At 0 degree Celsius, water molecules slow down enough to bond with each other and ice starts to form. By adding more salt or sodium chloride the freezing point of water becomes even lower, why is that? could it be that when water molecules rip apart sodium chloride (fragile ionic bonding) it gains some energy which prevents itself from bonding with other water molecules? Sounds weird because I always thought that the hydrogen bonding is the weakest among the different types of chemical bonding.
Related questions have been asked, but (to my surprise) I couldn't find this specific question being answered before. (Some answers come close, but are not quite there.)
The way that salt affects the temperature of a mix of water and ice involves the concept of entropy. Therefore I will first write about the aspect of entropy that is relevant here.
As introduction I discuss a simpler case of entropy being a relevant factor.
It involves a molecule that is heavier than air, that (on average) moves against gravity. It was demosntrated to a class of students as follows:
The demonstration involved two beakers, stacked, the openings facing each other, initially a sheet of thin cardboard separated the two.
In the bottom beaker a quantity of Nitrogen dioxide gas had been had been added. The brown color of the gas was clearly visible. The top beaker was filled with plain air. Nitrogen dioxide is denser than air.
When the separator was removed we saw the brown color of the Nitrogen dioxide rise to the top. In less than half a minute the combined space was an even brown color.
And then the teacher explained the significance: in the process of filling the entire space the heavier Nitrogen dioxide molecules had displaced lighter molecules. That is: a significant part of the population of Nitrogen dioxide had moved against the pull of gravity. This move against gravity is probability driven.
Statistical mechanics provides the means to treat this process quantitively. You quantify by counting numbers of states. Mixed states outnumber separated states - by far.
What this demonstration illustrates is that in specific circumstances tendency to increase entropy and tendency to go down an energy gradient can be acting in opposite direction, and in this demonstration the entropy increasing tendency dominated.
Dissolution of salt in water
Interestingly, the dissolution of salt in water is by itself already an endothermic process. That is: if you start with water at a particular temperature, and salt at that same temperature, and you allow the salt to dissolve in the water, then the homogeneous solution will be at a (slightly) lower temperature.
So: purely from the point of view of energy level it is unfavorable for salt to dissolve. The point is: the dissolved state is more probable. Without going into more detail, the is-more-probable property is correlated with the fact that the dissolved state is more homogeneous than the not dissolved state.
Ice and brine
The ratio of ice and brine is a dynamic equilibrium. There is a rate of water molecules joining the existing solid ice, and there is a rate of water molecules being knocked off the ice, and joining the brine.
A major factor, of course, affecting those two (opposite) rates, is temperature. At lower temperature the water molecules move slower, reducing the probability of a water molecule being knocked off the ice.
There is a very high energy barrier to incorporating ions of the salt into the ice crystal structure. That is, the crystallization is a process that makes the total system less homogeneous.
As mentioned earlier, being more homogeneous is correlated with being more probable.
Comparing ice-and-water to ice-and-brine: the presence of the salt shifts the probability, moving the equilibrium state of the two (opposite) rates to a lower temperature. As mentioned earlier, that equilibrium is dynamic equilibrium of rate of water molecules joining the ice, versus rate of water molecules being knocked loose from the ice.