Question: It is a well known fact that freezing point decreases on adding impurities. I feel that it should increase on adding impurities. 

Reason: I have watched [this](https://youtu.be/ph8xusY3GTM) video on supercooled water. It says that when ice forms, it needs some nucleation points. If water is pure and left undisturbed, then there would be no nucleation points and water won't freeze even below $0^o$C. 

So, my reasoning is that when impurities are added, they provide additional nucleation points where water crystals can gather. This would cause water to freeze faster.

But it doesn't happen. Why?

Answer: 
No, but good question. *Freezing* is a **thermodynamic** process. *Nucleation* is a **kinetic** process. 

**Kinetic Explanation:** At the freezing point of water, water wants to become ice (thermodynamically driven). In order for freezing to initiate and ice to form a temperature dependent minimum number of water molecules must arrange them selves in a crystal or else the particle will dissolve and no freezing will occur. Impurities or containers with rough surfaces can help arrange and hold molecules which allows freezing to occur with a fewer number of molecules.

**Thermodynamic Explanation:** Freezing is a thermodynamic process dictated by $\Delta G\_f = 0 = \Delta H\_f -T\Delta S\_f$. When water freezes it must dispel the impurities to form an ice crystal (reverse mixing). Since mixing increases entropy, this means that for water to freeze the negative change in entropy ($\Delta S\_f$) is larger than that of pure water. This must be compensated by a lower temperature ($T$) neglecting and differences in ethalphy. The enthalpy ($\Delta H\_f$) of mixing will contribute as well to the freezing temperature of water and must be accounted for. In the case of Sodium chloride though the enthalpy mixing is positive which would favor a higher melting point, but the entropy contribution is large and magnified by the temperature such that entropy dominates and reduces the temperature of freezing. 

If you look at the phase diagram of water and salt you will see that the mixing of the salt and water depresses the melting temperature due to the increased change in entropy from mixing water and salt to make brine from ice and salt.

[![enter image description here](https://i.stack.imgur.com/IK0SD.gif)](https://i.stack.imgur.com/IK0SD.gif)
Think in terms of needing to remove the dissolved substance: the water that crystallizes is (fairly) pure $\ce{H2O}$, and the remainder is a concentrated solution (e.g. brine, if the solute is $\ce{NaCl}$. Work is done to separate the water from brine, so it takes more "effort" to freeze than does pure water.

There are many good explanation for the phenomenon on the web, e.g. [Physics Animations](http://www.animations.physics.unsw.edu.au/jw/freezing-point-depression-boiling-point-elevation.htm).

BTW, some bacteria nucleate water freezing, such as [Pseudomonas syringae](https://microbewiki.kenyon.edu/index.php/Bacterial_nucleation_in_pseudomonas_syringae). The protein from these bacteria is used in [artificial snow-making](https://en.wikipedia.org/wiki/Snowmaking). The water still has to be below 0 C to freeze, but supercools less.