Indeterminate error of dilution with pipette and flask is studied based on experiments, statistics, Monte Carlo simulation and probability theory. Equations which describe the error of sample concentration after the dilution are probabilistically derived and verified experimentally and statistically. The uncertainty structure of dilution is shown to be different for the pipette-pipette dilution and the pipette-flask dilution. The theory for dilution error developed here will be a basis to predict the precision of some chemical analyses such as the internal standard method in chromatography.

Tokyo 158, JapanRecently, a probability theory to predict the precision or relative standard deviation (RSD) of measurements in analytical instruments has been proposed. The aim of this paper is to examine the precision of data obtained by a high-performance liquid chromatograph (HPLC) equipped with photodiode detector and photomultiplier on the basis of the abovementioned theory. The baseline drift, which is often formulated as 1/f noise, is approximated by the mixed random process of white noise and Markov process. Of six parameters necessary for the uncertainty prediction, three parameters are determined from the power spectral density of the baseline drift: the standard deviations (SD), w, of the white noise and the SD, m, and retention parameter, p, of the Markov process. The others are signal domain, kf, signal area, A, over domain, k f, and independent error, I (mainly from the injection error). No arbitrary constants are involved. The prediction is shown to be superb for peaks with various areas, heights and widths over a wide concentration range in the HPLC analysis for some aromatic compounds. The applicability of the uncertainty prediction in analytical chemistry is discussed.