Beer Math!

I was mentally noodling with the idea of CO2 and brewing, and I came to wonder how much Carbon Dioxide a typical batch of beer puts out during fermentation.

I did my own math, and I came up with about 783 grams for a 5.5% ABV beer.

Has anyone else done the calculation? Does anyone want to check my work?

The math looks good to me. This is awesome, thanks!

Nice!

I like it! Although it brings back horrible memories of chemistry classes in college. Why couldn't they talk about beer instead of the boring stuff..

It's so funny being in a Biology class now that I'm into brewing. Hydrolysis of polymers? Yeah, that's the mash. Anaerobic cellular respiration? Yeah, that's fermentation.

All I had to do was relate the info to beer, and I was all set

******** is a bad word here.

what?

Interesting idea, but the actual amount is probably higher(maybe only slightly).

The only assumption that you made that may overlook a significant contribution is that all of the co2 is generated from anaerobic fermentation.Some co2 would be generated from aerobic fermentation while the yeast multiply/ use the o2 present from aeration.

As I recall (for glucose, not sure how the chemistry would change for maltose) aerobic fermentation produces 6mol co2 per mol of sugar as apposed to anaerobic which produces 2mol co2 per mol of sugar.

With the levels of o2 dissolved in the wort, this amount of co2 may be insignificant. If you feel like investigating further it could be interesting to compare the co2 contributions.

This is why I always tell people about how brewing satisfies both my creative *and* scientific sides!!! I love that there are a bunch of other geeky people out there brewing!!!

Here's the empirical equation:

2.0665g of fermentable extract -> 1 g of ethanol + 0.9565g of CO2 + 0.11g of losses."

SuperBreeze said:

Interesting idea, but the actual amount is probably higher(maybe only slightly).

The only assumption that you made that may overlook a significant contribution is that all of the co2 is generated from anaerobic fermentation.Some co2 would be generated from aerobic fermentation while the yeast multiply/ use the o2 present from aeration.

As I recall (for glucose, not sure how the chemistry would change for maltose) aerobic fermentation produces 6mol co2 per mol of sugar as apposed to anaerobic which produces 2mol co2 per mol of sugar.

With the levels of o2 dissolved in the wort, this amount of co2 may be insignificant. If you feel like investigating further it could be interesting to compare the co2 contributions.

Click to expand...

true but you get the other 4 mol of co2 after the alcohol is consumed/decomposed

Nice work! Takes me back to the many chem classes I have had. That being said I can't proof your math much because my last classes were Biochem!

NyQuil_Driver said:

It's so funny being in a Biology class now that I'm into brewing. Hydrolysis of polymers? Yeah, that's the mash. Anaerobic cellular respiration? Yeah, that's fermentation.

All I had to do was relate the info to beer, and I was all set

Click to expand...

Anerobic cellular respiration is NOT fermentation! Anerobic respiration still utilizes electron transport like aerobic respiration, but uses a different terminal electron acceptor than O2. ATP can then be made in a number of ways through gradient flow of H+ ion across the cellular membrane.

Fermentation is the process of generating ATP via oxidant/reductant(ie. NAD+/NADH) equilibration. The electron acceptor in this case is usually an organic molecule known as an electron sink(ie. Ethanol). Also fermentation doesn't usually involve the cell membrane to produce ATP. Fermentation usually results in smaller quantities of ATP produced vs Cellular Respiration. That being said that means more secondary metabolites are produced, which is beneficial in the case of the brewer cause that means your brew becomes chalk full of alcohol.

JKoravos said:

Here's the empirical equation:

2.0665g of fermentable extract -> 1 g of ethanol + 0.9565g of CO2 + 0.11g of losses."

Click to expand...

OK, I'll do it.

1 gallon of beer with 1% alcohol.

3.785 Liters, .03785 liters of alcohol

.03785 L x .789 kg/L = 29.9 g EtOH/gallon-%ABV

29.9 x .9565 g CO2/g EtOH = 28.6 g CO2/gallon-%ABV

Use ideal gas law: 22.4 L/mol at ATM

22.4L/mol x 28.6 g/44.01g/mol = 14.5 L CO2/gal-%ABV

Volume of CO2 per batch of beer: 14.5*Vbeer*ABV

i.e. 5 gallons of 5.5% beer

14.5 x 5 x 5.5 = 398.8 L of CO2

pv=Mrt

M=pv/rt

M=(100*398.8)/(178.9*293)

M=773.3g

I've been doing this for quite a while now...

https://www.homebrewtalk.com/f11/weight-based-gravity-measurement-88821/

And yep, a 5% beer will lose about 755g as it ferments. (some will stay in solution making up for the other 28g of CO2)

Ideal-gas approximation for CO2 isn't particularly good at STP:

398.8 L * 1.815 g/L = 723.8 g

So basically, making huge ammounts of beer causes global warming... I hate Inbev

Four different posts from Indiana... wow. Is this a sign?

Four people from Indiana who can do math? A sign of the apocalypse, maybe.

oldschool said:

So basically, making huge ammounts of beer causes global warming... I hate Inbev

Click to expand...

Let's not get talking about global climate change. Conversation on both sides of the issue tends to get way too heated (BaDump-Pshhhh!) for the "Beer Discussion" forum.

but really makeing beer does not make co2, the decomposition of grain makes CO2 the same amount of gas would be made if the barley was alowed to rot in the field.

a10t2 said:

Four people from Indiana who can do math? A sign of the apocalypse, maybe.

Click to expand...

Speaking of the apocalypse, I've been wondering how I can pressurize (for serving) my kegs if/when I can't buy CO2. So it seems that 10 gal of beer ~= 5 lb tank of CO2. So we just need a practical DIY way to capture and pressurize the CO2 given off, and we can keep drinking kegged beer (forgetting of course where we'll get barley & hops and keep the fridge cold).