AMI. Chem. 1001, 63,2424-2429
2424
Development of the H-Point Standard-Additions Method for Ultraviolet-Visible Spectroscopic Kinetic Analysis of Two-Component Systems Francisco Bosch-big, Pilar Campins-Falc6,*Adela Sevillano-Cabeza,Rosa Herrkez-HernPndez,and Carmen Molins-Legua Departamento de Quimica Analitica, Facultad de Quimica, Universidad de Valencia, Burjasot (Valencia),Spain Thls work establishes the fundamentals of the Hpolnt standard-addltlons method (HPSAM) to kinetic data for the slmuhaneous determinationof h a r y mixtures or the calculation of analyte concentratlons, completely free from bias error. Two variants of the method are proposed; one Is applied when the reactlon of one component Is faster than that of the other or the latter does not take place at all; the other Is used when the rate constant of the two components are timedependent. Also it Is demonstrated that the shown accuracy of the method a l k w its appkatbn as a dlagnostk tool for the rdiabUlty of analytlcal results. The method was applied to the determlnatlon of manganese and vanadlum by simultaneous 0x1datlon of Pyrogallol Red and also to the determlnatlon of creatlnlne In serum samples and to the simultaneous determlnatlon of creatinine and albumin by the Jaff6 method.
INTRODUCTION The development of methods for the simultaneous determination of binary occassionally ternary mixtures of closely related species on the basis of differences in their rates of reaction with a common reagent is one of the great successes of kinetic analysis. The evaluation of kinetic data obtained by a kinetic method of analysis based on the reaction of a mixture of substances with a given reagent depends on the ratios between the rate constants of the different reactions involved. For a binary system consisting of two species X and Y that react with a common reagent R, if the reaction of X is faster than that of Y and the former finishes at a fixed time while the other continues to take place or if the difference between the rates of the two reactions is large enough, component X can be accurately determined in the presence of Y. On the other hand, if the rate of the reaction between Y and R is quite low but conditions can be changed on completion of the reaction of then the reaction of Y can be sped up and this component determined as well (1). The kinetic determination of the more reactive species in a binary mixture is subject to a positive error arising from the slow reaction that takes place in parallel. The magnitude of such an error will depend both on the rates of the reactions involved and on the concentration ratio of the reactants in the mixture. Some compounds react at a similar rate with a given reagent, so they have to be determined by differential reaction-rate methods. The literature abounds with differential rate procedures, many of which were reported in the last few years. Most of such methods are aimed at the determination of inorganic species in general, and to transition metal ions and non-metal anions in particular ( I ) . Logarithmic-extrapolation, single-point, tangent, proportional-equation, and linear graphical methods are some of the
x,
* To whom correspondence should be addressed. 0003-2700/91/0363-2424$02.50/0
differential kinetic methods most frequently used to determine two-component mixtures from rate measurements (2). Of these, the proportional-equation method appears to be the most flexible for simultaneous determinations; however, it involves the accurate evaluation of rates and proportionality constants and is only applicable in the absence of synergistic effects. On the other hand, we recently developed a modified equilibrium standard-addition method called the “H-point standard-additions method” (HPSAM) ( 3 , 4 )for the determination of unbiased analyte concentrations in the event that the presence of a direct interferent and/or the total Youden blank (TYB) is known. The method relies on the use of multipoint signal data (analytical signal data obtained at two accurately selected wavelengths) to transform otherwise uncorrectable to correctable errors and evaluate the analyte and interferent concentrations. The HPSAM has been applied with analytical