AMI. zyxwvuts chem. zyxwvu 1882, 84, 2359-2305 Processing Analytical Data Obtained from Second-Order Reactions by Using Continuous Reagent Addition zyxwvutsrqponmlkjihgfedcbaZYXWVU Antonio Velasco, Manuel Silva, and Dolores P6rez-Bendito' zyxwv Department zyxwvutsr of Analytical Chemistry, Faculty of Sciences, University of Cbrdoba, E-14004 Cbrdoba, Spain Thk paper reporb a new approach to secondorder klnetlc analyses based on the contlnwm addHlon of the reagent to the analyte rolutlon at a constant rate. A mathematkal model was dev.loped to zyxwvutsr study the k l n e t h of the process. Methods for the determlnatlon of the analyte and the -der rate constant were developed and tested experbnentally. The Fe( I I)/SCN- system Inthe presence of hydrogenporoxlde as analyte was zyxwvutsrqp used as the model reactlon. The method$ for the determlnatlon of hydrogen peroxlde thus developed are compared by urlng a Ieast-squares ffl procedure; those used to obtain the wcondorder rate constant perform qulte well wtth relatlve standard devlatlona between 24%. INTRODUCTION The significance of kinetic approaches to analytical chem- istry has been widely recognized1J and emphasized in recent reviews.314In the last few years, new techniquesfor the kinetic determinationof first- and general-orderdirect reactions have been developed." In this work we developed a novel approach to processing analytical data from second-order reactions by using a mathematical treatment that relates kinetic parameters with the experimental variables involved in a open system based on the continuous addition of a reagent solution at a constant rate to another solution containing the analyte to be determined. This mathematical treatment also allows the second-order rate constant of the system to be determined. The chief advantages of this approach lie in the fact that it allows the kinetic response curve to be readily obtained from both slow and fast reactions (for which the first-order condition is commonly used) with straightforward instrumentation since the reaction is made second-order. Two unconventional analytical kinetic methods and five procedures for determining the second-order rate constant by using the above-mentioned treatment are presented and discussed. The Fe(II)/SCN-/H202 system was chosen to illustrate the applicability of this new approach. THEORETICAL BASIS OF THE METHOD For a second-order irreversible reaction such as that shown A+R-P (1) where A is the analyte, R the reagent, and P the product in (1) Mottola, H. A. zyxwvutsrqponm Kinetic AsDects of Analvtical Chemistry: Wilev: New York, 1988. Chemietrv: Ellin Horwood: Chicheater. U.K.. 1988. (2) PBrez-Bendito, M.; Silva, M. Kinetic Methods in Analytical (3) PGdue, H. L. Anal. Chim. Acta'1989,216,69. (4) Mottola, H. A,; PBrez-Bendito, D.; Mark, H. B. Anal. Chem. 1990, (5) Laios, I.; Fast, D. M.; Pardue, H. L. Anal. Chim. Acta 1986,180, (6) Sarson, J. A.; Pardue, H. L., Anal. Chim. Acta 1989,224, 289. (7) Fitzpatrick, C. P.; Pardue, H. L. Anal. Chem. 1989,61,2551. (8) Schechter, I. Anul. Chem. 1991,63,1303. 62,441R. 429. 219 0.1 0.2 03 Vr I Flgwe 1. Simulated plots of transformed fraction vs v o l w t d c ratio of added reagent for the hypothetical secondorder reactlon of eq 1 at different y values, with reaction monitoring vla (-) the product or (- - -) zyxwvu the analyte. Curve (-) zyxwv corresponds to the dliutkn process. These curves also correspond to the varletton of the addltkn rate for 3,12,30, and 00 mL/mln and y between 1000 and 50, respecthrely. (k = 1.0 s-1 M-l, [R], = 1.0 M, and V, = 50 mL). formed, the reaction rate can be written as -[?I reaction = k[A][RI where k is the second-order rate constant. If a solution of a reagent at a concentration [Rl, is added at a constant rate u to a volume Vo of a solution containing the analyte, ita concentration can be expressed by If [Rl, >> [A], and the addition rate is such that throughout the amount of reagent consumed is very much smaller than that which is added, this equation can be simplified to The dilution rate of the analyta A is given by -[d[Al] =[A]- U dt dilution vo + ut (4) and the overall rate is found to be 0003-2700/92/0364-2359$03.00/0 0 1992 Amerlcan Chemlcal Society