Linear least squares analyses, vapor

Least squares analyses, linear, vapor pressure vs. reciprocal... 

An experiment using thermobalance yields a record of the cell mass with sample as a function of time. From the slope of this curve, the rate of mass loss is determined. The inert gas pressure in the furnace is read on a manometer, and is lowered stepwise in the course of the experiment. Thus a set of corresponding values for n2 and P, which may be considered as knowns in Eq. (7.15) is obtained. On the other hand, the parameters A, B, C, P, and y are generally unknown, since the molecular mass of the vapor, which is included in the parameter y, is not known a priori. The problem may be handled by means of a suitable, non-linear least-squares analysis computer program, which fits Eq. (7.16) for the observed set of data. 

In some problems, it is not certain in advance what variables should be used for a linear least-squares fit. In the vapor pressure case, we had the Clausius-Clapeyron equation, Eq. (11.43), which indicated that ln(P) and l/T were the variables that should produce a linear relationship. In the analysis of chemical rate data, it may be necessary to try two or more hypotheses to determine which gives the best fit. In a reaction involving one reactant, the concentration c of the reactant is given by Eq.(l 1.45) if there is no back reaction and if the reaction is a first-order reaction. If there is no back reaction and the reaction is a second-order reaction, the concentration of the reactant is given by... 

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