ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
could facilitate new applications of flame techniques which are a t the present time marginal in sensitivity.
ACKNOWLEDGMENT We acknowledge the assistance of F. E. Greene in generating the experimental data.
LITERATURE CITED (1) Wolf, W. R.; Stewart, K . K. Pmsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, 1977:paper #loa. (2) Stewart, K . K.; Beecher. G. R.: Hare, P. E. Anal. Biochem. 1976. 7 0 , 167-173. (3) Stewart, K. K.; Beecher, G. R.; Hare, P. E. U S . Patent 4013413,March 22, 1977. (4) Ruzicka, J.; Hansen, E. H. Anal. Chim. Acta 1975, 78, 17. (5) Ruzicka, J.; Hansen, E. H. Danish Patent Application No. 4846/84, September 1974;U S . Patent 4 022 575. (6) Betteridge, D. Anal. Chem. 1978, 5 0 , 832A-846A. (7) Stewart, K. K.; Beecher. G. R. 176th National Meeting, American Chemical Society, Analytical Division, Miami, Fla., 1978;paper No. 87. (8) Fisher, C. G.; Barnett; W. B.; Wilson, D. L. At. Absorpt. Newsl. 1976, 17(2),33-36.
1205
(9) Fry, R. C.; Northway. S. J.; Denton, M. B. Anal. Chem. 1978. 50, 1719. (10) Sabastiani, E.; Ohls, K.: Riemer, G. Fresenius' Z . Anal. Chem. 1973, 264,105. (11) Manning, D. C. At. Absorpt. Newsl. 1975, 1 4 . 99. (12) Jackworth, E.; Berndt, H. Spectrochim. Acta, Part B 1975, 30, 169. (13) Stewart, K. K. Anal. Chem. 1977, 4 9 . 2125-2126. (14) Rockbnd, L. B.; Wolf, W. R.; Hahn, D. M.; Young, R. J . FoodScl. in press. (15) Wolf, W. R., Greene, F. E., Stewart. K. K . Pittsburgh Conference on Analytical Chemistw and ADplied Spectroscopy, Cleveland, Ohio, 1978: .. paper #68. (16) Szivos, K.; Polos, L.; Pungor, E. Spectrochlm. Acfa, Part8 1976, 3 1 , 289-294 -.. _. .
(17) Menis. 0.C.: Rains. T. C. I n "Analytical Flame Spectroscopy"; Mavirodineaneu, R., Ed.; Springer-Verlag-New York, Inc.: New York, 1970.
RECEIVED for review November 16, 1978. Accepted March 2'7,1979. Mention of a trademark or proprietary product does not constitute a guarantee or warranty of the product by the L1.S.Department of Agriculture, and does not imply its approval to the exclusion of other products that may also be suitable.
Kinetics of Gas-Phase Reactions in Flameless Atomization J. A. Holcombe," R. H. Eklund, and J. E. Smith Department of Chemistry, University of Texas at Austin. Austin, Texas 78712
Observed interference effects in atomic spectral techniques employing a flameless atomizer may result from gas phase reactions between analyte and interferent species. Equilibrium (or thermodynamic) control may not adequately characterize the extent of the reaction. At partial pressures encountered in these systems, reaction kinetics may play a significant role in predicting the degree to which the analyte and the interferent react. "Steady state" and pulsed atomization of Sn, Ga, Fe, and Cu analytes into an Ar sheath containing trace amounts of O2 are used to analyze the time and height-dependent absorbance data resulting from the respective metaVoxygen reactions. Explanations of the resulting curves based on reaction kinetics are presented.
