Kinetic Study of the Cyanogen Bromide-Pyridine Reaction Applied to Thiocyanate Determinations in Serum J. B. Landls, M. Rebec, and H. L. Pardue" Department of Chemistry, Purdue University, West Lafayetfe, Indiana 47906
I t Is shown that cyanogen bromide produced by the reactlon of thlocyanate with bromlne follows apparent firstorder kinetics In Its reactlon wlth pyrldlne. Effects of pH, lonlc strength, temperature and pyrldlne concentration on apparent flrst-order rate constants are reported, and the data are used to establsh condltlons for a fast kinetic method for thlocyanate In serum. Stopped-flow mlxlng Is used and measurements are completed In about 20 s for each sample. Data reported for aqueous standards, standard additions to pooled sera, and multiple sera show uncertainties In the range of f0.5% to fl% (95% confidence level). Rate constant data for sera are used to evaluate the effects of sample matrlces on the uncertalnty of the klnetlc method. For 42 serum samples, the average and the total range Uncertainty (95% confidence level) Is fl% Is 2.6%.
Because the toxicity of low levels of cyanide appears to be related to the ability of the body to metabolize cyanide to thiocyanate (1,2),numerous methods for the determination of thiocyanate in body fluids have been developed (3-8). Many of these methods are extensions of early work ( 4 , 5 ) in which the Konig synthesis of pyridine dyes (9,lO) was used to determine thiocyanate. In these procedures, cyanogen bromide or chloride produced by the reaction of thiocyanate with bromine or chlorine reacts with pyridine and an aromatic amine to produce a colored reaction product. Most of the more recent methods differ in the choice of aromatic amine (6-8). All of these methods have been based upon equilibrium procedures and none of the studies have characterized the kinetic behavior of the reactions. Goals of the present work were to characterizethe kinetic behavior of pertinent reactions and to develop a fast kinetic method for thiocyanate. Although the initial plan was to use p-phenylenediamine in the reaction system, preliminary work demonstrated that solutions containing this amine were unstable. Subsequent work showed that a yellow product of the reaction between cyanogen bromide and pyridine could be used to monitor the reaction which exhibited pseudo-first-order kinetics after a brief induction period. Accordingly, our attention was focused on a simpler reaction system involving only cyanogen bromide and pyridine. Samples containing thiocyanate are treated with bromine water to produce cyanogen bromide. SCN-
+
4Br,
+ 4H,0
--t
CNBr
+ 7Br- + SO,
2-
+ 8"
(1)
After a brief reaction time, the excess bromine is reduced with As(II1) and the cyanogen bromide-pyridine reaction CNBr
+ Pyridine
-+
Yellow Product (eqoonm = 4
(2)
x l o 4 L mol-' c m - ' ) is monitored by stopped-flow spectrophotometry. Effects of ionic strength, pH, temperature, and pyridine concentration on the apparent first-order rate constant were evaluated and used to establish analysis conditions. The recommended conditions result in an apparent rate constant
for reaction 2 of about 0.18 s-l and a half-life of about 3.85 s. Accordingly, the reaction is essentially complete in 20 s. The thiocyanate concentration in a sample is computed as the average of 110 values obtained from 110 slopes of the response curve computed at 40-ms intervals. Results are reported for aqueous standards, for recoveries of thiocyanate added to a serum pool, and for thiocyanate in several sera obtained from a local hospital. A comparison of stopped-flow kinetic results for the sera with results obtained using the Pettigrew-Fell method (8)yielded a regression equation of y = 0 . 9 8 3 ~ -0.13~ mol/L. Recoveries ranged from 96 to 100%. The discussion includes an error analysis based upon apparent rate constants determined during each determination. GENERAL CONSIDERATIONS Computation of Analyte Concentration. As we indicated above, reaction 2 follows pseudo-first-order kinetics after a brief induction period. For a first-order reaction monitored by the absorbance of a reaction product, it is easily shown (11) that the initial concentration, Cot of the rate limiting species is related to the slope of the absorbance vs. time plot, dA/dt, by
(3) where k , is the apparent first-order rate constant, t is the time, is the molar extinction coefficient of the reaction product and b is the cell path length. The quantity in parentheses is a time-dependent proportionality constant which relates the slope at any point in time to the initial reaction concentration. In the present work, we used a standard to compute the quantity, Qt (ekof/ka&)= Co,/dA/dt, at several points in time and stored these Qt in a "look-up table" in the computer. These Qt values were then used to compute unknown concentrations, Co,o,from slopes determined at several points along the curve, and the unknown sample concentration was determined as the average of all of these individual values. In the standardization and analysis procedures, 250 absorbance values were recorded at 40-ms intervals for each sample and slopes were computed for data points 63 through 163 (2.52 s through 6.52 s) using a 21-point derivative routine (12). These slope values are used as described above to compute analyte concentration. E r r o r Analysis. One important source of error in any kinetic method of analysis is the uncertainty in the rate constant. It has been suggested that pseudo-first-order rate constants can serve as unique diagnostics for potential analysis errors because the rate constant is independent of analyte concentration and because procedures for determining the first-order rate constants require no prior knowledge of analyte concentration (13). For example, the A vs. t data used to compute analyte concentration can also be used in ln(A, A,) vs. time plots to determine k,, and the resulting value of the rate constant should be independent of concentration. Thus, if observed rate constants were indeed constant among different samples containing the same or different analyte concentrations, then the analyst can be relatively confident ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
785
that variations in reaction conditions such as ionic strength, pH, temperature, etc., and matrix variations are not introducing errors via the kinetic behavior of the reaction. On the other hand, if the observed rate constant varies from one sample to another, then the analyst will know there is a problem. T o make effective use of this built-in “error diagnostic”, it is useful to have an analytical expression which describes concentration errors in terms of uncertainties or errors in the rate constant. In general, the relative concentration error, Re,, resulting from an uncertainty in the rate constant, t k , will be given by
When these operations are applied to Equation 3 above, the following equation which is applicable a t any time t results. =
( t - )+)Ek. Response curve for cyanogen bromide-pyridine reaction. Ascending plot: absorbance vs. time. Descending plot: In(A, - A) vs. time. Conditions: = 1.0 mol/L, pH = 6.15, p = 1.05, T = 25 O C , GNBr = 10 Mmol/L (These are serum concentrations before dilutlon) Figure 1.
