1. To determine the rate constants for the second order consecutive reactions, a number of chemometrics and hard kinetic based methods are described. The absorption spectroscopic data from the reaction was utilized for performing the analysis. Concentrations and extinctions of components were comparable, and all of them were absorbing species. The number of steps in the reaction was less than the number of absorbing species, which resulted into a rank-deficient response matrix. This can cause difficulties for some of the methods described in the literature. The available knowledge about the system determines the approaches described in this work. The knowledge includes the spectra of reactants and product, the initial concentrations, and the exact kinetics. Some of this information is sometimes not available or hard to be estimated. Multiple linear regression for fitting the kinetic parameters to the obtained concentration profiles, rank augmentation using multiple batch runs, mixed spectral approach which treat the reaction with pseudo species concept, and principal components regression are the four groups of discussed methods in this study. In one of the simulated datasets the spectra are quite different, and in the other one the spectrum of one reactant and the product share a high degree of overlap. Instrumental noise, sampling error are the considered sources of error. The aim was investigation of relative merits of each method. augC: augX: References: 1 T. J. Thurston and R.G. Brereton, Analyst 2002, 127, 659. 2 A. R. Carvalo and R.G. Brereton, T. J. Thurston, R. E. A. Escott, Chemom. Intell. Lab. Syst. 2004, 71, 47-60. 3 T. J. Thurston and R.G. Brereton, D. J. Foord, R. E. A. Escott, J.Chemom, 2003,17, 313-322. 4 R.Tauler, Chemom. Intell. Lab. Syst. 1995, 30, 133. 5 S. Wold, K. H. Esbensen and P. Geladi, Chemom.Intell. Lab. Syst. 1987, 2, 37. augmentation PCR: Conclusion:  When the pure spectra of each component are available, MLR is the best choice, and gives accurate estimates of rate constants in this catalytic system, without requiring any knowledge of initial concentrations.  When pure spectra are not available, and data from three or more reactions are available, rank augmentation can be used to obtain estimates for the pure spectra of all species and to calculate the more accurate estimates of the rate constants than mixed spectra and PCR methods.  When the pure spectra of each component are not available and the data from three or more reactions is not available, PCR and mixed spectra are suggested. The accuracy of the estimated rate constant is similar. The choice between mixX and mixD or pcrT and pcrC or pcrD, depends on the type of error and level of noise or error present in response matrix. In presence of instrumental noise, mixX and pcrT is better than mixD and pcrC or pcrD. In contrast, in presence of sampling error, it is better to use mixD and pcrC or pcrD.  To estimate the rate constants of this system, it is better to use two or more of these proposed methods and compare the obtained results to give the most accurate rate constants, as possible.  pcrT is less sensitive to noise than pcrC and pcrD. pcrC and pcrD are less sensitive to sampling error. Underestimation of k 2 and Overestimation of k 1 At high levels of sampling error Maryam Khoshkam and Mohsen Kompany Zareh * Institute for advanced studies in basic sciences (IASBS), Zanjan Dataset2: high overlap Sampling error: pcrT C into T pcrC C into T pcrD D into T, completely  augX shows higher tolerance limit to noise, compared to augC and mixX.  augX is sensitive to sampling error, similar to mixX. Specially for highly overlapped data.  augC has accurate results in presence of sampling error, similar to mixD. Instrumental noise: Dataset1: low overlap Second order consecutive reaction: Concentration profile 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 02468101214161820 Time Concentration Concentration profile obtained from runge kutta algorithm by solving ordinary differential equations of component. Noise level% Average Relative Standard deviation (RSD)% Accuracy % k1k1 k2k2 k1k1 k2k2 k1k1 k2k2 Dataset 1 Instrumental noise 0.11.99 9 0.600.160.06-0.020.05 12.00 5 0.600.610.280.270.06 22.020.601.270.590.890.05 Sampling error 0.11.99 8 0.600.130.06-0.060.02 11.99 6 0.60 1 1.260.71-0.170.13 21.99 1 0.60 2 2.171.28-0.420.37 