T h e ideal situation in the development of any analytical method is to understand completely all chemical and physical processes occurring in the system. With this information, a priori knowledge of interference effects and the development of techniques t o minimize the analytical error can be accomplished readily without resorting t o trial and error methodology. However, in many methods, the complexity of the chemical environment makes this task extremely difficult. Flameless atomization using a n electrothermally heated atomizer (EHA) for atomization followed by atomic absorption or fluorescence analysis presents a system which can be operated a t different levels of complexity, e.g., a simple vs. a complex sample matrix. This fact allows for a step-wise study of the system to be conducted in pursuit of a functional model which can be useful for predicting analyte behavior if the general matrix composition is known. Prior to atomization. solid-state reactions on the surface undoubtedly occur. An understanding of matrix effects resulting from solid-state reactions requires a knowledge of the chemical form of the analyte, and the thermal characteristics. viz., decomposition temperatures and/or vaporized form of analyte. Sturgeon et al. ( I ) have done an excellent job in 0003-2700/79/0351-1205$01.00/0
treating both the kinetic and thermodynamic aspects of the vaporization process. In their treatment of this process, consideration is given to both the solid-state reactions with the atomizer and the activation energy barrier which needs to be overcome before the onset of vaporization. A number of other papers have dealt with the time-dependent appearance of the atomic vapor and have presented mathematical expressions describing the time-dependent analytical absorbance profile ( 2 4 ) . In light of this work, it appears that the availability of thermodynamic constants and the complexity of the matrix should represent the only limitations in understanding these processes. Once the analyte and matrix components have been vaporized, the existence of gas phase interactions which affect the free atom population must be treated. Unlike the solid state reactions considered previously, the vapor constituents are quite mobile, and localized gas phase homogeneity can be assumed. The existence of local thermal equilibrium, i.e., translational, electronic, vibrational, and rotational equilibrium, is likely due to the relatively low heating rates available and the gas pressure 1 atm above the atomizer. However, the small value for the collision frequency resulting from the relatively low concentrations of analyte and interferent may be insufficient to ensure local chemical equilibrium. In this case. kinetic control of the processes responsible for the gas phase interference may override the equilibrium or thermodynamic considerations in predicting the extent of reactivity.
-
THEORY Equilibrium Model. The two generalized reactions to be considered in this paper are given as follows: M +AB
M
2
MA
+B
+ C + X F! M C + X
(1)
(2)
where M is the metal analyte. AB and C the interferent species, and X a third body, e.g., Ar, which makes reaction 2 mechanistically feasible. The appropriate equilibrium C 1979 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
constants are given by the ratio of their partial pressures, P.
In writing Equation 4 it is assumed that the partial pressure of the third body is invarient and approximately one atmosphere, i.e., the inert sheath gas. Kinetic Model. T h e rate expressions for reactions 1 and 2 are given by -a[M]/-at -a[M]/-at
= h,f[M] [AB]
h,f[M][C]
(5)
(6)
where the bracketed terms represent the concentrations of the respective species expressed in molecules/mL by convention, and klf and h2f represent the second-order rate constants for the respective forward reactions. Subsequent treatment of only reaction 1will be made since both Equations 5 and 6 are of the same general form. T o facilitate dealing with the rate expressions, a simplifying assumption that [AB] >> [MI will be made. This is justifiable since interference effects are most often apparent when an excess of some matrix component is present in the sample. With this assumption, the second-order rate constant can be reduced to the pseudo first-order rate constant approximation since negligible change in [AB] now can be assumed. h’lf = hlf[ABl
(7)
Substituting Equation 7 into Equation 5 results in the pseudo first-order rate expression - ~ [ M ] / a t = k’lf[M]
(8)
Integration of Equation 8 describes the time dependent free atom population when placed under kinetic restraints where [MI, and [Moltrepresent the free metal concentrations a t some time t with and without the presence of reactant AB, respectively. Using the relationship in Equation 9 with Equation 7 should result in an expression showing the time dependent depletion of M corrected for processes such as diffusion which are relatively independent of trace amounts of added AB.
Figure 1 shows the time variations as a function of the concentration of [AB] for different values of the second-order rate constant. In all instances, it is assumed that 99% of M has reacted and the equilibrium constant for the formation of MA is infinitely large, Le., the reverse rate constant k, for reaction 1 is zero. If formation of MA is thermodynamically favored over M by a t least 100:l but h, is not zero, the time required to react 99% of M will be longer than that shown in Figure 1 for any given value of kf. The dashed line represents the collision limited rate constant at 1600 Kelvin and assumes the hard sphere approximation (7) for a bimolecular reaction with collisional diameters of 3 X cm. To provide some intuitive feeling for abscissa values, lo-’ g of an interferent with a molecular weight of 50 g would result in a concentration of 5 x 1014 if it could fill a tube furnace with a 5-mm diameter and 15-mm length. However, it is likely t h a t the finite vaporization rates of the sample from the atomizer surface coupled with gas diffusion will result in significantly lower molecular densities than those calculated above. Additionally, finite values for the actual equilibrium constant and, thus, contributions from the reverse reaction will apparently increase the time required to reach predicted thermodynamic concentrations.