I t is apparent from this equation that the effect of the uncertainty in the rate constant could be minimized by making the slope measurement at a point in time when t = l/k4. Such a single-point measurement would, of course, be subject to random variations in the response curve. In order to reduce the effects of random signal noise, we averaged slopes measured at several points during the response curve. Thus the average error resulting from the uncertainty in the rate constant would be the sum of the individual errors ((tl - 1/kJ t k + (t2- l/k4)tk + ... + ( t , - l/ka)tk) divided by the total number, n, of points summed. This statement is expressed mathematically as
For the measurement procedure outlined above (n = 110, tl = 2.52 s, t 2 = 2.56 s, ..., t, = 6.52 s), Equation 4c becomes
This expression is used later to evaluate contributions of rate constant variations among samples to the analysis error. EXPERIMENTAL Instrumentation. All response curves describing the kinetic dependencies of the reaction were made on an automated stopped-flow system using a stabilized photometer previously described ( 1 1 , 1 4 , 1 5 ) . Data were collected and processed using a hierarchicalcomputer system (16) consisting of a minicomputer (2100A, Hewlett-Packard Corporation, Palo Alto, Calif. 94304) and a microcomputer (Model 8008, Intel Corp., Smta Clara, Calif. 95051). pH measurements were made on a digital pH meter (Model 109, Corning Scientific Instruments, Medfield, Mass. 02052) using a combination electrode. All serum and thiocyanate standards were run on an Aminco-Morrow stopped-flow system (American Instrument Company, Silver Springs, Md. 20910) interfaced to the Hewlett-Packard 2100 A computer. Response curves consisted of 250 data points collected over the first three half-lives of the reaction. Equilibrium absorbance values (A,) were determined as the average of 30 points taken after three additional half-lives. Reagents. Boiled, distilled, deionized (Amberlite MB-3 column) water was used for the preparation of all solutions. Pyridine. A 5.0 M pyridine stock solution was prepared from reagent grade pyridine (Fisher Scientific Co., Fair Lawn, N.J. 07410). No signs of decomposition occurred over the four-month period of the study. Hydrochloric Acid. A 4.17 M hydrochloric acid solution was prepared from reagent grade HC1 (Mallinckrodt, St. Louis, Mo. 63160). Aliquots were diluted and standardized against tris(hydroxymethy1)aminomethane (THAM). 786
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
Trichloroacetic Acid. A 20% solution by weight of trichloroacetic acid was prepared from reagent grade trichloracetic acid (Mallinckrodt, St. Louis, Mo. 63160). Aliquots were diluted and standardized against THAM. Sodium Perchlorate. A 3.0 M stock solution of sodium perchlorate was prepared from reagent grade NaC104(G. Frederick Smith Chemical Co., Columbus,Ohio) without further purification. Bromine Water, Arsenic(1IZ) Oxide, p-Phenylenediamine“ 2HC1. Bromine (Fisher Scientific Co., Fair Lawn, N.J. 07410) water, arsenic(II1) oxide (Mallinckrodt, St. Louis, Mo. 63160) and p-phenylenediaminem2HCl (Matheson Coleman and Bell, Norwood (Cincinnati)Ohio) solutions were prepared as previously described (8). p-Phenylenediamine2HClwas purified as described in (17). KSCN Standards. A 0.1 M potassium thiocyanate stock solution was prepared from reagent grade KSCN (Fisher Scientific Co., Fair Lawn, N.J. 07410). This solution is stable for 3 months. Standards for analysis were prepared from the stock solution by diluting aliquots and adjusting the ionic strength to 0.6 with the 3.0 M NaC104solution. Standards were prepared fresh weekly. Pyridine Reagent. The pyridine reagent used in the analysis was prepared by adding 100 mL of 5.0 M pyridine, 23 mL of 4.17 M HC1, and 18.0 mL of 3 M NaC104to a 250-mL volumetric flask and diluting to volume. The pH of the reagent was 6.15 and ionic strength was 0.6. NaOH. A 3.95 M sodium hydroxide (Baker Chemical Co., Phillipsburg,N.J.) solution was prepared and standardized against a standard HCl solution. Sample Treatment. KSCN Standards. One drop of bromine water was added to approximately 5 mL of KSCN standard with mixing and followed immediately by 1 drop of arsenic(II1)oxide solution to reduce the excess bromine. Serum Samples. To 500 pL of serum was added 2 mL of water, 250 MLof 3.0 M NaC104,and 1.25 mL of 20% trichloracetic acid. The sample was centrifuged for 20 min at 2000 rpm and 2.5 mL of the clear supernatant was treated with 250 pL of 3.95 M NaOH. One drop of bromine water is added with mixing followed immediately by one drop of arsenic(II1) oxide. The NaOH added was just enough to neutralize the bulk of the acid while still maintaining an acid filtrate which was required for the thiocyanate-bromine reaction. RESULTS AND DISCUSSION Kinetic Dependencies. The ascending plot in Figure 1 represents a typical response curve (absorbance vs. time) for the reaction. After an induction period which lasts for 1 to 2 s, the curve approaches a logarithmic response which is characteristic of first-order reactions. The apparent first-order behavior is confirmed by the linear descending plot of ln(A,
Table I. Summary of Error Data for Different Sample Typesa
Sample type
Rate constant, s-l AverStd Range age dev
Standards 0.174-0.185 0.180 0.004 Stdaddn 0.171-0.181 0.177 0.003 Sera 0.169-0.189 0.179 0.008 a Errors are computed using Equation 4d.
