Is one volume of Co2 one point of ABV?

Question

So, I'm bottle conditioning. Went back to my high school days to compute the grams of sugar I need to add to get a specific volume of CO₂ per gallon (because I do such small batches).

What I'm wondering is, when I'm computing (however accurately) the volume of CO₂ that's going to be produced for carbonation, can I say something about how many points ABV it will change? For example, what ABV does a 5% beer with enough sugar for 2 additional volumes of CO₂ end at?

I'm thinking 1 volume of CO₂ should corresponds to 1 volume of alcohol, which by volume should be exactly 1 point? In my example, that would mean a 5% beer + 2 volumes CO₂ would be 7%? But that seems high and I can't figure out what's wrong with my math here.

Answer 1

I think you are off by about a factor of 10. To hit 2 volumes CO2, by my calcs (complicated), I figure you will need about 19 grams of sugar per gallon. This will, in effect, add about 2 gravity points to the total gravity of the beer, which will ferment out completely and increase your alcohol by a very small amount, by about 0.2% ABV. So it does look like all these numbers are related, on a per-gallon basis. So then if you wanted 3 volumes CO2, you will need to add extra sugar per gallon (3/2 times 19, I guess) which will result in roughly 0.3% ABV added.

I think you were on the right track, but might have missed a decimal point in there somewhere.So, bottom line, your 5.0% ABV beer with sugar to hit 2 volumes CO2 should turn out at about 5.2% ABV. If it matters much to you. Most people don't really care about tiny alcohol percentages. If you're selling it and/or putting on a label, though, then maybe it matters more.

Answer 2

TL;DR: it's less than 1/4 point ABV per volume of CO₂ added at bottling time. As @rob said, that is negligible for my personal level of homebrew measurement precision.

To provide some math to back up @dmtaylor's answer, here's what I found:

From this thread https://www.homebrewersassociation.org/forum/index.php?topic=5882.0

100 grams of sugar in enough water to make 1 liter total gives you a solution that is 10% sugar. This corresponds to 10 brix, which is ~1.040.

From this article https://byo.com/article/master-the-action-carbonation/#:~:text=The%20amount%20of%20CO2,Temperature%20and%20Pressure%20(STP), I computed that 1 volume of CO₂ is 15.25 g sugar per gallon, which divided into 3.8 L, is approximately 4 g sugar per L of beer. Assuming that 4 g has negligible volume displacement, that gives me 0.4^oBx ~= 2 gravity points (1.002). At 100% Apparent Attenuation, that would give me about 0.25% ABV per volume of CO₂, or 0.5% ABV for a typical (for me) 2 volumes CO₂.

Combine that with this article about apparent attenuation https://beerandbrewing.com/everything-you-need-to-know-about-attenuation/ and typical attenuation around 70-80%, should give me <= 80% * 2 GP = 1.6 GP of fermentation.

According to this calculator https://www.brewersfriend.com/abv-calculator/ 1.002 -> 1.0004 gravity drop, I get up to 0.2% ABV per volume CO₂

Since that validates what @dmtaylor said, I'll consider that good enough math for now. If somebody can do the math from moles ethanol to points ABV, I'll be very happy.