Why does ice melt slower at higher altitudes? [closed]








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> Why does ice melt slower at higher altitudes and how does Le Chatelier's principle play a role in this? 
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This question appeared right after this chapter in my text book and I've also read a very rough explanation from another source which cited this principle.




A simplified attempt.
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For a simplified answer that *attempts* at a solution using Le Chatelier's principle, you'll need a constraint: Ice and water are at an equilibrium at $\pu{0^\circ C}$.



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> $$\ce{Ice <=> Water}$$
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Simple enough, now pull up the values of densities of ice and water, $\rho\_{ice}= 0.9167~\pu{g/cm3}, \rho\_{water}= 0.9998 ~\pu{g/cm3}$. Mass being the same, you can conclude that volume of ice is greater than that of water, so in accordance with *Le Chatelier's* principle, when you move at higher altitudes, the atmospheric pressure falls, thus the equilibrium is favored towards a side where the species occupy a higher volume, i.e. towards the formation of ice. This works antagonistically for $\ce{Ice->Water}$.




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Alternatively, have you heard of phase diagrams? This might help you to understand things a bit more clearly after you go through its definition from other sources: <https://chemistry.stackexchange.com/a/72732/43942>


The phase diagrams for water are different though.


<https://d2gne97vdumgn3.cloudfront.net/api/file/m1GFJVbQSBmwkDXRvglV>


[![enter image description here](https://i.stack.imgur.com/P759t.jpg)](https://i.stack.imgur.com/P759t.jpg)


This, too indicates that for water, at lower pressures, the formation of solid (i.e. ice) is *more favored*.




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A realistic insight.
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To be more realistic, as MaxW pointed in the comments, the pressure difference is rather small. The summit pressure at Mt. Everest is $\pu{33.7 kPa}$, while at the sea level it is $101.3$, which gives us a difference of $\pu{67.6 kPa}$ which converts to a mere $\pu{0.676}$ Bar. 


Although this is quite a significant pressure (see Jon's comment) for *our* perception, it doesn't affect freezing that much. For a comparison, this answer <https://chemistry.stackexchange.com/a/8883/43942> states that the pressure required to solidify $\ce{CO2}$ to make it into dry-ice at room temperature, you'll need a pressure of about $\pu{56 bar}$.


Freezing at higher latitudes, requires us to also ponder on the ambient temperature. You probably wouldn't want to talk about latitudes *as high* as the Everest, because then the temperatures will be extremely low (averaging about $\pu{-19^\circ C}$ in summers!) and you'll have to apply an external pressure to adjust the melting point. Latitudes where the ambient temperature is (say) $\pu{3^\circ C}$ have a less temperature gradient when compared to a place (probably at the sea level) with an ambient temperature of (say) $\pu{25^\circ C}$. A higher magnitude of a gradient means a high rate of heat transfer, which hints at a *slower* melting of ice at higher latitudes.


Also, airhuff suggested that thermal conductivity of *thin* air at high latitudes may have a role to play in this. I searched this up, you might want to look at this paper: <http://nist.gov/data/PDFfiles/jpcrd269.pdf>


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Easy. As you get higher, there is less air, making the area colder. So, the ice is surrounded by colder and colder tempatures.


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