level can have substantial effects on the performance of the material. To compound the problem further, the behavior of any elemental impurity depends on the crystal site it occupies. Consequently, concentrations from bulk chemical analysis must be compared
to crystal site specific methods with caution. While we cannot review solid-state spectroscopy terminology in detail, we add for those unfamiliar with the terms that an acceptor is a lattice site deficient of electrons while a donor contains surplus electrons. For example in gallium arsenide, cadmium (a group I1 element) is an acceptor if located on a gallium lattice site while sulfur (a group IV element) is a donor if located on an arsenic lattice site. Interstitial atoms, impurity clusters, and intrinsic defects do not have predictable electrical behavior. Among the most promising developments in the spectroscopic characterization of bulk gallium arsenide is the work initiated by Wan and Bray ( I ) . They reported the first sharp structure for the electronic Raman (ER) scattering of the excited states of shallow acceptors. They also point out the utility of using the LO phonon intensity as an internal standard for comparing spectra of different samples. This spectrum has the unusual property of being visible only in bulk undoped semi-insulating crystals using 1.064-pm radiation. The observations were explained by the high purity of this material and the unique optical behavior of the midgap defect EL2 ( 2 ) . This spectroscopic process is complex, and the reader is referred to ref 2 for detail. In summary, absorption of 1.064pm radiation converts the midgap defect first to a neutral charge state and then to a nonabsorbing metastable species. Holes released by the photoneutralization of EL2 bind to the normally ionized acceptors, converting them
0003-2700/89/0361-0994$01.50/0@ 1989 American Chemical Society
