Anal. Chem. 1981, 53,2349-2350
2,2’-I)iphenic acid is considerably more soluble in aqueous base than 4-biphenylauboxylic acid, apparently because there is a carboxylic group on each aromatic ring. Its decreased hydrophobicity is refllected in its ready elution during the pH gradient. The first and second pK, values of 2,2‘-diphenic acid are 3.53 and 5.42, respectively (9). Since diphenic acid eluted at a lower pH than benzoic acid, pK, = 4.20, ionization of a single carboxylic group was sufficient to desorb the former from the resin. Salting out was observed for 1-naphthoic acid, 9-anthranoic acid, and 1-naphthol. These were the more strongly retained compounds. Also, salting out was greater for 9-anthranoic acid than for 1-naphthoic acid. Similar phenomena were observed by Pietrzyk and Chu (6) for other organic acids eluted by reversed-phase chromlatography on XAD resins. It is believed to result from ion pairing, which causes the solute to interact with the resin in a flatwise orientation. The resulting increase in retention should be greater for the more hydrophobic acids. All of these results are relevant to fractionations of humic acids using either stepwise or continuous pH gradients. Since humic acids encompass a wide molecular weight range and contain multiple aromatic rings in a molecule, the hydrophobicity of a given species is an important parameter in the
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fractionations of these mixtures by pH gradient elution.
LITERATURE CITED (1) Curtis, M. A.; Witt, A. F.; Schram, S. B.; Rogers, L. 9, Anal. Chem. mi. 53. i i ~ 5 - 1 1 9 9 . (2) Pideaux. ‘E. 9.k. Proc. R. Soc.London, Ser. A 1916, 92, 463-468. (3) Schnitzer, M.; Desjardins, J. G. Soil. Sci. SOC. Am. Proc. 1962, 26, 362-365. (4) Pietrzyk, D. J.; Chu, C. H. Anal. Chem. 1977, 49, 860-866. (5) Sargent, R.; Rieman, W. J. Org. Chem. 1956, 27, 594-594. (6) Pietrzyk, D. J.; Chu, C. H. Anal. Chem. 1977, 49. 757-764. (7) Kortum, G.; Vogei, W.; Andrussow, K. “Dissociation Constants of Organic Acids in Aqueous Soiutlon”; Butterworths: London, 1961; Chapter 4. (8) Horvath, C.; Melander, W.; Molnar, I. J. Chromatogr. 1976, 125, 129-156. (9) Kolthoff, I. M.; Chantooni, M. K. J. Am. Chem. SOC. 1976, 98, 7465-7470.
Michael A, Curtis L. B. Rogers* Department of Chemistry University of Georgia Athens, Georgia 30602
RECEIVED for review July 31,1981. Accepted September 16, 1981. Supported in part by National Science Foundation Grant No. CHE 78-13269.
