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Optimal Experimental Designs for Estimating Henry's Law Constants via the Method of Phase Ratio Variation
Adam Kapelner, Abba Krieger, William J. Blanford
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When measuring Henry's Law constants (k_H) using the phase ratio method via headspace gas chromatography (GC), the value of k_H of the compound under investigation is calculated from the ratio of the slope to the intercept of a linear regression of the the inverse GC response versus the ratio of gas to liquid volumes of a series of vials drawn from the same parent solution. Thus, an experimenter will collect measurements consisting of the independent variable (the gas/liquid volume ratio) and dependent variable (the inverse GC peak area). There is a choice of values of the independent variable during measurement. A review of the literature found that the common approach is a simple uniformly spacing of the liquid volumes. We present an optimal experimental design which estimates k_H with minimum error and provides multiple means for building confidence intervals for such estimates. We illustrate efficiency improvements of our new design with an example measuring the k_H for napthalene in aqueous solution as well as simulations on previous studies. The designs can be easily computed using our open source software optDesignSlopeInt, an R package on CRAN. We also discuss applicability of this method to other fields.
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