spectroscopy to resolve mixtures of two components with extensively or fully overlapped spectra (5).One modification of the HPSAM uses absorbance increments as analytical signals as these only depend on the analyte concentration (6). Such a modified method is of special use when only the analyte concentration is to be calculated or only the overall sample spectrum is available, and in applying the single-standard calibration method. This work was aimed at establishing the fundamentals for application of the HPSAM to kinetic data for the simultaneous determination of binary mixtures or the calculation of analyte concentrations completely free from bias errors. For this purpose we used two variants of the HPSAM one is applied when the reaction of one component is faster than that of the other or the latter does not take place at all; the other is used when the rate constants of the two components are time-dependent. Theoretical Background. (A) Analysis of Two Species of Which Only One Evolves with Time. The HPSAM as applied to equilibrium and spectrophotometric data allows the determination of two species X and Y in a mixture, even if their spectra are completely overlapped or only the analyte concentration free of bias error when the spectrum of the sample matrix is known. The determination of the concentration of X by the HPSAM under these conditions entails selecting two wavelengths XI and X2 lying on each side of the absorption maximum of Y-and at the same distance if the peak is regularly shaped-such that the absorbances of this latter component are the same at both. Then, known amounts of X are successively added to the mixture and the resulting absorbances are measured at the two aforesaid wavelengths. The two straight lines thus obtained intersect at the so-called “H-point” (-CH,AH), where -CH (=-Cx)is the unknown concentration of X and AH ( = A y )is the analytical signal of Y in the former case and represents the constant bias error of the sample in the latter. The foundation of the HPSAM for the treatment of kinetic data under the assumption that only one of the species, X, 0 1991 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 63,NO. 21, NOVEMBER 1, 1991 2425
b
a
A
A’+ A ,
11
b,+ b
A,+d
b
L
A’
CH
C ladded
Figure 1. (a) Required shape of the A -t curves for X and Y in case A (see text). (b) Plot of the H-point standardadditions method for case A. CXaM is the added concentration of X.
evolves with time, is exposed below. In this case, the variables to be fixed are two times tl and t 2 at which the species Y, which does not evolve with time or over the range between these two times, should have the same absorbance,rather than two wavelengths hl and X2 as in the HPSAM as applied to analytical signals obtained at equilibrium (3, 4). The absorbances of X at a given wavelength X and two times tl and t2 will be bi and Ai (Figure la), while those of Y under the same conditions will be b and A’-equal in this case. They will be related through the following equations: (tl I t j I t2;i = 0, 1, n ...) (1) (X) Ai = bi mitj
+
A ’ = b + mti (m = 0) (2) where the subscripts i and j denote the different solutions for n additions of the X concentration prepared to apply the HPSAM and for a time comprised in the tl-t2 range, re-
(Y)
spectively. Thus, the overall absorbances of the x-Y mixture at tl and t2 will be A,, = bi b, and A,, = Ai + A‘, respectively. On the other hand, application of the HPSAM at the two aforesaid times will yield A,, = bo b M,,Ci (3)
+
+ + A,, = A $ + A ’ +
Mt,Ci
(4)
which intersect at point H (-CH, AH) (-&, AY) (Figure Ib). At the intercept bo b Mt,CH A b A ’ + M,,CH (5)
+ +
+
Hence
C H = [ ( A ’ - ~ ) + ( A o - ~ o ) I / ( M , , - M , , ) (6) As species Y is assumed not to evolve over time, then A’ = b and CH = (A0 - bo)/ (Mt, - Mt,) (7)
which is equivalent to the existing CX (=bo/Mt,= A 0 / M , J . Likewise, substitution of CX into eq 3 yields AH = b. k the method of standard additions entails calculating the unknown concentration by extrapolation at a zero ordinate, taking into account that, according to the HPSAM A i= f ( t j )
- cH=- c x
c
Figure 2. Plot of the H-point standard-additions method using absorbance increments for case A.
