title: Raoult's law revisited: accurately predicting equilibrium relative humidity points for humidity control experiments.
abstract: The humidity surrounding a sample is an important variable in scientific experiments. Biological samples in particular require not just a humid atmosphere but often a relative humidity (RH) that is in equilibrium with a stabilizing solution required to maintain the sample in the same state during measurements. The controlled dehydration of macromolecular crystals can lead to significant increases in crystal order, leading to higher diffraction quality. Devices that can accurately control the humidity surrounding crystals while monitoring diffraction have led to this technique being increasingly adopted, as the experiments become easier and more reproducible. Matching the RH to the mother liquor is the first step in allowing the stable mounting of a crystal. In previous work [Wheeler, Russi, Bowler & Bowler (2012).Acta Cryst.F68, 111-114], the equilibrium RHs were measured for a range of concentrations of the most commonly used precipitants in macromolecular crystallography and it was shown how these related to Raoult's law for the equilibrium vapour pressure of water above a solution. However, a discrepancy between the measured values and those predicted by theory could not be explained. Here, a more precise humidity control device has been used to determine equilibrium RH points. The new results are in agreement with Raoult's law. A simple argument in statistical mechanics is also presented, demonstrating that the equilibrium vapour pressure of a solvent is proportional to its mole fraction in an ideal solution: Raoult's law. The same argument can be extended to the case where the solvent and solute molecules are of different sizes, as is the case with polymers. The results provide a framework for the correct maintenance of the RH surrounding a sample.
authors.affiliation: Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK.
authors.forename: Michael G
authors.initials: MG
authors.lastname: Bowler
authors.affiliation: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
authors.forename: David R
authors.identifier: https://orcid.org/0000-0001-7853-1520
authors.initials: DR
authors.lastname: Bowler
authors.affiliation: European Molecular Biology Laboratory, Grenoble Outstation, 71 avenue des Martyrs, CS 90181, Grenoble F-38042, France; Unit for Virus Host Cell Interactions, Université Grenoble Alpes-EMBL-CNRS, 71 avenue des Martyrs, CS 90181, Grenoble F-38042, France.
authors.forename: Matthew W
authors.identifier: https://orcid.org/0000-0003-0465-3351
authors.initials: MW
authors.lastname: Bowler
keywords: Flory–Huggins entropy; controlled dehydration; humidity control; macromolecular crystallography; statistical mechanics