Correlation Coefficients for Evaluation of Analytical Calibration Curves Sir: Recently, the literature of analytical chemistry has seen a very desirable increase in the use of various statistical procedures for planning experiments and for data analysis. One area where statistical techniques can be used to great advantage is in the correct establishment of analytical Calibration curves. It is a simple matter to put response signals and analyte standard concentrations into a computer which provides a linear (or higher order) least-squares fit to the data. Analyte signals for uinknowns are then readily converted to concentrations according to the fitted equation. Unfortunately, full benefit is often not extracted from such a least-squares analysis. Ideally, variance ratios should be calculated to test “lack of fit” as successive constants are added to the equation. Some replication of measurements is required to perform this test. Where appropriate, the intercept should be tested to see if a model through the origin is justified; Le., it should not be assumed. Procedures for performing these tests are fully described by Box et al. (I) and elsewhere. One practice which should be discouraged is the use of the correlation coefficient (r) as a means off evaluating goodness of fit of linear models. Although r, which can have values from +1.00 to -1.00, does provide a measure of the adequacy of fit of a linear model, analybical calibration c w e s often give values very close to 1.00 when there is a significant departure of the experimental points from linearity. It is generally considered that 100r2 provides an estimate of the percentage of total variation in a set of points that is explained by fitting a linear least-squares equation. Thus, an r value of 0.980 indicates that 96.0% of the variation is explained by the model. It must be remembered, however, that the 4.0% of unexplained variation may be concentrated in one portion of the curve. It is an instructive exercise to produce a calibration data set with slight curvature in the low concentration region and to see how large relative error can remain after fitting a linear least-squares equation where r is approximately 0.980. To illustrate the lack of sensitivity of r as a diagnostic tool, we have analyzed the calibration data recently published by
Schubert et al. (2). In their Figure 2, log emission intensity for sulfide is plotted vs. log of the weight of sulfide. Two sets of data are plotted: one based on CuS as the source of sulfide and one based on PbS. The authors conclude on the basis of inspection that the scatter in the points warrants combining the two data sets. A least-squares analysis of the pooled data yields a straight line with an r value of 0.91. The authors feel that this “tends to support the premise that these data are similar”. This is an important conclusion because it indicates that the determination of sulfide by time-resolved molecular emission spectrometry is free of matrix effects associated with the cationic species combined with sulfide. Since the r value of 0.91 for the pooled data does not provide strong support for this conclusion, we decided to examine these data further. A fine grid was placed over their Figure 2 in order to extract estimates of the original numerical values. While this procedure introduces some error, the estimates thus obtained are apparently reasonable because the r value calculated from them is 0.90, in good agreement with the published value. Linear least-squares models fitted to each data set yield the following equations: For CuS log I = 0.89 log C 8.99 ( 1)
+
For PbS
+
log I = 0.48 log C 6.76 (2) where Z is the intensity of emission and C is the weight of sulfide, in grams. Standard deviations of the residuals are 0.139 and 0.142 for eq 1and 2, respectively. The calculated ‘‘t” statistic for comparison of the two experimental slopes is 4.57, which is greater than the tabular value of 3.64 for a two-tailed a risk of 0.001. Stated another way, a hypothesis of no difference in the slopes is unacceptable at the 99.9% confidence level. The clarity of this result is in stark contrast to the inconclusive information provided by correlation coefficients (0.88 for the PbS data set, 0.97 for the CuS set,
0003-2700/81/0353-2349$01,25/0 0 1981 American Chemlcal Society
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Anal. Chem. 1981, 53,2350-2351
and 0.90 for the composite set). Further evidence to support the conclusion that matrix effects may cause sulfides to produce different response functions can be found in Figure 3 of the Schubert et al. paper. The calibration plots in this figure are based on seven standards of a four-component mixture containing S2-/SoJ S O ~ ' / S O ~ - .No statistical analyses are reported for these plots. However, when we extracted sulfide data as before, the linear least-squares equation provided a slope estimate of -0.13! A confidence interval calculation indicates that this slope does not differ from 0.0. Thus, in contrast to the impression given in Figure 3, no significant functional relationship has been demonstrated for this set of sulfide data. In conclusion, thorough statistical analysis of analytical calibration data should be used to provide optimal evaluation of results. The correlation coefficient is not an effective statistic for this purpose.
LITERATURE CITED (1) Box, G. E. P.; Hunter, W. G.; Hunter, J. S. "Statistics for Experimenters";Wiiey: New York, 1978; Chapter 14. (2) Schubett, S. A.; Clayton, J. W., Jr.; Fernando, Q. Anal. Chern. W80, 52, 963-967.
Mark D. VanArendonk* Rodney K. Skogerboe Deparment of Chemistry Colorado State University Fort Collins, Colorado 80523
Clarence L. Grant Department of Chemistry Parsons Hall University of New Hampshire Durham, New Hampshire 03824 RECEIVED for review June 29,1981. Accepted August 27,1981.