= 0, then bi = 0 and mi = m = 0, this will be the H-point, at which the slope of the A vs X concentration plot equals that of species Y. The overall equation for the absorbance at such a point will thus simplify to A ’ = b = A H = AY (8)
The intercept of the straight lines represented by eqs 3 and 4 will thus directly yield the unknown X concentration
(Cx)
and the analytical signal of species Y ( A y )corresponding to tl and t2in the original samples, as the two times were chosen in such a way that the latter species had the same absorbance at both. This analytical signal will enable calculation of the concentration of Y from a calibration curve, as this corresponds to the zero point in the calibration curve of the analyte in the presence of the sample according to the basis of the standard-addition method (MOSA). If the version of the HPSAM involving the use of the absorbance increment as analytical signal is employed by use of AA,,-,, instead AA,,+, (6),the resulting graph will be similar to that shown in Figure 2 and will allow the analyte concentration, Cx,to be calculated with no systematic, constant, or
2426
ANALYTICAL CHEMISTRY, VOL. 63,NO. 21, NOVEMBER 1, 1991
I
-c:
-cx=-c"
C
:dded
Flgurr 3. (a) Shape of the A -t curves for X and Y in case B. (b) Plots of the H-point standardadditions method for case B treated according
to case A.
proportional error thanks to the intrinsic features of the HPSAM and the nature of the MOSA. This variant should be of use whenever only the analyte is to be determined or when the A-t curve rather than the composition of the matrix is known. It should also be useful to apply the single-standard calibration method, which features greater simplicity and rapidity. This version can often be comparable with the classical kinetic method based on the AA vs Cplot. This method can also be used to diagnose the occurrence of interferences with a given analytical procedure as, in the absence of errors, the plot of any AA,,-,, against the added analyte concentration will have a common point (-CH,0). (B)Analysis of Two Species with Overlapped Time Evolutions. When the two species in a mixture, X and Y, evolve with time, Cx and Ai can be calculated as shown below by plotting the analytical signal AAt,_,, against the added concentration of X at two wavelengths hl and h2, provided the absorbances of the Y component at these two wavelengths are the same (Ay), and so are thus the AA,,,, values. Below are described the HPSAM bases that apply under these conditions, namely the use of two times tl and t 2 and two wavelengths X1 and Xz, additivity of absorbances and absence of synergistic effects. Thus, if the absorbance is plotted at the two above times and wavelength X1, and X is assumed to react faster than Y (Figure 3a), the intercept of the lines described by eqs 3 and 4 will not yield the data pair (-Cx, Ai), but rather larger values of these parameters, as can be seen from Figure 3b. By plotting AAt+ against Cxndded at X1, one obtains the straight line shown in Figure 4. The intercept of the line can be arranged to A A o = ( A , + A') - (bo b) = (A,-bo) (A'-b) = AAxO + AAyo (9)
+
+
which would correspond to the analytical signal obtained from the solution containing the sample alone. The analytical signal for any other solution would be given by AA" = AAx"
+ AAy"
AAx"
+ AAP
(10)
Thus, the intercept with the 3c axis (-Ck) will provide a concentration equivalent to the sum of the concentrations of the two species, X and Y, while the intercept with the y axis
Figure 4. Plot of the H-point standardgdditions method using absorbance increments between t , and t , for case B at A,.
will be equivalent to the s u m of absorbance increments (AA). This plot (Figure 4) provides information complementary to that supplied by Figure 3b. The application of an analogous procedure at X2 will yield absorbance values and plots of these against the added analyte concentration similar to those in Figures 3 and 4 and similar nonconclusive results. The problem can be solved by considering the results obtained at Xl and X2, jointly as these two wavelengthsare chosen in such a way that Y has the same absorbance and hence the same AAtl-tzvalue at both, as can be seen from Figure 5. "hii figure is similar to Figure 1,with the exception of the analytical variables. Point H in Figure 5 corresponds to the intercept of the straight lines
ANALYTICAL CHEMISTRY, VOL. 63, NO. 21, NOVEMBER 1, 1991
Xi
2427
A2
Flguro 5. (a) Required shape of the PA,,,, vs A, graphs in case B. (b) Plot of Kpoint standard-addltkms method for case 9. Table I. Results for Different Mixtures of Manganese and Vanadium