0 I
L
\ ‘\
IC“
013
10’2
~
l------LL2
-~
~~
10
[ A B ] :mo e c d l e s / m l ~
-
Figure 1. Time required to react 99% of M for the reaction M -I-AB MA B as a function of AB concentration for second-order rate constants of (a) (b) lo-’’, and (c) lo-’’ mL/molecule-s. The dashed line represents collision limited reaction rates at 1600 K. In
+
all cases, it is assumed that [AB] for the reaction is very large
> [MI and the equilibrium constant
Table I. Second-Order Rate Constants for MetaUOxygen Reactions at Elevated Temperatures k , mL molecule-’ temperature, 5.’ Kelvin ref.
react ion A1 + 0, Sn + 0, Ba + 0, Fe + 0,
- A10 +
-
-t
0 SnO - 0 BaO + 0 FeO + 0
-3 -2 -5 -4
X X X X
lo-”
lo-” lo-’’
300-1700 315 600 1600
8 9 10 11
There are only a small number of literature values giving rate constants for high temperature, gas phase, metal reactions (8-11). Real values for metal-oxygen reactions are cited in Table I. As can be seen, they range from lo-” to approximately mL/molecule-s. In the case of the slower reactions, Le., k = mL/molecule-s. Figure 1 shows t h a t several hundred milliseconds could elapse before equilibrium concentrations could be assumed. This time period may be lengthened additionally because of gas phase diffusion, which would further reduce the molecular densities and, consequently, the rates of reaction. It is thus conceivable that many potential interferent reactions may in fact be limited by the reaction kinetics involved. Verification of the role of gas phase kinetics was undertaken using gas phase metal/oxygen reactions above a carbon filament atomizer with Sn, Ga. Fe, and Cu as the analyte species.
EXPERIMENTAL A West-type filament atomizer (12) was used in all studies.
Operation and data collection was undertaken in two distinct modes: steady state ( 2 3 ) and the more conventional transient or pulsed heating mode. Analyte selection was based, in part, on their relative inertness toward graphite as well as on their thermodynamic and kinetic characteristics. When operating in the steady-state mode, milligram amounts of the metal were placed in a sample well in the rod and held at a constant temperature using the power supply temperature control circuitry capable of maintaining the temperature using a photodiode feedback circuit. Since multiple 30-s heating times were typically used, species such as A1 which readily react with the graphite were precluded from the study. While Fe forms a carbide, it did not appear to affect the general Fe vapor pressure predicted assuming no carbide formation. Additionally, no severe degradation of the graphite rod was noted when using Fe, and the absorbance signal with the
ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
1207
I -
Table 11. Experimental Conditions for Steady-State F e Studies atomizer temperature vapor pressure of F e at 1600 K O partial pressure of 0, molecular densities at 1600 K: Fe 0
h
0.56 Torr
2
linear gas velocity above atomizer
6.0 x lo'* m L - ' 3 . 4 x 10'' m L - ' 54 cm/s
\
a
'\ \ '
Ref. 18.
__
r
L
0 -2
L.--L-TI!e%A c a5 IO
15 d i s t a n c e inlrn)
time ( m s e c ) 7-
3
7
1
t\
\\.