L 54 58 62 66
O5 0
7 0
p l i ( U N C 0 R R E C T E D)
Figure 2. Effect of pH upon ,apparent first-order rate constant for cyanogen bromide-pyridine reaction. Conditions as in Figure 1
To establish appropriate analysis conditions, we have evaluated effects, of pyridine concentration, pH, temperature, and ionic strength ( p ) on the apparent first-order rate constant (k,). Because of the induction period observed in Figure 1, all rate constant data reported below are based upon the last 210 data poiints for each run where 250 data points represent three half-lives for the reaction. Also, pyridine concentrations, pll, and temperature dependencies were run at an ionic strength of 1.05. All uncertainties in numerical data presented below are quoted a t the 95% confidence level unless stated otherwise. Ionic Strength. Effects of ionic strength on the rate constant are slight. Comparison of rate constant vs. ionic strength at 25 “C and pH 6.15 yields a regression equation of k , = (0.038 f 0.016)~-I- 0.15 f 0.01 for ionic strengths between 0.4 and 1.05. Clearly, ionic strength is not a critical parameter in this system. The kinetic dependencies reported below were obtained at p = 1.05 in order to accomodate 1 mol/L pyridinium ion produced at low pH values. The analysis data were obtained at an ionic strength of 0.6. Thus, the rate constant applicable to the analysis conditions is about 10% lower for comparable conditions of pH and temperature in the kinetic dependency studies. Temperature. The temperature dependence of the reaction was evaluated between 24 and 37 “C for p = 1.05 and pH of 6.15. A plot of In k , vs. l / T was linear with a slope of 3.3 X lo3 f 2.7 X lo2, an intercept of 9.6 f 0.9 and a correlation coefficient of 0.996. The analytical data reported below were obtained at 25 f 0.1 “C. p H . Figure 2 represents the dependence of the apparent rate constant on pH in the range from 5.05 to 7.07. The pH values plotted here are not clorrected for ionic strength because the uncorrected values are most useful to potential users of the proposed method. It is observed that highest rates and lowest dependence on pH would be achieved for pH values between 6.6 and 7. For situations in which contributions to the solution pH by samples could introduce significant errors, it would be advantageous to use a buffer system which would adjust the pH to the region where the change vs. rate constant with pH approaches zero. However, in the present case we did not anticipate this problem and we chose a pH of 6.15 so that the pyridinium ion concentration would be sufficiently high that the pyridine would serve as the buffer for the system. Pyridine Concentration. The dependence of the apparent rate constant on pyridine concentration in the range from 0.1 to 1.25 mol/L was evaluated. The rate constant increased linearly with pyridine concentration and the regression equation for the data is k, = (0.183 f O.O04)C, - 0.004 A 0.002 with a correlation coefficient of 0.999. This linear dependence - A ) vs. time.
Concentration error, % Std Range dev 1.3 1.3
2.6
0.5 0.4 1
can be used to adjust the apparent rate constant to suit experimental requirements. In this case, we chose a pyridine concentration of 1 mol/L so that the reaction would be essentially complete in 20 s ( k , = 0.18 s-’, tljz = 3.85 5). This pyridine concentration caused some decrease in mixing speed, but in all cases solutions were completely mixed within the delay time imposed by the induction period (see Figure 1). Analysis Data. Data reported here include aqueous standards, standard additions of thiocyanate to human sera, and a comparison of serum values obtained by the stopped-flow kinetic method and by an equilibrium method (8). Statistical data for rate constants determined for each group of samples are included in Table I and used in the error analysis discussion below. Aqueous Standards. The system was standardized using a single 10 pmol/L aqueous standard, and then several aqueous standards in the range from 4 to 24 pmol/L were treated as unknowns. Regression of “found” (y) vs. “taken” (x) values yielded y = (0.993 f 0.018)~+ 0.13 f 0.28 Fmol/L for triplicate runs on each standard. The correlation coefficient for the data was 0.9994. The standard deviation of rate constants for all standards was 0.004 s-l (See Table I). Recovery Experiments. The thiocyanate concentration in a serum pool was determined by the kinetic method and then measured amounts (1.25 X lo-’ pmol to 7.5 X lo-’ pmol) of thiocyanate were added to 500-pL aliquots of the pool with a two-fold dilution. The resulting samples were analyzed by the kinetic method. A least squares fit of determined values (y) vs. expected values (x) gave a regression equation of y = (0.993 f 0 . 0 1 ) ~ 0.123 f 0.9 pmol/L with a correlation coefficient of 0,9999. Recoveries, computed as the difference between the determined values for the prepared samples and the pool divided by the expected value for the prepared sample, ranged from 96 to 100% for triplicate runs on each sample. Preliminary work in which deproteinization without the addition of sodium perchlorate confirmed earlier findings (3) that the perchlorate is necessary to ensure that all of the thiocyanate is determined by this method. Rate constant data for these experiments are included in Table I. Serum Samples. Several serum samples were obtained from a local hospital and processed by both the kinetic method described here and the equilibrium method described by Pettigrew and Fell (8). Results of this comparison are presented in Figure 3. The solid line in Figure 3 represents the regression equation, y = (0.983 f 0.032)~- 0.13 f 2.4 pmol/L with a correlation coefficient of 0.995 for these data. These results demonstrate reasonable agreement between the kinetic and equilibrium methods. Rate constant data for these samples are included in Table I. Error Analysis. Rate constant data from Table I and Equation 4d can be used to estimate the effect of kinetic variations among samples and sample types on the analysis error. For the aqueous standards, the average value of the rate constant is 0.18 s-’ and Equation 4d reduced to R E C=~