true concn, mg/L
proportional eqs
mean concn found and std dev, mg/L HPSAM 5 min
10 min
CV
CMll
CV
S
chill
S
CV
S
CMIl
S
CMIl
S
0.20 0.20
0.55 1.10
0.22 0.21
0.04 0.04
0.57 1.12
0.04 0.04
0.24 0.26
0.05 0.06
0.56 1.19
0.04 0.06
0.56 1.18
0.04 0.04
Likewise, species Y can be determined from M y o = A A H by one of two procedures, namely (a) by using AAH and a calibration graph for Y [My= f(Cy)]at either of the chosen wavelengths (A, or A,) or (b) by using the plot of Ax, or Ax, against the added concentration of X (Figure 3b). As can be seen from the figure, point H can be located at either wavelength by calculating the difference (A'- b) and subtracting it from the analytical signals obtained at t2;i.e. by subtracting = AAH we will obtain the Ai + b the calculated value Myo values and hence be in a position to apply the H-point method when the absorbance of species Y is constant. Thus,by tracing a parallel to the straight line obtained at t2,we shall obtain the actual H-point as the intercept with the straight line at t l , the intercepts on the x and y axis will be -Cx = CH and A' = b = AH, respectively. From a calibration curve for Y at tl, one can readily calculate the concentration of this species. Some Representative Examples. Manganese and vanadium can be determined simultaneously by oxidation of Pyrogallol Red (PGR) using an equation system in which the absorbance at a fixed time is assumed to be proportional to thL overall concentration of the two elements and their effects on the absorbance of PGR to be additive (7). This simultaneous determination can also be accomplished by using the abovedescribed procedure A, as between 5 and 10 min the oxidation of PGR is due to vanadium exclusively and the oxidation of manganese is finished in less than 5 min. Accordingly, the HPSAM was applied to two samples containing 0.20 mg/L V(V) and 1.10 mg/L and 0.55 mg/L Mn(VII), respectively. The procedure applied was described in detail elsewhere (7). The analyte, V(V), was added a t a concentration up to 1.63 mg/L, the absorbance was read after 5 and 10 min, and five replicates were run in every case. The application of the HPSAM allowed us to calculate the concentration of vana-
dium directly from the intercept of the two straight lines obtained by measuring the absorbance of the different solutions at 5 and 10 min. A calibration graph and the AH value allowed the concentration of manganese to be calculated. The results obtained are listed in Table I, which also gives those obtained by using the proportional equations given in ref 7. As can be seen, the two sets of results are quite consistent. The HPSAM will prove to be advantageous when there are bias errors, which it takes due account of, and when only vanadium is to be determined and thus no calibration graph for manganese needs to be run. Another example of the application of the HPSAM (case A) is the simultaneous determination of creatinine and albumin with alkaline picrate (6.6 X 10" M in picric acid and 0.2 M in NaOH) by measuring the absorbances at 45 and 180 s and a wavelength of 485 nm at 25 "C (8). Creatinine is added up to a concentration of 16.6 mg/L. We assayed a mixture of 8.3 mg/L creatinine and 15.4 g/L albumin; the concentration of the former was directly calculated from the intercept of the straight lines obtained a t 45 and 180 s on application of the HF'SAM. On the other hand, the albumin concentration was obtained from AH and its calibration curve, i.e. from Ad6 = 0.068 A,,
+ 8.05 X 10%
= 0.075
+ 7.98 X 10%
(g/L albumin) (r = 0.9995)
(g/L albumin) (r = 0.9995)
The results obtained, namely 8.9 mg/L creatinine and 14.5 g/L albumin, were consistent with the amounts added. The HPSAM based on the use of absorbance incrementa as analytical signals should be of use in determining creatinine
ANALYTICAL CHEMISTRY, VOL. 63, NO. 21, NOVEMBER 1, 1991
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Table 11. Equations of the MOSA Method in the Reading Interval 45-180 sa
creatinine concn, mg/L vol of serum, mL
no. of runs
180 - 45
60 - 15
At, s 180 - 15
120 - 60
60 - 10
1 2 3 4
1.8 1.6 1.5 1.8 1.7 f 0.2 2.3 2.1 2.1 2.21 f 0.08
1.4 1.4 1.4 1.7 1.5 f 0.2 2.3 2.0 2.1 2.0 f 0.3
1.6 1.5 1.5 1.7 1.6 i 0.1 2.4 1.8 1.9 2.21 i 0.08
1.7 1.5 1.5 1.5 1.6 f 0.1 2.1 2.2 2.2 2.16 f 0.05
1.4 1.4 1.5 1.5 1.4 f 0.1 2.4 1.8 2.1 2.1 f 0.3
0.4
Cfs 0.6
1 2 3
C f S a
Conditions: creatinine added 0-8 mg/L, picric acid 6.6 X
M, sodium hydroxide 0.2 M, and 25 "C.
