Entropy and enthalpy in thermodynamics can somebody clarify the statement thermodynamics teaches that the loss of entropy by a freezing salt solution can be overcome at temperatures much below 0 degree C because the gain in enthalpy by freezing water rises when temperature goes down
 A: When comparing the two processes of salt water vs. water freezing it is important to note that both processes result in the same end product. When salt water is frozen, the salt is "squeezed" out in order to allow the ice crystals to pack together in a lattice. Therefore the final entropy of frozen salt water is not different than that of water. Following this reasoning, salt water undergoes a greater decrease in entropy than water since it starts off at a higher state of disorder.
In order for any process to occur, the total entropy of the surroundings and system must increase. Since entropy decreases even more when salt water freezes, the entropy of the surroundings must increase even more for salt water to freeze. The formula for the entropy change of the surroundings based of the enthalpy change of the system and temperature of the system is: -$\Delta$H/T (Note $\Delta$H is negative). Furthermore, the enthalpy change between the two processes is no different (contrary to your assumption): in the salt water solution, only the water undergoes an energy change when it goes from solid to liquid, (negligible enthalpy change for salt). In order for entropy of the surroundings to increase, and knowing that -$\Delta$H does not vary between processes, the temperature at which salt water freezes must be lower to allow the total entropy change of the system and surrounding to increase.
Clarification: Salt water is more disordered because when you have a heterogeneous collection of particles it has more possible states. The more possible states, the greater the entropy. If I have two identical objects and two positions, there is only one possible state. If I have two different objects and two positions, there are two possible states.
A: If you make the assumption that entropy has decreased with the addition of salt, there are more micro states because of the salt ions.  the net entropy would be greater than water alone.  make an assumption that this occurs spontaneously, this would require heat to be released from then system.  if heat is released, it needs to go somewhere, and that would be the surroundings.