+
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
787
c ./
I
C s c N ( pmol/iifer - Equilibrium)'
Flgure 3. Comparison of thiocyanate serum samples determined by the kinetic and an equilibrium method (4. y = (0.98 f 0.03)~-0.13 f 2 wmol/L; r = 0.094
(473 - 110/0.18)tk~/110or Rtc, = -1.25tta. Substituting the between run value for the standard deviation of k, (tk, = 0.004) from Table I, the between-run uncertainty is estimated to be 0.5%. Similar computations lead to between run standard deviations of 0.4% and 1%for the recovery and multiple serum experiments. The range for the 42 sera (eka = 0.189 0.169 or 0.02 s-l) is 2.6%. The above computations suggest that the kinetic component of the random error is split about equally between the measurement system and sample-tosample variations. Equation 4d can be used along with ionic strength, pH, temperature, and pyridine concentration data to evaluate error coefficients for these parameters. For the conditions used in this work, the error coefficients for rate constants are about 0.038 s-l per unit of ionic strength, 0.1 s-'/pH unit and about 0.005 s-'/OC and the corresponding concentration coefficients are (assuming k, = 0.18 s-l) 4.8% per unit of ionic strength, 12.5% /pH unit, and 0.6% /"C. It is apparent from Equation 4c that these error coefficients could be reduced by selecting the points at which slopes are measured such that C;=lnti= Ilka. This refinement did not appear justified in the present work because kinetic errors were quite small; however, it could be useful for routine applications of this or other kinetic methods based upon first-order reactions. The most probable interference with this method k cyanide, because cyanide reacts quantitatively with bromine to produce cyanogen bromide. Accordingly, this method, like the related colorimetric methods, determines both cyanide and thiocyanate. This does not present a problem with serum samples because the cyanide concentration is usually very low com-
788
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
pared to thiocyanate. However, extensions of the method to other situations such as waste waters (18) would require proceduresto separate the species from one another or to mask one of the species chemically. We believe that it is not generally appreciated that the apparent first-order rate constant can be a useful diagnostic tool (13) in the evaluation of effects of sample matrices on the accuracy of kinetics methods based on first-order reactions. Because the rate constant is independent of concentration, it represents a common link among different samples which may have widely differing compositions. For a kinetic method to be valid, it is a necessary condition either that the rate constant must not vary from one sample to another, or that actual values of rate constants be determined and used in the computation step. We believe more use should be made of this diagnostic aid by those who develop and/or use kinetic methods of analysis. The induction period in Figure 1suggests that the reaction between pyridine and cyanogen bromide involves an intermediate. Other authors have proposed reaction schemes for pyridine (19, 20) and pyridine-like compounds (21) with cyanogen halides. We have made no attempt to verify these suggestions or to characterize the factors which influence the induction period.
LITERATURE CITED (1) J. Wilson, Clln. Sci., 29, 505 (1965). (2) I. A. Chisholm and A. R. Pettigrew, Trans. Opthalmol. SOC. U.K.,90, 827 (1970). (3) W. C. Butts, M. Kuehneman, and G. M. Widdowson, Clin. Chem., ( Winston-Salem, N.C.), 20, 1344 (1974). (4) W. N. Aidridge, Analyst(London), 69, 262 (1944). (5) W. N. Aldridge, Analyst(London), 70, 474 (1945). (6) J. Epstein, Anal. Chem., 19, 272 (1947). (7) G. V. L. M. Murty and T. S. Viswanatnan, Anal. Chim. Acta, 25, 293 (1961). (8) A. R. Pettigrew and 0. S. Fell, Clln. Chem., ( Wlnston-Salem, N.C.),16, 996 (1972). (9) W. J. Konig, J . frakt. Chem.. 69, 105 (1904). (IO) W. J. Konig, 2.Angew. Chem., 11, 115 (1905). (11) . . B. 0.Wlliis. J. A. Bittikofer, H. L. Pardue. and D. W. Maraerum. Anal. Chem., 42, 1340 (1970). (12) A. Savitzky and M. J. E. Goiay, Anal. Chem., 36, 1627 (1964). (13) T. E. Hewitt and H. L. Pardue, Clin. Chem., ( Winston-Salem, N.C.) 19, 1128 11973\. \
- I
(14) D. Sanderson, J. A. Bittikofer, and H. L. Pardue, Anal. Chem., 44, 1934 (1972). (15) S. N. Deming and H. L. Pardue, Anal. Chem., 43, 192 (1971). (16) G. E. Mielina, R. W. Taylor, L. G. Hargls, J. Enoiish, and H. L. Pardue, in press. (17) Org. Synth. Coll. Vol., 2, 150 (1943). (18) G. Nota and R. Palombari, J . Chromatogr., 84, 37 (1973). (19) J. Epstein, Anal. Chem., 19, 272 (1947). (20) G. Schwarzenbachand R. Weber, Helv. Chim. Acta, 25, 1628 (1942). 1211 H. A. Warsman and C. A. Elvehiem. . . Ind. €nu. Chem.. Anal. Ed.. 13. 221 (1941). .