3
1600 K 0.0010 Torr
23
rl
Figure 2. Absorbance-height profiles for steady state Fc studies (a) without added 0,and (b) witn 0.56 Torr O2 added to Ar sheath gas
rod heated to 1600 K was stable for several hours. This is in contrast to steady-state measurements made using .41 which Lisibly reacted with the atomizer and displayed short and long term variations in the absorbance signal magnitude. Other metals, such ag Pb, were not used since they exhibited an appreciable vapor pressure below a temperature at which the heating circuit was capable of maintaining accurate temperature control. Transient studies were conducted using the spatial isolation wheel to obtain time and spatial absorbance data from a single shot t 14). Data from 5 shots were averaged to obtain a representative data set for each experimental condition investigated. For the transient studies Sn, Fe, and Ga metals were dissolved as the reagent grade nitrate salt in triply distilled water. Cu was introduced as the sulfate since Cu(NO3I2may sublimate at relatively low temperatures and would introduce an unwanted variable in these studies (25). The solutions used were 2.0, 5.6, 1.0, and 0.5 ppm in Sn, Ga, Fe. and Cu, respectively. A 2-pL sample was used in all studies. An Ar sheath gas flowing at 1.3 L/min was introduced below the atomizer and produced a linear gas velocity of 10 cm/s exiting the laminu flow gas box located below the carton filament. The addition of O2 was accomplished by introducing the appropriate amount of a 1% O2 in Ar mixture into pure Ar while maintaining a total gas flow of 1.3 L;rnin.
RESULTS AND DISCUSSION Steady-State Studies. T o demonstrate that kinetics do play a role in the gas phase reactions, two metals, Fe and Sn, for which published rate data are available, were placed on the modified carbon filament atomizer ( 1 9 ) and heated to a temperature that produced an absorbance signal of a few tenths of a n absorbance unit within 0.25 mrn ~f the rod surface. Absorbance measurements were then made a t 0.25-mm increments above the surface using the optical system previously described (IL?). Absorbance--height measurements were made using a sheath gas of pure Ar and Ar plcs oxygen. In all cases where O2was added, a partial pressure of 0.66 Torr of O 2 in Ar (0.073%)was used. T h e possibility of the O2 reacting with the atomizer was explored by heating the rod t o 1600 K with a N2 sheath gas containing 02.A syringe was used to extract gas samples immediately above the atomizer surface and subsequent analysis for O2 conducted using the gas chromatographic method described previously ( 1 6 ) . N, was used in place of Ar since the analytical method used could not adequately separate Ar and 02.Gas mixtures containing 0.7%, 1.5%',and 2.2% O2 were used. Each O2 concentration showed on!y a 20 k 2% decrease in the O 2 partial pressure as a result of any reaction with the hot atomizer. The absorbancedistance profiles for Fe are shown in Figure 2. T h e decrease in absorbance in curve a for the Fe signal without added O2 is expected and likeiy results from a number
t
\
d stonce I m m )
Figure 3. Logarithmic plot of data from Figure 2. See text for ex-
planation. Second-order rate constant of 2.8
X
mL/molecule-s
derived from data
of processes including diffusion, reactions with oxidants entrained in the system, and possibly, nucleation. It is expected that the addition of the small amount of O p t o the sheath gas will have a negligible effect on the rates of diffusion and other kinetic processes, e.g., metal/entrained-oxidant reactions, and can be corrected for by normalizing the data comprising the O2studies in curve b by the corresponding data points in curve a. 'Thermodynamic or equilibrium control of the reaction would predict a n absorbance signal more than three orders of magnitude smaller than that observed. This is predicted on the assumption of FeO(,, being the most stable and only form of iron oxide above the atomizer. Inclusion of other stable forms in these calculations, e.g., Fe20,, forces the expected free atomic F e t o even lower values. In considering kinetic treatment of the data, the distance axis also can be translated into time increments. Direct thermal velocities of t,he metal leaving the atomizer are expected to rapidly approach sheath gas velocities because of the large collision number in the instance of a local pressure of 1 atm, Thus, conversion from distance to time domain is accomplished by assuming local pressure of 1 atm a t all spatial regions and correcting for the expected gas velocity increase due to thermal expansion from the atomizer which is held a t 1600 K. With these assumptions, a corrected, linear gas velocity above the atomizer of 54 c m / s is arrived a t for the steady-state studies. Table I1 summarizes the calculated operating conditions for the Fe studies. It can be seen that the conditions needed t o use pseudo first-order kinetic treatment of the data are present, Le., [O,] > [Fe]. Using the relationship presented in Equation 9, one would expect a linear relationship by plotting In [M],/[Moltas a function of time. Absorbance values were used for these respective m ~ a s u r e ments of [MI,; and [Mol: (see, e.g., Ref. 11). A representative plot of these data is shown in Figure 3 and an average value of of 760 s-l obtained. It should be noted that these data were measured over a distance of only 1.75 mm above the atomizer surface. Independent temperature measurements using the two-line absorbance method for Ga ( I 7) showed a temperature drop of less than 200 K over this region. A kIlf
1208 ~~
ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979 ~
Table 111. Second-Order Rate Constants (mL/molecule-s) metal
cu Fe Ga
transient peak area peak height 1 . 2 x 10-14 4.5 X 7.7 X
1.6x 4.2 X 7.2 X
10-14
steady state 5.0 x 1 0 - 1 ~
2.8 4.5
X X
:I
10.”
