Freezing Point Depression and Temperature Decrease

Question

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.

Answer 1

Phase change is not at constant temperature, phase equilibrium is

[OP] it's a phase transition so the temperature of the ice should remain constant

Here is a counter example: If you add ice cubes to hot water, the ice will melt, cooling down the hot water. In this system, there is no thermal equilibrium, so not all of the components are at the melting point of water. If you wait a while, you might see the following: All the ice is gone, or some ice and some water remains, or (if the ice was really cold) all the water is frozen. Only if there is some ice and some water left do you know the equilibrium temperature - equal to the melting point.

A system can gain thermal energy from other types of energy

If you stir a viscous solution, it will get measurably warmer. (This is a classic experiment of thermodynamics.) There is no heat transfer - nothing gets colder. For melting ice, it is a conversion of thermal energy into chemical energy (breaking hydrogen bonds).

How can the ice be cooling as it melts?

It can't, at least not for pure water (see below for adding water). The temperature of the ice is below the melting point (or at it), and the temperature of the water is above the melting point (or at it, or a bit lower if it is super-cooled). The thermal energy will come from the liquid water, cooling it. If everything is at the melting point, melting and freezing will happen at the same rate, and nothing changes temperature. In a real system where surrounding is warmer, thermal energy from the surrounding flows into the system, melting the ice while the system stays at the melting point (there will be small fluctuations so that the thermal energy reaches the ice).

Scenario of adding salt

Starting with an ice/water equilibrium (at melting temperature), we can add salt (at the same temperature, and let's say there is no enthalpy of dissolution). After adding the salt, the temperature is still the same, but the melting temperature is lower. With the temperature higher than the melting temperature, water molecules break away from the ice, which requires energy. This energy comes from thermal energy in the liquid and in the remaining ice. As a result, the entire system cools down.

Will the temperature change?

In your example where ice cubes were added to hot water, wouldn't the pure water ice cube remain at 32 F until it fully melted? How is this any different than having an ice cube on a hot plate and melting it? The temperature during the heating of the cube doesn't increase because the absorbed heat is being used to break the chemical bonds of the solid ice.

If the system is not at thermal equilibrium (different temperatures within the system), some parts of the system have to change temperature before equilibrium is reached. The hot water will certainly decrease in temperature. If the ice cubes are colder than the melting point at the start, they will warm up until they have reached the melting point. (Ice can have any temperature below the melting point. For example, ice from a freezer is at about $\pu{-20^\circ C}$.)

If the system is at thermal equilibrium from the start but not at phase equilibrium (or not a chemical equilibrium for a reaction that is endothermic or exothermic), the temperature will also change. In my example of adding salt to a water: ice mixture, the process of melting is endothermic, so the temperature at equilibrium will be colder (and equal to the freezing point of the salt solution). As ice melts, the temperature decreases and the freezing point increases (because the pure melt-water dilutes the salt solution). Once the two temperatures match, the system is at equilibrium (thermal equilibrium and phase equilibrium).

Answer 2

First of all, it is useful to envision an adiabatic process: add ice at the normal melting temperature to water or cold brine slightly above the MP in a perfectly insulated container (zero heat transfer to the outside) at constant pressure. What do you expect to happen? If the salt concentration is nil (pure water) then ice will melt and the temperature of the liquid will decrease until it matches the MP at that pressure, then not much more: equilibrium will be established. If the solution contains brine, ice will continue to melt until the temperature has sunk below the MP of pure ice (the normal MP). That's freezing point depression. Why does it happen? Because dissolved salt reduces the chemical potential of water in the solution relative to that in the solid: at the normal MP water prefers to be in the salty solution ($\Delta G<0$ for transfer of water from ice to solution). However, melting requires breaking bonds in the solid lattice ($\Delta H>0$). Heat is therefore transferred to the melting solid from the rest of the substance. As both ice and water get colder, both of their chemical potentials decrease, but that of the liquid decreases faster than that of the solid, eventually converging to the same value ($\Delta G = 0$) and establishing equilibrium.