• Karyoplasma@discuss.tchncs.de
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      3 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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        3 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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        3 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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          3 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.

      • thisbenzingring@lemmy.sdf.org
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        3 days ago

        there’s a bar in Edinburgh Scotland called Panda and Sons, they bring the spirits to that spot where they can remove the water ice and then add other stuff or mix it up. They have their menu online that gives some details.

        My wife and I sampled most of the drinks. Interesting approach but you need some skill and the right equipment to make more than a mess

      • anarchrist@lemmy.dbzer0.com
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        3 days ago

        I actually like Jaeger but can’t find what this recipe would be. I saw someone made Jaeger pops out of cranberry juice and Jaeger which sounds OK but not this color. I’m guessing they used white grape juice and a shitload of food coloring for this, assuming it’s not just a stunt for the gram