‘T;
second-order rate constant for the Fe/Oz reaction of 2.8 f U.6 x mL/molecule-s was obtained using the O2 density corrected for 20% reduction due to reaction with the graphite. This is in good agreement with Fontijn’s value of 4 X 10 mL/molecule-s ( 1 1 ) . Thus, it appears that reaction kinetics rather than equilibrium or thermodynamic control may govern the extent of reaction between Fe and O2 in the spatial zone studied. From inspection of Table I. it can be seen that the literature value for the rate constant of the S n / 0 2 reaction is a t 350 K. Consideration of this reaction at approximately 1600 K would result in a rate constant comparable or larger in magnitude to t h a t given for 350 K. Thus, Sn combustion with O2 represents a reaction which is at least 100 times faster than the Fe/O reaction. As a result of the rapid kinetics coupled with the thermodynamic favorability for forming the oxide, a free atomic Sn signal was observed only a t the first observation zone with O2 added to the sheath gas. The absorbance in this region was reduced from 0.660 to 0.028 absorbance unit by the addition of 02.Using the rate constant given in Table I and the flow and temperature parameters given in Table 11, Equation 10 would predict attainment of 99% of equilibrium concentrations within 0.085 ms or only 0.046 mm above the atomizer and is consistent with the observed absorbance profiles. Cu and Ga were used for qualitative comparisons. The absorbance-distance profiles for the steady-state experiments with and without added O2and subsequent kinetic treatment of these data predict second-order rate constants of apmL/molecule-s for Ga proximately 4.5 x lo-’’ and 0.5 x and Cu, respectively. While thermodynamic data are not available for GaO, the metal oxide bond strength of CuO is more than 50% greater than that of GaO. Thus, in this instance, the observed relative reactivity of these species with O2 is completely contradicted by anv projections made by metal-oxide bond strengths, a representative measure of relative equilibrium or thermodynamic values for the formation of the respective oxides ( 1 3 ) . In brief, predictions of extent of reactivity with O Lbased on bond strength would predict the order Sn > Fe > Cu > Ga where experimental evidence shows the order Sn > Ga > Fe >> Cu. Transient Studies. Extensions of these studies to the transient or pulsed operation of the atomizer using 2 FL of sample exhibited the same general relative reactivities toward 02. lJsing the spatial isolation wheel and the computer software developed for data reduction, both peak absorbance and time integrated absorbance data a t each height up to 9 mm are available. An attempt was made to extract rate constants from the transient data using a procedure similar to that described for the steady-state experiments. The results are presented in Table 111. All calculated rate constants were lower than those obtained from the steady-state experiments, with Fe and Ga deviating to a greater degree than Cu. The exact cause of this deviation is not known at this time. Sn again disappeared too rapidly to obtain data for more than one observation zone. Plots used to obtain the rate constants for Ga and C u were linear over the distance observed. The log absorbance plot for Fe used in calculating the rate constant from the transient is shown in Figure 4. Each point represents an average of
-3 8 -IO
i 0 1
2
3
4
d starce
Figure 4.