AA
AA
a
a
/
1.0
180.10
0 .a8 '
0.4
Jr
0.5
0
-0
B
:t:
I
/ II
0
0
4
8
12
le
Cadded
12
16
20
20
\
mg C1
AA b 0.0
406 404 606
180.15
1.o
180-30
620
0.4 180-45
0.5 80-30 120-60 60-30
0 0
4
8
12
I6
20
Gadded\ mg
L-' Figure 6. AA vs added creatlnine concentration at different time Intervals and 486 nm for (a) serum 1 and (b) serum 2. Condltions: concentration of added creatinlne 0-20 mg/L, volume of serum 0.6 mL, picric acid 6.6 X M, sodium hydroxide 0.2 M, and 25 O C . by the Jaff6 method; in this case, the HPSAM could be comparable with the classical &4-C method, but the inherent features of the HPSAM allow one to draw some conclusions on the accuracy of the method on analyzing the results obtained. In this work we used the variant reported elsewhere (8,9), a picric acid and NaOH concentration of 6.6 X and
0
0
4
8
12
16
Cadded
20
\ mg L"
Figure 7. AA vs added creatinine concentration. Conditions: 0.4 mL (a) and 0.6 mL (b) of serum, concentration of added creatinlne 0-20 mg/L, picrate 6.6 X M, sodium hydroxkle 0.2 M, and 25 O C .
0.2 M, respectively, a readmg interval of 45-180 s, a wavelength of 484 or 486 nm, a temperature of 25 O C , a serum volume of 0.4 or 0.6 mL in the cuvette, an overall volume of 2.5 mL, and calibration by the standard-addition method. We assayed two sera with creatinine contents liable for transfusion and used an HP-8452A diode-array spectrophotometer as the detector. Application of the HPSAM yielded plots in which the H-point provided the creatinine concentration and the constant systematic error introduced by the sample, which could not be attributed to a specific component as the analytical signal (AH)would correspond to the s u m of the contributions from the species making up the mixture. The application of
ANALYTICAL CHEMISTRY, VOL. 63, NO. 21, NOVEMBER 1, 1QQl 2429
Table 111. Standard-Additions Method: Concentrations of Creatinine for Different Intervals of Timea concn of creatinine, mg/L vol of serum, mL
180 - 15
180 - 30
180-45
90- 30
120 - 60
60 - 30
concn of creatinine mean values (n = 6),mg/L
0.4 0.6
1.8 2.4
1.76 2.6
1.79 2.7
1.71 2.6
1.74 2.6
1.77 2.7
1.76 i 0.03 2.6 i 0.1
At, s
Conditions: concentration of added creatinine 0-8 mg/L, picric acid 6.6 X
listed in Table IV for s e w 2. All the lines intersect at a point
Table IV. Concentration of Creatinine at Different Wavelengths, in the Interval of Time 45-180 sa concn of creatinine, mg/L 484 486 500 506 520 nm nm nm nm nm
vol of serum, mL 0.4
1.8
1.9
1.8
1.8
1.5
2.7
2.6
2.7
2.1
2.4
C = 1.8 f 0.1 , , ,C , = 11.3
0.6
-
M,sodium hydroxide 0.2 M, and 25 ‘C.
