RESULTS AND DISCUSSION When fluoride ion is added in excess to aluminum in slightly acidic solutions, p H 4 to 5 , t h e formation of the series of fluoro complexes reduces the free A13+ concentration and, hence, prevents precipitation of aluminum hydroxides and also reduces the extent of formation of polymeric hyFT droxo complexes. For example, for A ~ Tand precipitation does not occur below p H 6 and the polymeric species, e.g., Als(OH):,f form at most 1%of t h e total alumin u m Concentration. Consequently, under t h e conditions of our method, all aluminum complexes are thought to be monomeric. This means that, for a fixed activity of F-, t h e ratio of F bound t o aluminum is independent of the total concentration of Al. This is confirmed by the results in Figure 2. If the amount of fluoride bound to aluminum, as calculated from t h e difference in volume a t constant emf between the aluminum standards and the blank solution, is plotted vs. aluminum concentration over the range -20 mV t o +20 mV, linear lines are obtained. T h e slope of these lines is the ratio of F- bound per Al. At -15 mV F-/Al N 2.6 and a t +10 mV F-/Al N 3.0. T h e constancy of the F- bound per A1 is demonstrated by the calibration results in Table 11. From the slope of the A V vs. A1 concentration plot, the bound F- per A1 = 3.0. Several ions commonly present in mill waters, such as Ca2+, Fe", and Mg2+, form complexes or insoluble solids with fluoride and may therefore be a source of interference with this ion selective electrode method. Consequently, samples containing varying amounts of aluminum were prepared with these interfering ions in excess of concentrations frequently found in practice. Sulfate ions were also included because of possible complexation with A1 according t o Table I. T h e results of these tests as given in Table
I11 indicate t h a t calcium is the only ion which does cause interference; however, its effect is small provided t h e concentration of Ca is below 200 mg/l. T h e accuracy of the determination is excellent and t h e relative standard deviation as determined on repeated (7) titrations of samples containing 10 mgh. aluminum was 1.1%. LITERATURE CITED (1) R . M. K. Cobb and D. V. Lowe, TAPPI, 38, 49 (1955). (2) A. W. McKenzie, V. Balodis, and A. Milgrom, Appita, 23,40 (1969). (3) J. D. Hem et al., "Chemistry of Aluminum in Natural Water", U.S. Geological Survey Papers 1827-A (1967), -B (1968), -C (1969), -D (1972), -E (1973). U S Govt. Printing Office, Washington, D.C. 20402. (4) P. L. Hayden and A. J. Rubin, in "Aqueous-Environmental Chemistry of Metals", A. J. Rubin, Ed., Ann Arbor Science, Ann Arbor, Mich., Chap. 9. (5)J. P. Casey, "Pulp and Paper", Vol. 11, Interscience, New York, 1960, p 1056. (6) K. E. Shull and G. R . Guthan, J. Am. Water Works Assoc., 59, 1456 (1967). (7) R. C. Turner Can. J. Chern., 47, 2521-2527 (1969). (8) S. H. Watkins, TAPPI, 45, 216A (1962). (9) R. E. Mesrner and C. F. Baes inorg. Chern., I O , 2290 (1971). (IO) R . E. Mesrner and C. F. Baes, "Hydrolytic Behavior of Toxic Metals", Atomic Energy Commission Oak Ridge, Tenn.. ORNL-DWG 731441 (1974). (11) L. G. Sillen and A. E. Martell, "Stability Constants", Chemical Society, London, Special Publication No. 17 (1964) and No. 25. (12) E. W. Baumann, Anal. Chern., 42, 110 (1970). (13) D. D. Perrin and I. G. Sayce, Taianta, 14, 833 (1967). (14) R. 0. James and E. Bate, unpublished results. (15) C. Brosset and J. Orring, Sven. Kern. Tidskr., 55, 101 (1943). (16) D. D. Perrin and B. Dempsey. "Buffers for pH and Metal Control", Chapman & Hall, London, 1974.