I
RECEIVED for review November 15,1976. Accepted January 24,1977. This work was supported in part by Grant No. CHE 75-1550 A01 from the National Science Foundation.
I t Is shown that cyanogen bromide produced by the reactlon of thlocyanate with bromlne follows apparent firstorder kinetics In Its reactlon wlth pyrldlne. Effects of pH, lonlc strength, temperature and pyrldlne concentration on apparent flrst-order rate constants are reported, and the data are used to establsh condltlons for a fast kinetic method for thlocyanate In serum. Stopped-flow mlxlng Is used and measurements are completed In about 20 s for each sample. Data reported for aqueous standards, standard additions to pooled sera, and multiple sera show uncertainties In the range of f0.5% to fl% (95% confidence level). Rate constant data for sera are used to evaluate the effects of sample matrlces on the uncertalnty of the klnetlc method. For 42 serum samples, the average and the total range Uncertainty (95% confidence level) Is fl% Is 2.6%.
Because the toxicity of low levels of cyanide appears to be related to the ability of the body to metabolize cyanide to thiocyanate (1,2),numerous methods for the determination of thiocyanate in body fluids have been developed (3-8). Many of these methods are extensions of early work ( 4 , 5 ) in which the Konig synthesis of pyridine dyes (9,lO) was used to determine thiocyanate. In these procedures, cyanogen bromide or chloride produced by the reaction of thiocyanate with bromine or chlorine reacts with pyridine and an aromatic amine to produce a colored reaction product. Most of the more recent methods differ in the choice of aromatic amine (6-8). All of these methods have been based upon equilibrium procedures and none of the studies have characterized the kinetic behavior of the reactions. Goals of the present work were to characterizethe kinetic behavior of pertinent reactions and to develop a fast kinetic method for thiocyanate. Although the initial plan was to use p-phenylenediamine in the reaction system, preliminary work demonstrated that solutions containing this amine were unstable. Subsequent work showed that a yellow product of the reaction between cyanogen bromide and pyridine could be used to monitor the reaction which exhibited pseudo-first-order kinetics after a brief induction period. Accordingly, our attention was focused on a simpler reaction system involving only cyanogen bromide and pyridine. Samples containing thiocyanate are treated with bromine water to produce cyanogen bromide. SCN-
+
4Br,
+ 4H,0
--t
CNBr
+ 7Br- + SO,
2-
+ 8"
(1)
After a brief reaction time, the excess bromine is reduced with As(II1) and the cyanogen bromide-pyridine reaction CNBr
+ Pyridine
-+
Yellow Product (eqoonm = 4
(2)
x l o 4 L mol-' c m - ' ) is monitored by stopped-flow spectrophotometry. Effects of ionic strength, pH, temperature, and pyridine concentration on the apparent first-order rate constant were evaluated and used to establish analysis conditions. The recommended conditions result in an apparent rate constant
for reaction 2 of about 0.18 s-l and a half-life of about 3.85 s. Accordingly, the reaction is essentially complete in 20 s. The thiocyanate concentration in a sample is computed as the average of 110 values obtained from 110 slopes of the response curve computed at 40-ms intervals. Results are reported for aqueous standards, for recoveries of thiocyanate added to a serum pool, and for thiocyanate in several sera obtained from a local hospital. A comparison of stopped-flow kinetic results for the sera with results obtained using the Pettigrew-Fell method (8)yielded a regression equation of y = 0 . 9 8 3 ~ -0.13~ mol/L. Recoveries ranged from 96 to 100%. The discussion includes an error analysis based upon apparent rate constants determined during each determination. GENERAL CONSIDERATIONS Computation of Analyte Concentration. As we indicated above, reaction 2 follows pseudo-first-order kinetics after a brief induction period. For a first-order reaction monitored by the absorbance of a reaction product, it is easily shown (11) that the initial concentration, Cot of the rate limiting species is related to the slope of the absorbance vs. time plot, dA/dt, by
(3) where k , is the apparent first-order rate constant, t is the time, is the molar extinction coefficient of the reaction product and b is the cell path length. The quantity in parentheses is a time-dependent proportionality constant which relates the slope at any point in time to the initial reaction concentration. In the present work, we used a standard to compute the quantity, Qt (ekof/ka&)= Co,/dA/dt, at several points in time and stored these Qt in a "look-up table" in the computer. These Qt values were then used to compute unknown concentrations, Co,o,from slopes determined at several points along the curve, and the unknown sample concentration was determined as the average of all of these individual values. In the standardization and analysis procedures, 250 absorbance values were recorded at 40-ms intervals for each sample and slopes were computed for data points 63 through 163 (2.52 s through 6.52 s) using a 21-point derivative routine (12). These slope values are used as described above to compute analyte concentration. E r r o r Analysis. One important source of error in any kinetic method of analysis is the uncertainty in the rate constant. It has been suggested that pseudo-first-order rate constants can serve as unique diagnostics for potential analysis errors because the rate constant is independent of analyte concentration and because procedures for determining the first-order rate constants require no prior knowledge of analyte concentration (13). For example, the A vs. t data used to compute analyte concentration can also be used in ln(A, A,) vs. time plots to determine k,, and the resulting value of the rate constant should be independent of concentration. Thus, if observed rate constants were indeed constant among different samples containing the same or different analyte concentrations, then the analyst can be relatively confident ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
785
that variations in reaction conditions such as ionic strength, pH, temperature, etc., and matrix variations are not introducing errors via the kinetic behavior of the reaction. On the other hand, if the observed rate constant varies from one sample to another, then the analyst will know there is a problem. T o make effective use of this built-in “error diagnostic”, it is useful to have an analytical expression which describes concentration errors in terms of uncertainties or errors in the rate constant. In general, the relative concentration error, Re,, resulting from an uncertainty in the rate constant, t k , will be given by
When these operations are applied to Equation 3 above, the following equation which is applicable a t any time t results. =
( t - )+)Ek. Response curve for cyanogen bromide-pyridine reaction. Ascending plot: absorbance vs. time. Descending plot: In(A, - A) vs. time. Conditions: = 1.0 mol/L, pH = 6.15, p = 1.05, T = 25 O C , GNBr = 10 Mmol/L (These are serum concentrations before dilutlon) Figure 1.
