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# Estimation of the Rate Constants of Second Order Reactions Using Mean Centering of Ratio Spectra

*S. Gorji*^{a}, M. Bahram^{a,}* and A. Golshan^{b}

^{a}, M. Bahram

^{a,}* and A. Golshan

^{b}

^{a}Department of Chemistry, Faculty of Science, Urmia University, Urmia, Iran

^{b}Faculty of Chemistry, Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159, Iran

A new application of the mean centering of ratio spectra method is proposed for estimation of the rate constants of second order reactions, using kinetic-spectrophotometric data. The method is based on the mean centering of the ratio spectra to obtain a kinetic profile of the product. Using computational fitting, the rate constant can be obtained without any ambiguity.** **An interesting feature of second-order reactions is that the number of steps in the reaction is less than the number of absorbing species, resulting in a rank-deficient response matrix. Through using row mean centering of ratio spectra, the pure response of the product of the reaction could be obtained, and thus an accurate estimation of rate constant would be possible. The applicability of the method was evaluated by using several model data. The reaction of 1,2-naphthoquinone-4-sulfonate sodium (NQS) and 3-nitroaniline (TNA) in ethanol as a real system was also studied applying the proposed method.

**Keywords:** Mean centering of ratio spectra, Kinetic-spectrophotometric data, Rate constant, Second-order reactions