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why does salt melt ice and make it colder
Salt melts ice on roads, yet salt isn't warm. Stranger still, ice mixed with salt gets colder than ice alone, down to about minus twenty-one Celsius.
So salt isn't heating anything. Two things happen: salt lowers water's freezing point, and then the melting ice steals heat from everything around it.
At zero Celsius, pure ice and water are in balance: water molecules leave the ice as fast as others join it. Nothing changes.
Add salt and it splits into sodium and chloride ions among the water. They crowd the surface, fewer water molecules join the ice, and melting wins.
Melting needs energy, about 334 joules for every gram of ice. It takes that heat from the mix itself, so the mix gets colder and colder.
It stops at a limit. At 23 percent salt by mass the mix bottoms out near minus 21.1 Celsius. Below that, salt can't melt more ice, so road salt fails in deep cold.
So, the whole picture: salt in the water blocks refreezing, melting wins, melting steals heat, and the mix cools until it hits its new, lower freezing point.
Salt never warmed the ice; it just made freezing harder, so melting stole the heat and the whole mix grew colder.