Stressbaby
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I got a small task you could do. Should not take more than 20 minutes. Wana give it a go?
Sure if you don't have a deadline.
I got a small task you could do. Should not take more than 20 minutes. Wana give it a go?
I feel like the best way moving forward is for one of us to take 100 ml of water. Add 3 grams of sugar to it. ( should give you 1.010) Then add 60 ml of 40% abv spirit to give you a solution at 15% abv. This will give you a total volume of 160ml. which give you 3 grams of sugar per .160 liters.
I stumbled across some interesting pages about this subject (searching for something else). This one gives five different formulas to calculate the Potential Alcohol. With a note that one of them seems to give close ebulliscope: http://www.brsquared.org/wine/CalcInfo/HydSugAl.htm (this may have been posted earlier).
This one is posted on a Beer making site, but says the more complicated formula seems to provide greater accuracy at the higher gravities used for wine making:
http://www.brewersfriend.com/2011/06/16/alcohol-by-volume-calculator-updated/
The more complicated formula is AVB = (76.08*(SG-FG)/(1.775-SG)) * (fg/0.794)
http://www.brewersfriend.com/2011/06/16/alcohol-by-volume-calculator-updated/
Well, technically speaking, the second equation's value (1.05/.79) is the K value you are looking for. This constant essentially tries to relate the volume of alcohol in the mixture to its density, adjusting the variables (specific gravity) appropriately. Other than relating alcohol to CO2 (I see the connection, I just don't see why they're using it in this equation because after degassing, density should be irrespective of CO2 produced), I think this is a fairly good value to use. However, if I were you, I wouldn't use "K," as in chemistry "K" most often stands for Kelvin or, in the lower case, a rate or equilibrium constant for a chemical reaction. Just my 2 cents there, though.
Essentially, the value (SG-FG)/FG relates the change in specific gravity, or density relative to water, as a decimal percentage. Multiplying by 100 turns this into a more familiar percent change value (percentage). This equation uses density, however, and not molarity or some other total mass measurement, and so can only really approximate the total sugar and thus % abv.
An equation using degrees Brix would hypothetically be more accurate, as this is a % by weight measure. Say, for instance, you have 5 gallons of must, pre-ferment, at 22.5 degrees brix. Since 1 degree Brix is 1 gram of sucrose per 100 grams of water, you have 22.5 grams of sucrose, or roughly 45 grams of glucose (1 sucrose = 2 glucose dimerized), per 100 grams of water. We have 5 gallons of must, and since 1 gallon=3.785 Liters = 3785 grams of water, we have a total sugar mass of ((22.5g/100g) x 3785g) x 5 = 4258 g sucrose, or 9.38 pounds of sucrose. This is, in turn, equal to 12.44 moles of sucrose.
If we proceed to a FG of 1.000, with a degrees brix of 0.0, then all 12.44 moles of sucrose have, hypothetically, become CO2 and Ethanol. Since 1 mole of sucrose yields 4 moles of ethanol, we should now have 49.8 moles of ethanol. This is a molarity of 2.63 M, or 2.63 moles of ethanol per liter of solution. 2.63 moles of ethanol equals 121.g ethanol, which again is per 1L water or 1000g water, giving a percent by mass of 12.11%. To get % abv, you would have to convert this value, which I honestly do not know how to do. One would need to know the volume of the solution, which can really only be determined accurately by measuring.
I wouldn't consider this authoritative by any means. It's really just me tinkering with things stoichiometrically. I'm not a professional chemist, but have studied chemistry in college. Still, again don't consider this definitive. I'm sure I've made an error somewhere... This answer is fairly close, however, to the % abv you would get following the scales on a triple scale hydrometer (12.11% as opposed to 12.9%). This difference should be accounted for when converting to % by volume, though. I would honestly argue that % by mass is a better measure than % by volume, as % by mass doesn't change with temperature. Of course, you probably aren't serving wine in/at wildly fluctuating temperatures...
Anyway... that's a lot of calculations, enough to warrant my stopping for a while lol. As I've state elsewhere, I'm pretty new to wine-making. I do, however, know a little about chemistry...
This wouldn't provide 160 mL of solution, as adding solute and solvent produces a volume of solution that is actually less than that of the sum of the two volumes. This is because the solute, in a sense, 'meshes' with the solution. In other words, the solute molecules are interspersed in between the solvent molecules. It's kind of like pouring marbles into a ball pit; the marbles make up for a measurable increase in volume, but some fill the empty spaces between the balls and thus do not add to the total volume.
Interesting discussion.
Being a trained (although not practicing) scientist....cell and molecular biology, a handy education to transition into winemaking...I really try not to apply such rigor to a hobby. I go by the difference on the hydrometer, and declare it "close enough".
To determine the error, I would do the following. Say we are targeting a semi-sweet wine with a final SG of 1.010. So measure a sample of sugar water that reads 1.010...knowing the exact weight of sugar contained in that sample (start with distilled water, add sugar in weighed increments). Now, create a sample of equal volume with known ABV, containing the same weight of sugar. What is the difference in the SG reading? There is your error. Run the experiment and tell me the answer.
Now, this does not answer the question of the influence of other dissolved solids, which is a real concern. But from an academic standpoint it would isolate the error introduced by the alcohol. Truly, I am interested in the answer.
You won't ever be that close with a hydrometer. It is not just solids (which will increase during fermentation if you are using any such as skins, etc), but also other fermentable solids that may or may not be in the sample or be turned into alcohol. For me, .5% abv is not going to change a whole lot. A huge part of the wine making process is knowing your taste buds, IMHO.
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