Timeline for How does the composition of ice differ from that of water in a partly frozen solution?
Current License: CC BY-SA 3.0
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| Apr 5, 2018 at 15:30 | history | edited | Gaurang Tandon | CC BY-SA 3.0 |
fixed broken image via Web Archive; mhchem fixes
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| Sep 7, 2013 at 8:46 | comment | added | Karolis Juodelė | All I mean was that $\frac{n_{{pure~water}_1}}{n_{{salt~water}_1}} \cdot n_{{salt~water}_1} + \frac{n_{{pure~ice}_1}}{n_{{salt~ice}_1}} \cdot n_{{salt~ice}_1} = n_{{pure~water}_0}$. As for the salt term, when I say salt, I don't mean $NaCl$, I mean any soluble material. I assume a solution of $NaCl$ would have different equilibrium than, say $H_2CO_3$, but the equations say nothing about it. | |
| Sep 7, 2013 at 7:26 | comment | added | Nick T | $\chi$'s sum to 1...multiplying them is throwing me a bit. There is no salt in my simpler equations because it never changes state. In any case, these are vaguely the "general principles", and you're getting beyond what I know how to theoretically solve. | |
| Sep 7, 2013 at 6:46 | comment | added | Karolis Juodelė | So the equilibrium I'd need to solve for $T$ is $\mu_{water}(T) + RT\ln \chi_{water_1} = \mu_{ice}(T) + RT \ln \chi_{ice_1}$ with a constraint $\chi_{water_1}\chi_{salt+water_1} + \chi_{ice_1}\chi_{salt+ice_1} = \chi_{water_0}$ (intended to be conservation of mass) where $_1$ indicates state in equilibrium and $_0$ indicates state before any freezing? Does the chemical potential of "salty ice" have some other expression? And do $\mu(T)$ have algebraic approximations? And, most importantly, how come there is no term describing the salt in the equations? | |
| Sep 6, 2013 at 19:49 | comment | added | Nick T | That said, in practical systems the concentration of entrapped solute probably increases as the temperature drops...a much more difficult problem to solve theoretically. Analytically it's easy, chip off some of the frozen bit and measure. | |
| Sep 6, 2013 at 19:47 | comment | added | Nick T | @KarolisJuodelė For your problem you'd just need to find the intersection of curves at the appropriate temperature. If impurities are being trapped in the ice (at a constant rate) it's still the same problem, you just don't make the assumption the ice is pure, so its chemical potential curve will be at some other value (your 'spectrum of curves'). If you find the equilibrium temperature and solution composition you can determine the chemical potential of the ice (at that temperature) which should allow you to determine its composition. | |
| Sep 6, 2013 at 18:00 | comment | added | Karolis Juodelė | Thanks, that was informative, but I'm not sure it answers my question. In my problem the graph also has a curve named "salty ice". Or rather a spectrum of curves for ice with different amounts of salt in it. Where do those go? | |
| Sep 2, 2013 at 21:31 | history | answered | Nick T | CC BY-SA 3.0 |