I don't have a problem understanding the chemical mechanisms underlying freezing point depression or colligative properties in general, but what I cannot seem to grasp is how if you add salt to ice you end up with a salt-ice-water solution that is actually colder than the ice you started with.
Two other places on this site go into detail about this matter but I feel like it is either not totally correct or just not fully explained. I assume I must not fully understand in the first place, also. The two links are posted immediately below pertaining to the subject.
Where does the energy come from to lower the temperature of a brine solution?
Why does ice water get colder when salt is added?
How can the ice be cooling as it melts, as these links seem to claim? I understand that it would be cooling its surroundings by needing to absorb heat to melt, but it's a phase transition so the temperature of the ice should remain constant. Furthermore, if the temperature remains constant, and the ice continues to absorb heat from the water surrounding it in order to melt since it's above its depressed freezing point, wouldn't you have the impossible feat of heat flowing from cold to hot as the water gets continuously colder, as alleged?
Energy is being used in the phase change from solid ice to liquid water. Heat is being absorbed by the ice. Yes, the ice freezes at a much lower temperature and so it will be liquid at a certain range of higher temperatures than it otherwise would be without salt. As it melts it tries to approach its new ice-water-salt equilibrium which will be at a depressed freezing point. Why does the temperature fall? Especially if phase changes occur at constant temperature?
The energy must be coming from somewhere and going to somewhere, but where? And how can a hot-to-cold temperature difference for heat transfer actually be maintained if the salt solution is getting colder but the phase change (melting ice) is constant temperature?
I'd really appreciate some sort of insight to this.