• Karyoplasma@discuss.tchncs.de
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    4 days ago

    tl;dr Around -21°C (-9°F). Realistically probably a tad lower than that.

    Formula for freezing point depression is:

    ΔTf = i * Kf * m

    ΔTf = freezing point depression in absolute degrees (C or K)

    i = van 't Hoff factor, the number of particles the solutes splits into, ethanol does not split, so 1

    Kf = freezing point suppression constant, for water 1.86°C * kg / mol

    m = molality of the solution (aka how much you add), looked it up and it’s 11.42 mol for 40% ethanol/water mixture

    1 * 1.86 * 11.42 = 21.2412°C
    

    In reality, Jägermeister is not a pure water/ethanol mixture and all that other stuff in there drops the freezing point by a bit as well. Ethanol is the biggest contributor tho. So maybe add 1° or 2° to this.


    Is Jägermeister really that green in the US?

    • Hacksaw@lemmy.ca
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      4 days ago

      I did not know about that formula, very cool. It seems linear (unless the molality is a non-linear term), whereas the empirical data gets pretty whacky at higher concentrations. Maybe its validity is for low concentrations? I’m getting closer to -27C from this plot

      Plot of freezing point of water vs alcohol concentration

      Source www.researchgate.net/figure/Melting-freezing-points-of-alcohol-aqueous-solutions-vs-solvent-concentration-Weast_fig6_273304489

      Either way that’s getting close to “don’t lick it” temperatures lol!

      • Karyoplasma@discuss.tchncs.de
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        3 days ago

        The figure you’ve linked plots concentration by weight (wt.%), while the alcohol content of drinks is usually given in volume percent (v/v). Ethanol is less dense than water, so a 30% concentration by weight is a higher concentration by volume.

        Imagine a 100g solution of 30wt.% alcohol. That means that 30g are ethanol and 70g are water. the 70g of water translate to 70ml volume (density 1g/ml) and the 30g of ethanol translate to 30/0.789 = 38.02ml. So in total, you would have 108.02ml of liquid and the concentration of ethanol by volume would be 38.02/108.02 = 35.2%.

        Why it gets wacky at the end: Ethanol freezes at -114°C, water freezes at 0°C, but at specific concentrations, the eutectic composition, the solution freezes at a lower point than either of its constituents. The eutectic point is the lowest possible freezing point of a solution. The formula I gave is not applicable to eutectic solutions and is an approximation based on perfect solutions (which in reality don’t really exist).

    • Tar_Alcaran@sh.itjust.works
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      4 days ago

      All the other stuff in the drink might lower it a bit though, especially the 14% (!!!) sugar. There’s a sugar cube in every shotglass.

      • Karyoplasma@discuss.tchncs.de
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        4 days ago

        Whoops. Well, I forgot to account for sugar and other stuff which decrease freezing temperature as well, so the result might still be around right. It’s an ok ballpark at least. Precisely calculating a solutions freezing temperature when it has that many different solubles is pretty hard.