# Calculation of equilibrium relative humidity (RH)

These equations will allow the calculation of the Relative Humidity that is in equilibrium with precipitant solutions based on Raoult's law and the Flory-Huggins model for the entropy of mixing of polymers. This is useful in finding the starting point for controlled dehydration experiments, assessing the degree of vapour diffusion and matching precipitant concentrations in protein crystallisation experiments

The EMBL HC1 Humidity Control device allows the modulation of the diffraction properties of crystals by controlled dehydration. The first step in a dehydration experiment is to define the relative humidity in equilibrium with the mother liquor of the system under study; this can often be quite time-consuming. In order to reduce the time spent on this stage of the experiment, the equilibrium relative humidity for a range of concentrations of the most commonly used precipitants has been measured. The relationship between the precipitant solution and equilibrium relative humidity is explained by Raoult's law for the equilibrium vapour pressure of water above a solution. The concentration of buffers, additives and detergents used will have a negligible effect on the RH in equilibrium with the mother liquor and is dominated by the primary precipitant.

A new applet is now available at the EMBL HC1 pages that allows the prediction of RH equilibrium points using both theoretical calculations and empirical data.

Equation 1 allows the calculation of the RH in equilibrium with salt solutions

Equation 2 allows the calculation of the RH in equilibrium with PEG solutions

Equation 3 allows the calculation of the RH in equilibrium with substances that neither dissociate into multiple species nor are polymers (e.g glycerol, ethylene glycol, sucrose, TMAO, etc)

Equation 4 allows the calculation of a salt concentration that is in equilibrium with a certain PEG solution for vapour diffusion and dehydration experiments. This would allow, for example, slow dehydration of crystals in a PEG solution by slowly increasing the salt concentration in the well above the equilibrium point.

Equation 5 allows the calculation of a salt concentration that is in equilibrium with solutions of substances that neither dissociate into multiple species nor are polymers (e.g glycerol, ethylene glycol, sucrose, TMAO, etc) for vapour diffusion and dehydration experiments.

Contact Matthew Bowler for help. Please cite Wheeler, M.J., et al. (2012) Acta Cryst. F68, 111-114 and Bowler et al. (2015) Cryst. Growth Des, 15, 1043-1045 if you use these equations to calculate the RH in equilibrium with solutions or for starting points for experiments using the HC1 humidity control device.

The HC1 is fully described in Sanchez-Weatherby et al. (2009) Acta Cryst. D65, 1237-1246, and recent examples are described in Russi et al. (2011) J. Struct. Biol. 175, 236-243, please use these references to cite the device in  any paper that reports or involved experiments performed with the HC1b.