Logarithmic plot of F e
data
1
1
5
6
(mm)
f r o m transient experiments
5 shots using the spatial isolation wheel data collection. The rate constant shown in Table I11 was derived using the first three observation zones. Figure 4 suggests negligible net change in relative amounts of Fe a t distances greater than 3 mm. The general shape of the curve in Figure 4 is similar to that expected for a reactant/product system reaching equilibrium within the observation time. In considering only the formation and dissociation of FeO(,, as being mechanistically favorable under the low partial pressures in this system, equilibrium calculations predict Fe/FeO partial pressure ratios to range from 0.18 to 1.5 between 1800 and 2200 K, respectively. These temperatures have been chosen to suggest the feasibility of such a postulate. While the gas temperatures above the atomizer are inhomogeneous. the atomizer is pulsed to approximately 2500 K, and gas phase temperatures in the range of those quoted above during the residense time of the Fe within the observation zone are possible ( 1 9 ) . I t should be recalled t h a t the steady-state Fe studies in Figure 2 showed linear behavior until no measurable Fe absorbance could be detected. This apparent discrepancy results from the mode of heating used in the two studies. As was noted above, pulsed heating in the transient operation could generate gas kinetic temperatures in excess of 1800 K. Conversely, the steady-state experiments precluded gas temperatures in excess of 1600 K, Le., the rod temperature. The equilibrium [Fe]/[FeO] partial pressure ratio for operations with O2 is 0.0006 a t this temperature. Thus, from a practical viewpoint, the conversion of Fe to E’eO should be nearly quantitative in the steady-state studies a t 1600 K or lower, once equilibrium is reached. It should be noted that CuO is considerably more stable at these temperatures and showed no deviation from a linear curve over a height of 8 mm. Thermodynamic data for GaO(,, is not available and cannot be used for exacting comparisons.
CONCLUSIONS I t is suggested that previous neglect of the potentially important role that reaction kinetics play in determining the extent of gas phase interferent reactions has hampered the establishment of a fundamental explanation to account for many of the observed “matrix” or “interference” effects. It is interesting to note that some of the earliest analytical results observed by several researchers may be explained from this view. For example, Alger and co-workers (20) noted that the extent of the analytical signal depression caused by an added interferent was less when smaller sample volumes were introduced onto the atomizer. Considering reactions 1 and 2 as representative of the two most likely gas phase reaction mechanisms responsible for depleting the free atom population, then only the equilibrium expression K 2 would predict an enhanced, relative free atom density by reducing the sample size. For reaction 1, a proportionate reduction in the partial pressures of metal and interferent should not alter the fraction converted to the molecular species. West et al. (21,22) have also shown t h a t
A N A L Y T I C A L CHEMISTRY, VOL. 51, NO. 8, JULY 1979
matrix effects could also be minimized by "limited viewing". Le., observing the zone immediately above the surface of a filament-type atomizer. Here again, for reaction 1 and K l , thermodynamics would predict minimal change in the relative amount of free metal with respect to the system which does not employ limited viewing. since the ratio of the partial pressures should be nearly constant a t all heights, assuming that the diffusion rates of metal and interferent are not significantly different. Using reaction 2 and the respective expression for K 2 ,the expected increase in the partial pressure of M and C immediately off the rod would suggest a decreuse in the relative concentration of M. Conversely kinetic control of these processes would qualitatively account for the observed reduction in the interference effects in ail cases cited above. For facile reactions, atomizer designs which permit long residence times or samples with relatively high concentrations of interferents, thermodynamic data and the assumption of equilibrium control should be useful in predicting the extent of gas phase interactions. For example, this has been used successfully in explaining several cases where a signal entzuncement w a observed as a result of adding an "interferent" to the sample ( 1 3 ) . On the other hand, it may be necessary to employ gas phase kinetics in order to completely understand reactions which are slow andior are being observed a t low concentrations.
LITERATURE CITED ( 1 ) R. E. Sturgeon, C. L. Chakrabarti. and C. H. Langford, Anal. Chem., 48, 1792 (1976).
