# Deliquescence/efflorescence: How can I convert between salt concentration and RH?

I am looking at two phase diagrams, one has axes of $T$ and $\%\ce{MgClO4}$ in a $\ce{H2O-MgClO4}$ mix, and the other has axes of $T$ and relative humidity. The authors of the second phase diagram say "The stability diagram is modiﬁed from [the earlier phase diagram] by converting salt concentration to relative humidity using the Pitzer model and parameters." How does changing the salt concentration affect the relative humidity, and how can I reproduce this calculation?

(I am a geologist with minimal chemistry background).

Top figure from Chevrier et al., GRL, 2009; bottom figure from Gough et al., EPSL, 2011.

## 1 Answer

You can't. The two phase diagrams are for two different parts of the system. There isn't enough data to go between the two phase diagrams. You have to use the two diagrams together to estimate the missing data (Relative humidity as a function of temperature over wt% magnesium percolate).

The top figure (Chevrier et al., GRL, 2009) is for a salt in solution. Think of having a sealed bottle with air over solution. The phase diagram shows the relative humidity of the gas as a function of temperature. So at about 240 degrees the equilibrium system has about 45 wt% magnesium percolate in solution.

The solid circles in the lower figure (Gough et al., EPSL, 2011.) show relative humidity as a function of temperature. So at 240 degrees the relative humidity is about 50% for the the equilibrium system.

So at a temperature of equilibrium 240 degrees a solution of magnesium percolate will have about wt 45% of salt and the relative humidity of the air over the solution will be about 50%. You have to combine data from the two phase diagrams to figure out the whole system.

The open circles in the bottom bottom figure (Gough et al., EPSL, 2011.) shows a solid salt in various hydration states (5 vs 6 waters). This sort of detector would be like a crystal oscillator with a coating. As the hydration in the coating changes, then mass of the oscillator changes which changes its fundamental frequency. The chemical reaction (between hydrates with 5 and 6 molecules of water) is not temperature dependent hence the near vertical line.