I t is apparent from this equation that the effect of the uncertainty in the rate constant could be minimized by making the slope measurement at a point in time when t = l/k4. Such a single-point measurement would, of course, be subject to random variations in the response curve. In order to reduce the effects of random signal noise, we averaged slopes measured at several points during the response curve. Thus the average error resulting from the uncertainty in the rate constant would be the sum of the individual errors ((tl - 1/kJ t k + (t2- l/k4)tk + ... + ( t , - l/ka)tk) divided by the total number, n, of points summed. This statement is expressed mathematically as
For the measurement procedure outlined above (n = 110, tl = 2.52 s, t 2 = 2.56 s, ..., t, = 6.52 s), Equation 4c becomes
This expression is used later to evaluate contributions of rate constant variations among samples to the analysis error. EXPERIMENTAL Instrumentation. All response curves describing the kinetic dependencies of the reaction were made on an automated stopped-flow system using a stabilized photometer previously described ( 1 1 , 1 4 , 1 5 ) . Data were collected and processed using a hierarchicalcomputer system (16) consisting of a minicomputer (2100A, Hewlett-Packard Corporation, Palo Alto, Calif. 94304) and a microcomputer (Model 8008, Intel Corp., Smta Clara, Calif. 95051). pH measurements were made on a digital pH meter (Model 109, Corning Scientific Instruments, Medfield, Mass. 02052) using a combination electrode. All serum and thiocyanate standards were run on an Aminco-Morrow stopped-flow system (American Instrument Company, Silver Springs, Md. 20910) interfaced to the Hewlett-Packard 2100 A computer. Response curves consisted of 250 data points collected over the first three half-lives of the reaction. Equilibrium absorbance values (A,) were determined as the average of 30 points taken after three additional half-lives. Reagents. Boiled, distilled, deionized (Amberlite MB-3 column) water was used for the preparation of all solutions. Pyridine. A 5.0 M pyridine stock solution was prepared from reagent grade pyridine (Fisher Scientific Co., Fair Lawn, N.J. 07410). No signs of decomposition occurred over the four-month period of the study. Hydrochloric Acid. A 4.17 M hydrochloric acid solution was prepared from reagent grade HC1 (Mallinckrodt, St. Louis, Mo. 63160). Aliquots were diluted and standardized against tris(hydroxymethy1)aminomethane (THAM). 786
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
Trichloroacetic Acid. A 20% solution by weight of trichloroacetic acid was prepared from reagent grade trichloracetic acid (Mallinckrodt, St. Louis, Mo. 63160). Aliquots were diluted and standardized against THAM. Sodium Perchlorate. A 3.0 M stock solution of sodium perchlorate was prepared from reagent grade NaC104(G. Frederick Smith Chemical Co., Columbus,Ohio) without further purification. Bromine Water, Arsenic(1IZ) Oxide, p-Phenylenediamine“ 2HC1. Bromine (Fisher Scientific Co., Fair Lawn, N.J. 07410) water, arsenic(II1) oxide (Mallinckrodt, St. Louis, Mo. 63160) and p-phenylenediaminem2HCl (Matheson Coleman and Bell, Norwood (Cincinnati)Ohio) solutions were prepared as previously described (8). p-Phenylenediamine2HClwas purified as described in (17). KSCN Standards. A 0.1 M potassium thiocyanate stock solution was prepared from reagent grade KSCN (Fisher Scientific Co., Fair Lawn, N.J. 07410). This solution is stable for 3 months. Standards for analysis were prepared from the stock solution by diluting aliquots and adjusting the ionic strength to 0.6 with the 3.0 M NaC104solution. Standards were prepared fresh weekly. Pyridine Reagent. The pyridine reagent used in the analysis was prepared by adding 100 mL of 5.0 M pyridine, 23 mL of 4.17 M HC1, and 18.0 mL of 3 M NaC104to a 250-mL volumetric flask and diluting to volume. The pH of the reagent was 6.15 and ionic strength was 0.6. NaOH. A 3.95 M sodium hydroxide (Baker Chemical Co., Phillipsburg,N.J.) solution was prepared and standardized against a standard HCl solution. Sample Treatment. KSCN Standards. One drop of bromine water was added to approximately 5 mL of KSCN standard with mixing and followed immediately by 1 drop of arsenic(II1)oxide solution to reduce the excess bromine. Serum Samples. To 500 pL of serum was added 2 mL of water, 250 MLof 3.0 M NaC104,and 1.25 mL of 20% trichloracetic acid. The sample was centrifuged for 20 min at 2000 rpm and 2.5 mL of the clear supernatant was treated with 250 pL of 3.95 M NaOH. One drop of bromine water is added with mixing followed immediately by one drop of arsenic(II1) oxide. The NaOH added was just enough to neutralize the bulk of the acid while still maintaining an acid filtrate which was required for the thiocyanate-bromine reaction. RESULTS AND DISCUSSION Kinetic Dependencies. The ascending plot in Figure 1 represents a typical response curve (absorbance vs. time) for the reaction. After an induction period which lasts for 1 to 2 s, the curve approaches a logarithmic response which is characteristic of first-order reactions. The apparent first-order behavior is confirmed by the linear descending plot of ln(A,
Table I. Summary of Error Data for Different Sample Typesa
Sample type
Rate constant, s-l AverStd Range age dev
Standards 0.174-0.185 0.180 0.004 Stdaddn 0.171-0.181 0.177 0.003 Sera 0.169-0.189 0.179 0.008 a Errors are computed using Equation 4d.