Determination of Diffusion Coefficients of Anions at a Rotating Silver Disk Electrode Sir: A preliminary screening of a number of inorganic ions has been carried out employing a rotating silver disk electrode (AgRDE). While the primary goal of this research was to investigate the utilization of this electrode for cathodic stripping voltammetry, it proved convenient to determine a number of diffusion coefficients of anions which depolarize silver. In the case of anions which depolarize silver, we have found, as previously reported for sulfide ( I ) , adherence to the Levich equation = (6.20 x 10-4)nA~~ov-1/6w1/202/3 (1) even though the anion reaction a t the electrode gives rise to a solid film on the electrode. In eq 1,co is the concentration of the anion (mol dm-3) and n is the number of electrons transferred in the oxidation process per anion reacting at the electrode surface. The other symbols have their usual meaning. Rearrangement of eq 1 obviously permits determination of the diffusion coefficient, D. We have investigated the behavior of ,sulfide ion as previously reported (1-3) and now investigate the behavior of iodide, bromide, cyanide, thiocyanate, selenide, and selenocyanate. EXPERIMENTAL SECTION Analytical grade potassium iodide and sodium bromide (Baker Chemical Co.), sodium cyanide, and sodium thiocyanate (Fisher Scientific Co.) were used. Sodium selenide and potassium selenocyanate (Alfa Products) were used without further purification. Solutions of selenide and selenocyanate ions were prepared in deoxygenated solution of supporting electrolyte (300 cm3)which was deaerated by bubbling argon purified by passing through acidic vanadium(I1)solution and water. Weighed amount of solid NazSe or KSeCN were then added to the solution. The electrode rotation rate in all the cases ranged from 400 to 3600 rpm. Other experimental procedures and apparatus have been described elsewhere (1). RESULTS AND DISCUSSION AgRDE voltammograms were scanned from negative to positive potentials. All the anions employed showed convective diffusion limiting currents, as indicated by limiting current plots against w1/2 showing strict linearity and passing
Table I. Experimental Conditions, n, and E , / ,
anion
medium
S2SeZ-
0.2M NaOH 0.2M NaOH
1-
Br-
0.1 M
CH,COOH
~ ~ 1 0 - 4
mol dm-,
products
Ag,S 2.47-14.1 Ag,Se 1.97-8.88 AgI 4.00-8.00 AgBr 1.77-8.85
n
E@
2 2 1 1
-0.82 -0.85 -0.17 0.08
1 1
0.08 0.03 -0.46
0.1 M
CH,COONa SCN4.00-8.00 AgSCN SeCN3.28-17.9 AgSeN CN0.1 M NaOH 4.00-24.0 Ag(CN);
a Half-wave potential of anodic voltammograms at concentration of about 5 X mol dm-3.
through the origin. Iodide, bromide, thiocyanate, selenide, and selenocyanate formed insoluble films at the electrode surface, as indicated by a cathodic scan giving rise to a sharp, cathodic stripping peak similar to that observed for sulfide ( I ) . The shape of the anodic voltammogram, in the case of I-, SCN-, and SeCN- was similar to that of S2-(2,3). Figure 1shows AgRDE voltammograms for SeCN- at various rotation rates. The front of the voltammogram for Br- has a much sharper rise than the other anions. Selenide has a prewave (Ellz= -0.93 V) of unknown origin. For I- and SeCN-, two stripping peaks were observed under some circumstances. Figure 2 shows a cyclic voltammogram for SeCN- at the AgRDE. However, for I-, if the concentration were sufficiently low (10-6-10-7 mol dm4), and deposition time limited, the two peaks merged into one sharp stripping peak. Obviously, more work is needed to characterize the behavior of these films under a variety of analytical conditions. In the case of CN-, the reaction product is soluble; the cathodic scan does not give rise to a reduction wave but merely retraces the anodic going scan, provided the scan rate is not too rapid. The overall reaction can be written as Ag
+ xCN- F! Ag(CN),(x-l)- + e-
(2)
The AgRDE anodic voltammogram for cyanide was analyzed by plotting various possible current functions against
0003-2700/81/0353-2350$01.25/00 1981 American Chemical Society