Dataset 2 Instrumental noise 0.12.000.600.180.060.02 11.99 9 0.60 1 0.750.29-0.010.11 22.000.60 1 1.820.600.020.16 Sampling error 0.11.99 9 0.600.290.09-0.020.01 12.010.59 9 2.610.790.66-0.06 21.980.605.371.72-0.840.63 augX augC Noise level% Average Relative Standard deviation (RSD)% Accuracy % k1k1 k2k2 k1k1 k2k2 k1k1 k2k2 Dataset 1 Instrumental noise 0.11.99 6 0.600.430.14-0.180.13 11.970.611.310.54-1.571.16 21.910.621.881.08-4.593.36 Sampling error 0.12.000.59 9 0.100.080.01-0.01 12.010.600.800.780.310.01 22.020.59 7 1.321.360.75-0.35 Dataset 2 Instrumental noise 0.11.990.600.420.12-0.190.24 11.930.612.140.65-3.582.24 21.720.645.162.22-14.016.97 Sampling error 0.11.99 9 0.60 0 0.100.06-0.020.02 12.00 1 0.60 1 0.940.540.080.09 21.990.60 1 2.171.22-0.260.24 Noise level % Average Relative Standard deviation (RSD) % Accuracy % k1k1 k2k2 k1k1 k2k2 k1k1 k2k2 Dataset 1 Instrumental noise 0.1 2.000.600.270.090.010.00 1 2.00 4 0.602.450.780.210.02 2 2.010.60 1 5.151.700.590.16 Sampling error 0.1 1.99 9 0.600.230.13-0.030.02 1 2.00 1 0.602.681.450.050.01 2 1.990.60 2 4.242.43-0.530.37 Dataset 2 Instrumental noise 0.1 1.99 9 0.600.230.09-0.040.01 1 2.00 4 0.602.080.820.220.00 3 2 2.000.59 9 4.351.570.02-0.02 Sampling error 0.1 2.000.59 9 0.5 9 0.220.02-0.01 1 1.980.606.162.33-0.880.46 2 1.970.6114.518.69-1.482.05 Mixed Spectra mixX mixD Application of chemometrics methods with kinetic constraints for estimation of rate constants of second order consecutive reactions mixX mixD Pseudo species Concentration matrix of pseudo species pcrD pcrT Nois e level % Average Relative Standard deviation (RSD) % Accuracy % k1k1 k2k2 k1k1 k2k2 k1k1 k2k2 Dataset 1 Instrumental noise 0.11.99 9 0.600.260.08-0.00 5 0.02 11.99 5 0.602.510.83-0.230.04 21.99 3 0.604.921.70-0.320.08 Sampling error 0.12.000.59 9 0.260.140.02-0.00 8 12.010.59 8 2.601.420.39-0.18 22.00 3 0.604.852.580.170.09 Dataset 2 Instrumental noise 0.11.99 9 0.600.220.09-0.010.00 11.99 8 0.602.120.73-0.100.05 22.00 5 0.604.361.580.280.14 Sampling error 0.12.00 1 0.59 9 0.600.210.05-0.01 11.980.60 4 7.175.46-0.760.72 22.060.59 8 13.274.333.12-0.19 Noise level% Average Relative Standard deviation (RSD) % Accuracy % k1k1 k2k2 k1k1 k2k2 k1k1 k2k2 Dataset 1 Instrumental noise 0.11.99 8 0.60 0.21-0.060.02 0.51.99 6 0.601.200.46-0.210.15 11.970.60 4 2.741.09-1.470.72 Sampling error 0.11.99 9 0.600.240.14-0.020.01 12.00 1 0.59 9 2.361.420.06-0.00 7 21.980.60 5 7.777.13-0.960.96 Dataset 2 Instrumental noise 0.11.99 9 0.600.800.29-0.040.02 0.51.99 3 0.60 1 1.830.70-0.340.23 11.950.60 7 5.272.89-2.401.17 Sampling error 0.12.000.59 9 0.250.150.03-0.02 11.99 3 0.60 1 2.681.66-0.340.26 21.980.60 5 7.236.81-1.250.97 Noise level% Average Relative Standard deviation (RSD) % Accuracy % k1k1 k2k2 k1k1 k2k2 k1k1 k2k2 Dataset 1 Instrumental noise 0.11.99 7 0.600.510.17-0.120.04 0.51.99 5 0.601.290.50-0.220.10 11.980.602.781.03-1.080.55 Sampling error 0.11.99 9 0.600.230.13-0.020.02 12.000.59 9 2.251.260.02-0.07 22.000.59 9 4.612.460.00 5 -0.02 Dataset 2 Instrumental noise 0.11.99 9 0.59 9 0.580.20-0.02-0.00 3 0.51.980.60 2 1.400.55-0.740.35 11.960.60 5 2.871.14-2.140.97 Sampling error 0.12.000.59 9 0.220.130.01-0.01 11.990.602.171.29-0.310.04 22.020.59 6 4.732.531.16-0.63 MLR Noise level % Average Relative Standard deviation (RSD) % Accuracy % k1k1 k2k2 k1k1 k2k2 k1k1 k2k2 Dataset 1 Instrumental noise 0.11.99 9 0.600.300.15-0.040.02 12.000.59 9 1.370.730.02-0.09 21.99 9 0.60 1 2.591.49-0.020.15 Sampling error 0.12000.59 9 0.090.050.00-0.00 5 11.99 9 0.600.450.30-0.00 5 0.05 21.99 9 0.600.930.59-0.00 5 0.01 Dataset 2 Instrumental noise 0.12.00 1 0.59 9 0.270.150.03-0.02 12.00 2 0.601.490.850.130.05 22.00 8 0.59 9 3.071.690.42-0.18 Sampling error 0.11.99 9 0.600.090.06-0.00 5 0.01 12.00 1 0.59 9 0.440.280.04-0.01 22.00 3 0.59 9 1.010.650.16-0.05 pcrC Noise level% Average Relative Standard deviation (RSD) % Accuracy % k1k1 k2k2 k1k1 k2k2 k1k1 k2k2 Dataset 1 Instrumental noise 0.12.000.5990.390.140.02-0.003 0.51.990.6011.640.66-0.470.20 11.960.6053.561.35-1.980.89 Sampling error 0.11.9990.600.220.14-0.040.02 11.9990.602.491.42-0.040.13 22.0050.5985.173.280.25-0.18 Dataset 2 Instrumental noise 0.11.9990.600.740.28-0.0050.02 0.51.9880.6011.650.64-0.590.28 11.960.6043.651.29-1.750.77 Sampling error 0.12.000.5990.260.150.00-0.005 12.010.5972.261.290.62-0.41 21.9980.607.456.81-0.060.31 Abstract: