system
Given the following post, respond as if you're commenting on Reddit:
human
When adding salt to a mixture of water and ice, why does the temperature drop?

So far I've understood that at 0 degrees celsius, there is an equilibrium between the ice and water that remains largely the same in ideal conditions. Salt binds up some of the liquid water molecules, making it harder for the ice to freeze the solution seeing as there are fewer free water molecules to freeze. (Correct me if I'm wrong.) This causes a freezing point depression.

* Why does adding salt cause an almost instant temperature drop?
* Salt is used to melt ice, so wouldn't the temperature drop freeze the water, or is the temperature drop still above the new freezing point?

I'm asking because of a small-scale experiment where I mixed snow, water and lastly ice; the temperature dropped very fast.
gpt
The temperature drops because the system is in equilbrium between the solid and liquid states of water, and in the presence of salt the liquid can exist at lower temperatures.  That is one of several properties called "colligative properties" of liquid solutions.  The mechanism is that the dissociated ions in the dissolved salt solution pull at the polar ends of the water molecules on the boundary between solution and solid, breaking the hexagonal crystalline structures that make the ice solid. (Edit: Note that the ions don't remain affixed to the water molecules, they only change the dynamics that are going on at the solid/liquid boundary.  Thanks, arble, for pointing that out.)

The reason the solution drops in temperature is that it takes energy to remove a water molecule from an ice crystal.  That energy comes from the kinetic energy of the surrounding liquid water molecules: when a water molecule is lifted from the ice crystal structure, it leaves with less speed than the impacting water and salt molecules that knocked it out.  Eventually, the average kinetic energy of the liquid water is less than it used to be (i.e. "the water is colder").

The temperature drop is rapid because (A) the heat of fusion of water is large (i.e. it takes a *lot* of energy to pull the water molecules out) and (B) the system is tightly coupled thermally, since it is after all an ice-water bath.

Contrariwise, if you flush the liquid salty water out and replace it with distilled water, the distilled water will freeze against the extra-cold ice, and warm up the system to 0 degrees C by releasing kinetic energy as the water molecules snap into place in the ice crystals.

Using salt to melt ice on a sidewalk depends on the fact that the sidewalk is in a large approximately-equal-temperature environment.  The sidewalk cools well below 0C right away, and begins absorbing heat from its (presumably near-freezing) environment.  That is different from an ice-cream maker or similar system, because in an ice-cream maker you isolate the ice cream and icy brine from the environment, to prevent it absorbing energy from outside.