What is the mechanism behind the absorption process? What are the driving forces that control the process? Simply, what does the lithium bromide do to change the evaporation of water to absorption of water vapour, from mass reduction to mass gain?
There is a certain equilibrium vapour pressure for water above the lithium bromide aqueous solution, which depends on both solution temperature and salt concentration. However, particularly for open containers, the actual vapour pressure of water at the atmosphere contacting the liquid surface can be higher or lower, depending on its humidity content. Hence, there may be a mass-transfer driving force for the solution to either uptake water from the atmosphere, or to lose water, respectively. In a (relatively small) closed container, equilibrium can be attained, so that the solution concentration is not expected to change noticeably. If the solution is losing water by evaporation and is non-saturated, its concentration increases, until it becomes saturated. For reference, you may want to check: J. F. Young, "Humidity control in the laboratory using salt solutions—a review", Journal of Applied Chemistry, 17(9) 1967, 241-245.
Well, after all, maybe it should be pointed out that in modern terms, saturation pressure relative to that of a pure substance would be proportional to this substance's activity in any given mixture (as opposed to its molar fraction, as was originally defined by Raoult).
However, I know Raoult's law. But I've asked this question trying to understand why the saturated pressure of the aqueous lithium bromide solutions obeys Raoult's law. What's the physical interpretation? Does adding lithium bromide to water increase the Surface tension for example? Why the vapour pressure decreases? Can adding nanoparticles to aqueous solutions increase or decrease the saturation pressure?