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Why the solubility of sodium chloride does not change with temperature?

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It's not true that the solubility of NaCl does not depend on T. Indeed it is a weaker dependence than that of other chemicals, but it still increases from 35 g per 100 g of water at 0C to 40 g at 100C. Pressure affects solubility too, but as said above, intermolecular forces and entropy changes are the main considerations.

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The solubility of sodium chloride does not change with temperature because the variation of solubility with temperature is due to the increasing effect of entropy on the solubility. When orderly crystals dissolve the system becomes more disordered, and this factor becomes more important as temperature increases.

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