Optimal experimental designs for estimating Henry's law constants via the method of phase ratio variation

When measuring Henry's law constants (k(H)) using the phase ratio variation (PRV) method via headspace gas chromatography (G(C)(-)), 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 inverse G(C) response versus the ratio of gas to liquid volumes of a series of vials drawn from the same parent solution. Thus, an experimenter collects measurements consisting of the independent variable (the gas/liquid volume ratio) and dependent variable (the G(C)(-1) peak area). A review of the literature found that the common design is a simple uniform spacing of liquid volumes. We present an optimal experimental design which estimates kH with minimum error and provides multiple means for building confidence intervals for such estimates. We illustrate performance improvements of our design with an example measuring the k(H) for Naphthalene in aqueous solution as well as simulations on previous studies. Our designs are most applicable after a trial run defines the linear G(C) response and the linear phase ratio to the G(C)(-1) region (where the PRV method is suitable) after which a practitioner can collect measurements in bulk. The designs can be easily computed using our open source software optDesignSlopeInt, an R package on GRAN. (C) 2016 Elsevier B.V. All rights reserved.