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The question makes little sense. One cannot really "add salt" to ice.

Water is made of up 2 hydrogens and one oxygen atom, bonded covalently (this is a very strong bond). Each molecule however is slightly polar, that is to say that while the electrons are shared amongst the three atoms, there is a "bunching" of electrons about the Oxygen atom, and away from the Hydrogen atoms.

Why this is important is that when you mix salt into water, the salt which is NaCl (sodium chloride), and is thus ionically bonded (weak bond) is broken apart by the polar water molecules, and thus forming a slightly stronger ionic bond between each Na/Cl atom and multiple water molecules.

The problem though is that frozen water forms ice due to a specific structural arrangement of water molecules formed by Hydrogen bonding between the polar water molecules. This cannot be achieved when they are bonded to Na/Cl atoms, and thus when freezing the water must expel the salt to form ice.

Similarly salt put on ice cannot be "added" to the structure of ice (it often melts the ice instead and bonds with the unfrozen water).

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Q: If you freeze a salt water solution would it melt at the same temperature as ice with the same amount of salt added after freezing?
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