Here's a hint -- Raoult's Law.
Actually, that would not be relevant to the question. It would apply to a mixture of volatile liquids. In this case we have a volatile solvent and a non-volatile solute, which by definition produces a vapor composed of only the solvent. There is no evaporation of NaOH any more than NaCl would evaporate from a cup of salt water.
During and just after dissolution of the caustic, lye droplets get into the air via an entirely mechanical process. Those droplets essentially spray from the surface with the same composition as the solution.
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