L 54 58 62 66
O5 0
7 0
p l i ( U N C 0 R R E C T E D)
Figure 2. Effect of pH upon ,apparent first-order rate constant for cyanogen bromide-pyridine reaction. Conditions as in Figure 1
To establish appropriate analysis conditions, we have evaluated effects, of pyridine concentration, pH, temperature, and ionic strength ( p ) on the apparent first-order rate constant (k,). Because of the induction period observed in Figure 1, all rate constant data reported below are based upon the last 210 data poiints for each run where 250 data points represent three half-lives for the reaction. Also, pyridine concentrations, pll, and temperature dependencies were run at an ionic strength of 1.05. All uncertainties in numerical data presented below are quoted a t the 95% confidence level unless stated otherwise. Ionic Strength. Effects of ionic strength on the rate constant are slight. Comparison of rate constant vs. ionic strength at 25 “C and pH 6.15 yields a regression equation of k , = (0.038 f 0.016)~-I- 0.15 f 0.01 for ionic strengths between 0.4 and 1.05. Clearly, ionic strength is not a critical parameter in this system. The kinetic dependencies reported below were obtained at p = 1.05 in order to accomodate 1 mol/L pyridinium ion produced at low pH values. The analysis data were obtained at an ionic strength of 0.6. Thus, the rate constant applicable to the analysis conditions is about 10% lower for comparable conditions of pH and temperature in the kinetic dependency studies. Temperature. The temperature dependence of the reaction was evaluated between 24 and 37 “C for p = 1.05 and pH of 6.15. A plot of In k , vs. l / T was linear with a slope of 3.3 X lo3 f 2.7 X lo2, an intercept of 9.6 f 0.9 and a correlation coefficient of 0.996. The analytical data reported below were obtained at 25 f 0.1 “C. p H . Figure 2 represents the dependence of the apparent rate constant on pH in the range from 5.05 to 7.07. The pH values plotted here are not clorrected for ionic strength because the uncorrected values are most useful to potential users of the proposed method. It is observed that highest rates and lowest dependence on pH would be achieved for pH values between 6.6 and 7. For situations in which contributions to the solution pH by samples could introduce significant errors, it would be advantageous to use a buffer system which would adjust the pH to the region where the change vs. rate constant with pH approaches zero. However, in the present case we did not anticipate this problem and we chose a pH of 6.15 so that the pyridinium ion concentration would be sufficiently high that the pyridine would serve as the buffer for the system. Pyridine Concentration. The dependence of the apparent rate constant on pyridine concentration in the range from 0.1 to 1.25 mol/L was evaluated. The rate constant increased linearly with pyridine concentration and the regression equation for the data is k, = (0.183 f O.O04)C, - 0.004 A 0.002 with a correlation coefficient of 0.999. This linear dependence - A ) vs. time.
Concentration error, % Std Range dev 1.3 1.3
2.6
0.5 0.4 1
can be used to adjust the apparent rate constant to suit experimental requirements. In this case, we chose a pyridine concentration of 1 mol/L so that the reaction would be essentially complete in 20 s ( k , = 0.18 s-’, tljz = 3.85 5). This pyridine concentration caused some decrease in mixing speed, but in all cases solutions were completely mixed within the delay time imposed by the induction period (see Figure 1). Analysis Data. Data reported here include aqueous standards, standard additions of thiocyanate to human sera, and a comparison of serum values obtained by the stopped-flow kinetic method and by an equilibrium method (8). Statistical data for rate constants determined for each group of samples are included in Table I and used in the error analysis discussion below. Aqueous Standards. The system was standardized using a single 10 pmol/L aqueous standard, and then several aqueous standards in the range from 4 to 24 pmol/L were treated as unknowns. Regression of “found” (y) vs. “taken” (x) values yielded y = (0.993 f 0.018)~+ 0.13 f 0.28 Fmol/L for triplicate runs on each standard. The correlation coefficient for the data was 0.9994. The standard deviation of rate constants for all standards was 0.004 s-l (See Table I). Recovery Experiments. The thiocyanate concentration in a serum pool was determined by the kinetic method and then measured amounts (1.25 X lo-’ pmol to 7.5 X lo-’ pmol) of thiocyanate were added to 500-pL aliquots of the pool with a two-fold dilution. The resulting samples were analyzed by the kinetic method. A least squares fit of determined values (y) vs. expected values (x) gave a regression equation of y = (0.993 f 0 . 0 1 ) ~ 0.123 f 0.9 pmol/L with a correlation coefficient of 0,9999. Recoveries, computed as the difference between the determined values for the prepared samples and the pool divided by the expected value for the prepared sample, ranged from 96 to 100% for triplicate runs on each sample. Preliminary work in which deproteinization without the addition of sodium perchlorate confirmed earlier findings (3) that the perchlorate is necessary to ensure that all of the thiocyanate is determined by this method. Rate constant data for these experiments are included in Table I. Serum Samples. Several serum samples were obtained from a local hospital and processed by both the kinetic method described here and the equilibrium method described by Pettigrew and Fell (8). Results of this comparison are presented in Figure 3. The solid line in Figure 3 represents the regression equation, y = (0.983 f 0.032)~- 0.13 f 2.4 pmol/L with a correlation coefficient of 0.995 for these data. These results demonstrate reasonable agreement between the kinetic and equilibrium methods. Rate constant data for these samples are included in Table I. Error Analysis. Rate constant data from Table I and Equation 4d can be used to estimate the effect of kinetic variations among samples and sample types on the analysis error. For the aqueous standards, the average value of the rate constant is 0.18 s-’ and Equation 4d reduced to R E C=~