1209
S. L. Paveri-Fontana. G. Torsi, and G. Tessari, Anal. Chem., 46, 1032 ( 19 74). G. Torsi and G. Tessari, Anal. Chem., 47, 839 (1975). G. Torsi and G. Tessari, Anal. Chem., 47, 842 (1975). D. J. Johnson, B. L. Sharp, and T. S.West, Anal. C > k m .47, , 1235 (1975). G. Torsi and G. Tessari, Anal. Chem., 48, 1318 (1976). W. C. Gardiner, Jr.. "Rates and Mechanisms of Chemical Reactions", W. A. Benjamin, New t'ork, 1969. A. Fontign, W. Felder, and J. Houghton, "XIV Symposium (International) on Combustion", Pittsburgh, Pa., 1975, p 775. W. Felder and A. Fontijn, J . Chem. Phys. W. Felder, R. Gould, and A. Fontijn, J . Chem. Phys., 685 (1977). A. Fontijn, S. Kurzius, and S.Houghton, "XV Symposium (International) on Combustion", Pittsburgh, Pa., 1973, p 167. J. F. Alder and T. S. West, Anal. Chim. Acta. 51, 365 (1970). R. H. Eklund and J. A. Holcombe, Anal. Chim. Acta, in press. S. G. Salmon and J. A. Holcombe, Anal. Chem.. 51, 648 (1970). K. H. Stern, J . Phys. Chem. Ref. Data, 1, 747 (1972). G. S. Vizard and A. Wynne, Chem. lnd. 196 (Feb. 7, 1959). M. P. Bratzel, Jr., and C. L. Chakrabarti. Anal. Chim. Acta, 63,1 (1973). R. E. Honig and D. A. Kramer, "Vapor Pressure Curves of the Elements", Radio Corp. of America, Princeton, N.J.. 1969. R . E. Sturgeon and C. L. Chakrabarti, Specfrochim. Acta, Part B , 32, 231 (1977). D. Alger, R. Anderson, I . Maines, and T. West, Anal. Chim. A c t a 57, 271 (1971). J. Aggett and T. West, Anal. Chim. Acta. 55, 349 (1971). R. Anderson. H. Johnson, andT. West, Anal. Chim. Acta, 57, 281 (1971).
RECEILXII for review August 14, 1978. Accepted April 2 , 1979. This material is based upon the work supported by the National Science Foundation under Grant No. CHE78-15438. One of us (J.E.S.)wcluld like to express our appreciation to the National Science Foundation for financial assistance through the NSF-URP program
Theoretical Assessment of Accuracy in Dual Wavelength Spectrophotometric Measurement K. L. Ratzlaff" Department of Chemistry, Northern Illinois University, DeKalb, Illinois 60 1 15
D. F. S. Natusch" Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523
Equations are presented describing the contributions of absorbing and scattering interferents, cell errors, stray light, optical bandpass, multiple scattering, and multiple internal reflections to the accuracy of dual wavelength spectrophotometric (DWS) measurement. It is established that cell errors are substantially reduced in DWS measurement with respect to single wavelength spectrophotometric measurement (SWS)? but the other sources of error may be significant. A scattering interferent produces error that cannot be reduced instrumentally. Otherwise, error may be diminished by employing secondary wavelength isolation, narrow slit widths, and an intense source.
Modern ratiometric spectrophotometry, as performed using instruments commonly referred to as "double beam spectrometers" may be carried out utilizing two distinct modes of operation. T h e mcire common of these is emplo:,-ed in conventional Single Wa\ elength Spectrophotometry (SWS) in which the log ratio of light intensities passing through 0003-2700/79/035 1-1209$01.OO/O
separate sample and referenw cells is determined and presented in terms of the analyte absorbance a t a single wavelength. A fundamentally different principle is. however, employed in Dual b'avelength Spectrometry (DLVS) in which two beams of different wavelengths pass through a siiigle sample cell. In this case. the difference between the sample absorbances a t the two wavelengths is recorded. The main operational advantage of DM S is its ability to distinguish the absorbance of an analyte in the presence of severe spectral interferences such as are produced by additional absorbing or scattering species in the sample. In such circumstances, which are frequently encountered in samples of biological origin, the use of SLVS is prohibited so that quantitative analyses can be performed only in the DWS mode. It is appropriate. therefore, to establish the precision and accuracy associated with D\VS measurement. Previous studies ( 1 ) have shown that under certain conditions the precision of ULVS meascirernent may be superior to that of SLVS measurement m e n in the absence of interferents. Acceptable precision can also be achieved over a limited absorbance range (0.1 t o 2.5) when interterents 1979 American Chemical Society