C = 2.6 f 0.1 ,,,C 10.8 M, sodium hydroxide 0.2 M, and a Conditions: picric acid 6.6 X 25 O C . Volume of serum: 0.4 and 0.6 mL. Concentration of added creatinine: 1.7-8 mdL.
the HPSAM in its AAq-$-Caddd variant yields the concentration of creatinine directly from the intercept on the y axis. However, in order to ensure the absence of constant and proportional errors from the calculated concentration, all the possible u t , - t 2 - C a d d & lines for creatinine should intersect at the same point, namely that corresponding to the unknown concentration, CH,as this would indicate that the time evolution of the matrix would be a horizontal line. This was the actual result of the determination of the two sera assayed, irrespective of the serum volume used in the reading cuvette (Figure 6). As can be seen from Tables I1 and 111, the creatinine contents found in sera 1 and 2 were independent of the reading time chosen, the most probable value being 9.4 f 0.9 and 11.0f 0.5 mg/L for serum 1 and 2, respectively. In view of these results, one could also calculate the creatinine content from the intercept of the L4tl-tz-Canaladdd lines. The result thus obtained would also be the most probable, as it would be calculated from a larger number of analytical data. The results obtained by this procedure were identical with those given above. The kinetic spectrophotometric determination of creatinine by the Jaff6 method can also be accomplished according to the above-described HPSAM procedure (B) by choosing two wavelengths at which the interferent (the sample matrix in this case) has the same absorbance and hence identical (or similar) ut,-,, values. The results obtained in the determination of creatinine at the wavelengths of interest (484-486, 500,506,and 520 nm) are shown in Figure 7 for serum 1 and
of zero ordinate, which indicates that, over the wavelength range 484-520 nm, the spectrum corresponding to the sample matrix is horizontal and therefore does not evolve with time, consistent with the HPSAM bases for case B. The creatinine concentrations found by this procedure are similar to those given above. All this allows one to assume that the determination of creatinine in sera from normal patients will be free from systematic errors provided it is conduded under the conditions described elsewhere (8,9), since the concentration obtained is independent of the serum volume taken, the time interval considered, and the wavelength set, consistent with the above HPSAM bases. The demonstrated accuracy of the method is such that it is of analytical utility. The method has been developed for the kinetic-spectrophotometric analysis but it could also be applicable to other methods of analysis using time as one of the measurement dimensions. HPLC with a diode-array detector and unresolved peaks (both spectroscopicand chromatographic) could be incorporated with the HPSAM. Work in this sense is in progress. Registry No. Manganese, 7439-96-5;vanadium, 7440-62-2; creatinine, 60-27-5. LITERATURE CITED Mottola, H. A.; Perez-Bendito, D.; Mark, H. B., Jr. Anal. Chem. 1998, 60, 181R.
Kopanica, M.; Stara, V. In Kinetic Methods in Chemlcal Analysis; Svehla, G., Ed.; Wilson and Wilson’s Comprehensive Analytical Chemistry; Elsevier: Amsterdam, 1983; Vol. XVIII. Boschfleig, F.; Campins-Falcb,P. Analyst 1988. 113, 1011. Boschdeig, F.; Campins-Falcb, P. Analyst IBOO, 115, 111. Campins-FaicB, P.; Bosch-Reig, F.; Molina-&net. A. Fresedus ’ J .
Anal. Chem. 1990, 338, 16. Camplns-Falcb, P.; Bosch-Reig, F.; Verdfi-Andr&, J. Td&mta, In press. Seviilano-Cabeza, A.; Medina-Escriche,J.; de la GuardlaCirugede, M. Analyst 1984. 109. 1303. Llobat-EstelYs, M.; Sevillano-Cabeza, A,; Campins-Falcb, P. Analyst
inae. 114.597. Campins-Faica, P.; Sevillano-Cabera, A,; Llobat-EstelOs, M. Analyst 1989, 114, 603.
RECEIVED for review October 10, 1990. Revised manuscript received July 8,1991. Accepted July 8,1991. We are grateful to the DGICyT for financial support received for the realization of Project PB 88-0495,