RECEIVEDfor review September 16, 1975. Accepted December 16, 1975. R.O.J. wishes to thank the Australian Government for a n ARGC Research Fellowship, and A.H. thanks Australian Paper Manufacturers P t y L t d for a Postdoctoral Fellowship.
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CORRESPONDENCE
Refractive Index Anomalies in Stopped-Flow Measurements Sir: T h e purpose of this communication is to alert users of certain designs of stopped-flow instruments to a potential source of error in measurements made a t temperatures other than ambient. Chattopadhyay and Coetzee ( I ) have warned of a n error arising from measurements on solutions originating in the Kel-F valve block of a Durrum Model D-110 stopped-flow spectrophotometer. T h e poor thermal contact between such solutions and t h e thermostating bath gives rise to systematic errors in the temperature a t which measurements are made. Therefore, it has been recommended ( I ) that a minimum volume of 0.34 ml be dispensed from each drive syringe in each mixing experiment. We have encountered a different source of error on using this instrument a t temperatures other than ambient with 0.375 ml dispensed per drive syringe. In the course of kinetic studies in 1,2-dichloroethane (DCE) solvent a t temperatures above ambient, an apparent formation and disappearance of a strongly absorbing intermediate species was observed. Further studies revealed t h a t this phenomenon was an artifact which appeared a t 778
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ANALYTICAL CHEMISTRY, VOL. 48, NO. 4, APRIL 1976
any visible wavelength on mixing DCE with DCE. A similar effect had been noted previously by Imamura ( 2 )in dichloromethane solvent. Stynes and James (3) have also mentioned an anomaly observed in toluene solvent. T h e upper curve in Figure 1 shows the absorbance vs. time trace observed a t 621 nm on mixing DCE with DCE a t 35 "C using the Durrum stopped-flow spectrophotometer equipped with Kel-F stopped-flow cell. T h e lower curve in Figure 1 shows the trace obtained without mixing both before and 1 min after the mixing experiment. Several further characteristics of this phenomenon were noted. A very similar phenomenon was observed on mixing DCE with DCE a t 45°C using the Kel-F dual-purpose stopped-flow temperature-jump cell. No change in absorbance was observed on mixing DCE with DCE a t 45 "C using the stainless steel cell, however. T h e magnitude of the maximum absorbance change during this phenomenon was found to be roughly in direct proportion to the difference between the thermostat temperature and the ambient temperature. T h e phenomenon was found to invert, giving apparent negative absorb-
L
,
'CGSy,
-
,
C
Figure 1. Absorbance anomaly in DCE due to refractive index gradient
ances, for thermostat temperatures below ambient. These observations led to t h e hypothesis t h a t this spurious phenomenon is due t o a radial gradient of t h e index of refraction of the solvent in t h e cylindrical spectrophotometric light path. This index gradient phenomenon may be explained as follows. Suppose t h a t t h e freshly-mixed solvent at some temperature T1 above ambient has just stopped in t h e cylindrical spectrophotometric light path. T h e direction of t h e light path is along t h e axis of a cylinder 20 m m long with a diameter of 2 mm. Suppose further t h a t the walls of this cylinder are a t a temperature T2 < TI. T h e index of refraction of all t h e solvent in t h e light path is n l , the refractive index at 2'1. T h e collimated light proceeds through the cell and zero absorbance is recorded at time zero. Now heat begins t o flow from t h e solvent into t h e walls of the cylindrical enclosure. At some time (-1 s) after mixing the refractive index of the solvent along the axis of t h e cell is n l , but t h e refractive index of t h e solvent along t h e walls of the cell is nearly n2, t h e refractive index at T2. T h u s a radial gradient of refractive index has been established in t h e cell, with n2 > nl This arrangement acts as a diverging lens. Light is bent away from t h e cylindrical axis