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"Brine rejection" is the effect of sea ice pushing out dissolved salts, forming sweetwater ice and brine. I understand "freeze distillation", a method to concentrate alcohol in fermented brews, is effectively the same thing.

Do liquids, if they form crystals, "reject" dissolved gases the same way they reject other dissolved substances? Is the brine from arctic ice enriched in $\ce{CO2}$, for example?

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    $\begingroup$ One difference is that the salt has nowhere to go, other than to remain in the brine or form a crystalline solid, whereas the gas can equilibrate with the atmosphere if the latter is in contact with the ice/brine, at least before ice completely covers the brine. After that the gas concentration under the ice can increase. This might be important in shallow areas. $\endgroup$
    – Buck Thorn
    Commented Apr 4, 2023 at 18:37

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While there may well be counterexamples, a paper in Cryobiology (G. Lipp, Ch. Körber, S. Englich, U. Hartmann, and G. Rau in Cryobiology Volume 24, Issue 6, December 1987, Pages 489-503) titled "Investigation of the Behavior of Dissolved Gases during Freezing" includes the statement:

In a manner similar to that of dissolved salts, gases are enriched in the liquid during freezing.

In particular, for oxygen the segregation (distribution) coefficient was measured to be 0.048. In other words, in steady state segregation one expects the oxygen concentration immediately in front of the solid-liquid interface to have about 20x the oxygen in the liquid as in the solid.

While perhaps overly broad, the general concept that gases that do not strongly interact with water would prefer to remain in the liquid vs the solid is straightforward as an entropy effect.

Bottom line, yes, ice has less dissolved oxygen than the liquid.

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