I am a first-time brewer trying my hand at two simultaneous 1 gallon batches of apple cider. I do not own a hydrometer/did not have a graduated cylinder on hand to take an SG reading, so I realize I will not be able to determine my exact ABV at the end of my brew. However, I was wondering if it wouldn't be possible to estimate an approximate potential ABV given my starting ingredients and a little chemistry knowledge.
The nutrition facts on my cider say there 384 grams of sugar in each gallon, which I'm assuming the majority of which is fructose, given that fructose is the "fruit sugar," and that the cider is advertised as "organic" with no added sweetening. I also added approximately 0.23 pounds of brown sugar, which would be sucrose.
Fermentation yields 2 moles of ethanol (and CO2) for every mole of fructose input, and 4 moles of ethanol (and CO2) for every mole of sucrose input. So, converting the masses of my starting sugars into moles, I get 2.13 mol fructose and 0.30 mol sucrose for each gallon as my starting sugars. Plugging those values into the stoichiometric ratios of the reactions, that yields 4.26+1.20 moles of ethanol or 5.46 mol ethanol in total per gallon, and when you multiply by the molar weight and then divide by the density of ethanol, I came up with 318.6 mL ethanol produced in a gallon of cider. Dividing that figure into a gallon of liquid gives me 8.4% ABV.
I'm pretty confident on the numbers, but I was wondering if anyone had anything to say about the veracity of this method. In theory, I figure this should be fairly accurate; however, this calculation depends on the yeast fermenting every last molecule of available sugar.
Basically, I'm asking if there's any reason why this method of prediction wouldn't be accurate.
Thanks for the input, and I look forward to delving deep into this hobby! It's absolutely fascinating!