223Table VII. Comparison of Different Methods from Noisy Simulated Data Corresponding to Mixed First-and m-Order (Input Conditions: k,' = k,' = 1 )" noise = 0.5b noise = 5 b k,' 12, ' kl' km' m = 1.5 this work 1.003 0.996 1.027 0,960 Toby 0.979 1.028 0.718 1,365 m = 2 this work 1.002 0.996 1.018 0.963 Toby 0.981 1.030 0.868 1.215 ShankC 1.001 0.999 0.981 1.047 Kelter and Camd 1.008 0.963 a ([AJ, -[AJN)/[A], = 0 . 8 0 ; N = 200 points. Noise = lOOe,,.Shank's method is based on plotting y = 1/ [A]jf vs. x = l/[A]j. Although the variances on the two variables are of the same order of magnitude and are not constant, these rate constants are obtained by using the ordinary least-squares treatment, ignoring the weighting factors which would be needed for rigorous calculations. No significant differences from the graphical procedure were observed.From ref 8 (180 points).
~ ~~ ~carried out calculations for m = 1.5 and m = 2 by using the two methods (input values: kl' = k,'= 1). As shown in Table VII, Toby's method is unsuitable for accurate determination of rate constants from very noisy data and can even lead to significant errors for a noise level as low as 0.5%. This is due to the very small variations with K of the curvature of the drawings obtained by plotting the left-hand term of eq 3 vs. time and consequently to unsignificant variations in the correlation coefficient r used to test the linearity (e.g., the following r values were observed for different arbitrary K input values with m = 2 and emax = 0.005: K = 1.1, r = 0.999933; K = 1.05, r = 0.9999345; K = 1.0, r = 0.9999344). Moreover, taking 2 as a goodness-of-fit parameter does not improve the method.For m = 2, the results obtained here have also been compared with those deduced by using the methods of Shank andKelter and Cam, which deal with this case only. As also shown in Table VII, accuracies of the calculations are of the same range of magnitude.
LITERATURE CITED(1) Toby. 6. H.; Toby, F. S.; Toby, S. Int. J. Chem. Kinet. 1078, 70, 12) Linschitz. H.: Sarkanen. K. J. Am. Chem. SOC. 1058. 80. 417-422.. .
4826-4832.(3) Fletcher, R.; Powell, M.A preconcentration method is descrlbed for the X-ray spectrometric analysis of several trace elements In seawater, NBS-SRM 1648 urban particulate, NBS-SRM 1632 trace elements in coal, and nickel in urlne at concentrations as low as 1 ppb. The elements in the coal and urban partlculate samples were loaded quantitatively on catlon exchange resin fllters and subsequently analyzed by energy-dispersive X-ray fluorescence spectrometry using secondary targets for monochromatic excitation of the fllter sample. Prior to the analysis of seawater and urine the trace elements from the matrlx were separated wlth a chelatlng resin. Comparison of the results obtained with NBS-SRM certificate values and/or those of other workers indicated agreement withln &lo%.Detectlon and quantitation llmlts for thls preconcentratlon method are also presented.The application of X-ray fluorescence (XRF) spectrometry to the analysis of environmental and...