Supercooling, freezing point depression, and finding the right freezing point

Pure liquid can be supercooled below its freezing point. Conversely, impurities in the liquid will cause a freezing point depression. How then is the freezing point accurate?




Melting (and boiling) points are only defined for pure substances. Rather than defining them as ‘the temperature when pure substance $\ce{X}$ melts/boils’ they are better defined as:



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> The melting point is the temperature at which for a certain defined pressure (usually $1~\mathrm{bar} = 10^5~\mathrm{Pa}$) **the liquid and solid phases** of a pure substance are **at equilibrium.**
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> The boiling point is the temperature at which for a certain defined pressure (usually $1~\mathrm{bar} = 10^5~\mathrm{Pa}$) **the liquid and gaseous phases** of a pure substance are **at equilibrium.**
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> 


(I didn’t copy that from anywhere, I made it up. Apologies to everyone who I was unintentionally quoting without attribuition.)


Thus, you can supercool pure liquids but if you allow the supercooled liquid to reach equilibrium at its supercool temperature (and standard pressure), it will solidify. Similarly, you can overheat solids but if you let the overheated solid reach equilibrium at the overheated temperature, it will liquidify. Thus, neither the supercool liquid’s nor the overheated solid’s temperature can be considered the melting point, because neither phase is stable at equilibrium.


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Melting (and boiling) points are ideally defined for the "pure" substances. But "pure" is a rather relative concept. With impurities the melting (and boiling) points will change slightly. However if the change is 1% per percent of impurity then for a substance with 1% impurity that actually melts at 50 degrees Celsius, (273+50 = 323 Kelvin) the observed melting would be slighly lower. Consider the table below:



```
  Purity     M.P. (Kelvin)
    99%        319.770
    99.9%      322.677
    99.99%     322.968
    99.999%    322.997

```

So the purity required for the melting point determination depends partly on the precision required for the melting point. If you just need +/- 1 degree Celsius, then 99% purity would be adequate for most chemicals. (Remember I made the 1% per percent impurity change up...)


For supercooling a liquid the idea is to observe the solid and liquid phases together. Remember that supercooling a liquid has a slight heat capacity compared to the amount of heat liberated when the solid forms. So the liquid can get below the melting point with a loss of heat and become supercooled, but when the solid phases starts to form then the temperature will increase to the melting point. With further loss of heat the temperature then stays at the melting point until all of the liquid phase has solidified, then the temperature of the whole solid phase can drop. 


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