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ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
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c ./
I
C s c N ( pmol/iifer - Equilibrium)'
Flgure 3. Comparison of thiocyanate serum samples determined by the kinetic and an equilibrium method (4. y = (0.98 f 0.03)~-0.13 f 2 wmol/L; r = 0.094
(473 - 110/0.18)tk~/110or Rtc, = -1.25tta. Substituting the between run value for the standard deviation of k, (tk, = 0.004) from Table I, the between-run uncertainty is estimated to be 0.5%. Similar computations lead to between run standard deviations of 0.4% and 1%for the recovery and multiple serum experiments. The range for the 42 sera (eka = 0.189 0.169 or 0.02 s-l) is 2.6%. The above computations suggest that the kinetic component of the random error is split about equally between the measurement system and sample-tosample variations. Equation 4d can be used along with ionic strength, pH, temperature, and pyridine concentration data to evaluate error coefficients for these parameters. For the conditions used in this work, the error coefficients for rate constants are about 0.038 s-l per unit of ionic strength, 0.1 s-'/pH unit and about 0.005 s-'/OC and the corresponding concentration coefficients are (assuming k, = 0.18 s-l) 4.8% per unit of ionic strength, 12.5% /pH unit, and 0.6% /"C. It is apparent from Equation 4c that these error coefficients could be reduced by selecting the points at which slopes are measured such that C;=lnti= Ilka. This refinement did not appear justified in the present work because kinetic errors were quite small; however, it could be useful for routine applications of this or other kinetic methods based upon first-order reactions. The most probable interference with this method k cyanide, because cyanide reacts quantitatively with bromine to produce cyanogen bromide. Accordingly, this method, like the related colorimetric methods, determines both cyanide and thiocyanate. This does not present a problem with serum samples because the cyanide concentration is usually very low com-
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pared to thiocyanate. However, extensions of the method to other situations such as waste waters (18) would require proceduresto separate the species from one another or to mask one of the species chemically. We believe that it is not generally appreciated that the apparent first-order rate constant can be a useful diagnostic tool (13) in the evaluation of effects of sample matrices on the accuracy of kinetics methods based on first-order reactions. Because the rate constant is independent of concentration, it represents a common link among different samples which may have widely differing compositions. For a kinetic method to be valid, it is a necessary condition either that the rate constant must not vary from one sample to another, or that actual values of rate constants be determined and used in the computation step. We believe more use should be made of this diagnostic aid by those who develop and/or use kinetic methods of analysis. The induction period in Figure 1suggests that the reaction between pyridine and cyanogen bromide involves an intermediate. Other authors have proposed reaction schemes for pyridine (19, 20) and pyridine-like compounds (21) with cyanogen halides. We have made no attempt to verify these suggestions or to characterize the factors which influence the induction period.
LITERATURE CITED (1) J. Wilson, Clln. Sci., 29, 505 (1965). (2) I. A. Chisholm and A. R. Pettigrew, Trans. Opthalmol. SOC. U.K.,90, 827 (1970). (3) W. C. Butts, M. Kuehneman, and G. M. Widdowson, Clin. Chem., ( Winston-Salem, N.C.), 20, 1344 (1974). (4) W. N. Aidridge, Analyst(London), 69, 262 (1944). (5) W. N. Aldridge, Analyst(London), 70, 474 (1945). (6) J. Epstein, Anal. Chem., 19, 272 (1947). (7) G. V. L. M. Murty and T. S. Viswanatnan, Anal. Chim. Acta, 25, 293 (1961). (8) A. R. Pettigrew and 0. S. Fell, Clln. Chem., ( Wlnston-Salem, N.C.),16, 996 (1972). (9) W. J. Konig, J . frakt. Chem.. 69, 105 (1904). (IO) W. J. Konig, 2.Angew. Chem., 11, 115 (1905). (11) . . B. 0.Wlliis. J. A. Bittikofer, H. L. Pardue. and D. W. Maraerum. Anal. Chem., 42, 1340 (1970). (12) A. Savitzky and M. J. E. Goiay, Anal. Chem., 36, 1627 (1964). (13) T. E. Hewitt and H. L. Pardue, Clin. Chem., ( Winston-Salem, N.C.) 19, 1128 11973\. \
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(14) D. Sanderson, J. A. Bittikofer, and H. L. Pardue, Anal. Chem., 44, 1934 (1972). (15) S. N. Deming and H. L. Pardue, Anal. Chem., 43, 192 (1971). (16) G. E. Mielina, R. W. Taylor, L. G. Hargls, J. Enoiish, and H. L. Pardue, in press. (17) Org. Synth. Coll. Vol., 2, 150 (1943). (18) G. Nota and R. Palombari, J . Chromatogr., 84, 37 (1973). (19) J. Epstein, Anal. Chem., 19, 272 (1947). (20) G. Schwarzenbachand R. Weber, Helv. Chim. Acta, 25, 1628 (1942). 1211 H. A. Warsman and C. A. Elvehiem. . . Ind. €nu. Chem.. Anal. Ed.. 13. 221 (1941). .
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RECEIVED for review November 15,1976. Accepted January 24,1977. This work was supported in part by Grant No. CHE 75-1550 A01 from the National Science Foundation.
