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

- We improve measurements of Henry's coefficient using the PRV method.
- We optimize the selection of gas-liquid ratios using experimental design principles.
- We improve estimates of the slope-to-intercept ratio in linear regression.

When measuring Henry's law constants (kH) using the phase ratio variation (PRV) method via headspace gas chromatography (GC), the value of kH of the compound under investigation is calculated from the ratio of the slope to the intercept of a linear regression of 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 collects measurements consisting of the independent variable (the gas/liquid volume ratio) and dependent variable (the GC−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 kH for Naphthalene in aqueous solution as well as simulations on previous studies. Our designs are most applicable after a trial run defines the linear GC response and the linear phase ratio to the GC−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.