title: Optimal experimental designs for estimating Henry's law constants via the method of phase ratio variation.
abstract: When measuring Henry's law constants (kH) using the phase ratio variation (PRV) method via headspace gas chromatography (GC), the value of kHof the compound under investigation is calculated from the ratio of the slope to the intercept of a linear regression of the inverse GCresponse 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-1peak 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 kHwith 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 kHfor Naphthalene in aqueous solution as well as simulations on previous studies. Our designs are most applicable after a trial run defines the linear GCresponse and the linear phase ratio to the GC-1region (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.
authors.affiliation: Department of Mathematics, Queens College, The City University of New York, 65-30 Kissena Blvd., Kiely Hall Suite 605, Flushing, NY 11367, United States. Electronic address: kapelner@qc.cuny.edu.
authors.forename: Adam
authors.initials: A
authors.lastname: Kapelner
authors.affiliation: Department of Statistics, The Wharton School of the University of Pennsylvania, 3730 Walnut St, Jon M. Huntsman Hall Suite 442, Philadelphia, PA 19104, United States. Electronic address: krieger@wharton.upenn.edu.
authors.forename: Abba
authors.initials: A
authors.lastname: Krieger
authors.affiliation: School of Earth and Environmental Sciences, Queens College, The City University of New York, 65-30 Kissena Blvd., Science Building Suite D202, Flushing, NY 11367, United States. Electronic address: william.blanford@qc.cuny.edu.
authors.forename: William J
authors.initials: WJ
authors.lastname: Blanford
mesh_terms: D000465:Algorithms; D002849:Chromatography, Gas / Q000379:methods*; D009281:Naphthalenes / Q000032:analysis; D012107:Research Design; D013696:Temperature; D014867:Water / Q000737:chemistry
chemical_list: D009281:Naphthalenes; D014867:Water; C031721:naphthalene
keywords: Headspace gas chromatography; Henry's coefficient; Henry's law constant; Linear regression; Optimal experimental design; Phase ratio variation method; Slope divided by intercept; Volatile organic compounds