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The anhydrous calcium chloride (CaCl₂) is a hygroscopic substance. That means that the substance has a very high affinity with water (H₂O).
Water vapor from the air reacts with CaCl₂ to form Hydrated complexes following this reaction:
CaCl₂ + nH₂O → CaCl₂*nH₂O
In this reaction, water vapor is consumed and removed from the air, lowering the humidity of the air inside the desiccator.