causing observation of a n apparent absorbance. After several minutes, t h e solvent is all a t Ta and, therefore, t h e refractive index is uniformly n2 and zero absorbance is again observed. If the solvent had initially been colder than the cell walls, a converging lens would have resulted after establishment of the maximum index gradient. I t is interesting t o note t h a t the change of refractive index per "C is -1.3 X lop4 for water, -5.0 X for acetone, and -5.1 X for DCE. T h e maximum amplitudes of t h e anomalous absorbance effects for these solvents were 1, 5, and 6, respectively. A test of the assumption t h a t the cell wall temperature is closer t o ambient than is t h a t of the incoming solution was made using a freshly made solution of 0.1 M KN03, 0.2 M glycine, and 2 X M phenolphthalein adjusted to p H 9.4 with carbonate-free NaOH. T h e absorbance of this solution was determined with a Cary 14R spectrophotometer at four temperatures between 39 and 47 "C and varied linearly with temperature according to t h e empirical equation A = 1.348 - 0.0172 T where A is absorbance for a 2-cm path length and T is t h e solution temperature in "C. Such solutions are used to determine t h e response times of temperature-jump spectrom-
7
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Figure 2. Absorbance change due t o temperature variation of phenolphthalein-glycine solution
eters ( 4 ) and are known to respond within less than 1 ws. T h e upper curve in Figure 2 shows t h e absorbance vs. time trace observed on mixing this solution with itself using t h e Kel-F stopped-flow cell with a thermostat temperature of 45.0 "C. T h e incoming solution was observed t o fall from 45.0 to 40.4 "C after about 15 min. T h e lower curve in Figure 2 shows t h e trace obtained without mixing both before and 15 min after the mixing experiment. No such change in temperature was observed using t h e stainless steel cell. T h e design error in t h e Kel-F cell is t h a t t h e circulating thermostat fluid (flowing a t 13 ml/s in our instrument) surrounds t h e drive syringes but only passes through a bathtub-shaped cavity t o one side of the optical path in t h e Kel-F cell. This design is apparently sufficient for highlyconductive steel, but inadequate for poorly-conductive Kel-F. T h e potential user of such Kel-F cells is therefore warned that significant systematic temperature errors can result from high temperature studies of aqueous-phase reactions with half-times of 500 ms or longer. Anomalous absorbances may also be observed on a much shorter time scale for aqueous systems whose absorbance change is small. Serious disturbances in absorbance are likely on any time scale if the medium has a high change of refractive index with temperature, as is t h e case for almost all organic solvents (5').
LITERATURE CITED (1)
(2) (3) (4) (5)
P.K. Chattopadhyay and J. F. Coetzee, Anal. Chem., 44, 21 17 (1972). T. Imamura, University of Iowa, private communication, 1972. D. V. Stynes and B. R. James, J. Am. Chem. Soc., 96, 2733 (1974). K. Kustin, Brandeis University, private communication, 1966. J. A . Riddick and W. B. Bunger, "Techniques of Chemistry", A. Weissberger, Ed., Vol. 11, "Organic Solvents," 3rd ed., John Wiley and Sons, New York, N.Y.. 1970.
Mark L. Miller Department of Chemistry University of Iowa Iowa City, Iowa 20042
Gilbert Gordon* Department of Chemistry Miami University Oxford. Ohio 45056 RECEIVED for review October 16, 1975. Accepted January 15, 1976.
Theoretical Comparison of the Signal-to-Noise Ratios of Fourier Transform Spectrometry with Single Slit Linear and Slewed Scan Spectrometric Methods for the Photon Noise Limited Situation Sir: Analytical spectrometry frequently requires the measurement of low intensity spectral components. When these measurements are a part of a quantitative analytical
procedure, it is usually desirable to achieve the greatest signal-to-noise ratio (S/N) possible in order t o maximize the precision of measurement and to realize the best limit of ANALYTICAL CHEMISTRY, VOL. 48, NO. 4 , APRIL 1976
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