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 k_H 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 CRAN.