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Uncertainty Calculation of Quantities Obtained by Least Squares Regression of Linearized Physical-Chemical Models, a Statistical and Metrological Approach

2020; Brazilian Society of Chemistry; Volume: 12; Issue: 5 Linguagem: Português

10.21577/1984-6835.20200099

1984-6835

W.F. Magalhães,

Fault Detection and Control Systems

This work presents the correct way to transfer the measurement uncertainties of the controlled and dependent quantities to the final measurands obtained from the intercept and the slope of the straight line fitted through the univariate or the bivariate least square regression on a linearized form of physical-chemical models.To exemplify the procedure the rough experimental or simulated data of the Clausius-Clapeyron equation of the vapor pressure of a liquid, of the first order kinetic law, of the Arrhenius equation for the temperature dependence of the reaction rate constant, of the Michaelis-Menten equation for enzymatic catalysis and of the Stern-Volmer equation for fluorescence quenching and positronium formation inhibition equations, are treated according their linearized form to leads to straight lines graphics.From the fitted intercepts and slopes as well as from their uncertainties and covariance other physical-chemical quantities and their uncertainties are estimated using the uncertainty propagation law -UPL as well as the Monte Carlo simulations method.The basic concepts of thermodynamic, of chemical kinetic, of the univariate regression by ordinary and weighed, and finally of the bivariate least square are presented.The uncertainty machine of the NIST of the USA is used for the Monte Carlo measurand combined uncertainty estimation, and the EXCEL based software XLGENLINE of the national Physical Laboratory -NPL of UK is used for bivariate regression.Finally, a statistical, metrological and extensive discussion is done on the rough initial data and final obtained measurands, to improve the comprehension of physical-chemical concepts into the experimental results.Esse trabalho apresenta a forma correta de se transferir as incertezas de medição das grandezas controlada e dependente para os mensurandos finais obtidos a partir do intercepto e da inclinação de uma reta ajustada pelos métodos de mínimos quadrados univariados ou bivariados sobre as formas linearizadas de modelos físico-químicos.Para exemplificar o procedimento os dados brutos experimentais ou simulados da equação de Clausius-Clapeyron para a pressão de vapor de um líquido, da lei cinética de primeira ordem, da equação de Arrhenius para a dependência com a temperatura das constantes de velocidades das reações e das equações de Michaelis-Menten para catálise enzimática e de Stern-Volmer para a extinção de fluorescência e inibição da formação de positrônio são tratados de acordo com suas formas linearizadas para levarem a gráficos de retas.Dos interceptos e inclinações ajustados, assim como de suas incertezas e covariâncias as incertezas de outras grandezas são estimadas usando a lei de propagação de incertezas -LPI e o método de simulações de Monte Carlo.