mooface

Recipes 

Hi,

I'm trying to answer 2 questions:
- how much gas will be produced during fermentation
- what would the pressure be in a 5g corny if used as primary fermenter will NO VENTING

I tried to calculate this, but the number is absurdly low. What did I do wrong?

CALCULATION:
-- Assume 5.5 ABV% in 5 gallons yields 1.041L of ethanol (EtOH).
-- 1.041L EtOH * (789 g / L) = 821 g EtOH
-- 821 g EtOH / (46.07 g / mole) = 17.82 moles EtOH
-- Yeast metabolism fermentation RXN: C6H12O6 → 2 CH3CH2OH + 2 CO2.
-- Therefore Ethanol to CO2 ratio is 1:1 = 17.82 moles CO2
-- 17.82 mole CO2 * (44.010 g/ mol) = 784 g CO2
-- 784 g CO2 / (1.977 g/L) = 396 L CO2 (at 0 deg C) (not used)
-- "Confined to 1L headspace: P = 17.82 **8.314472 * 273.15 / 1L = 40470 Pa
-- 40470 Pa = 5 PSI

jgourd

Recipes 

I can see a use for such a calculation! Maybe the government will cap how much beer we can make (at least lower than it is now) so that we don't harm the environment by pumping CO2 into the atmosphere. I mean what if all the beer makers of the world are the cause for global warming!

broadbill

Recipes 

The problem is that the rate of fermentation is going to slow as the pressure inside of the vessel increases.

Synovia

Recipes 

1) Why are we doing this calc at 0 Celsius?

You're going to be fermenting at say 20C (68f?), so we're looking at ~44K Pa. which would be 6.4 or so PSI.




I still think something is wrong here. The guys fermenting in closed vessels (check the fermentation in cornies thread) are using the last couple points to carb beer. One guy kept a sealed corny and IIRC< it was at like 60 psi.

Maybe we're missing CO2 being released when the yeast cleave larger sugars into smaller ones?

HairyDogBrewing

Recipes 

Volume should be cubic meters, not liters.
Multiply your answer by 1000.

http://www.chemicool.com/idealgas.html

AiredAle

Recipes 

You are right, 5 psi is a bit low. Here’s how I’d estimate it:

Assume an empty corny as this will make it easier, corny volume is 19 liters (5gal X 3.78 l/gal).

Assume about 800 grams CO2 produced, your pretty close, I recall 49% of fermentables are turned into CO2.

So, 800 g CO2 equals 18.2 moles CO2 (44 g per mole CO2)

At standard temperature and pressure 1 mole of any gas is 22.4 liters (STP is 1 atmosphere, 14.7 psi, at 0 degrees C.

So, 18.2 moles CO2 is 408 liters at STP (18.2 X 22.4).

To convert to 19 liters, use the old P1V1 = P2V2 equation, where
P1 = 14.7 psi, V1 = 408 liters, P2 is the unknown, and V2 is 19 liters

Solve the equation for P2, P1V1/V2 = 14.7 X 408 / 19 = 315 psi, at 0 C, will be higher at room temp.

So that’s your answer for putting all that CO2 into an empty corny, with it filled with fermented beer, I have no idea. I would assume it will be higher, but I don’t have any idea what the maximum solubility of CO2 is in beer, so I can’t really say. Of course, the pressure relief valve on a corny is supposed to blow at 130 psi, so maybe that’s the real answer.

Pivovar_Koucky

Recipes 

You can't do this calculation very easily without some fancy differential equations. The problem is that CO2 will become more soluble as the pressure increases (Henry's Law) and as the solubility increases, the marginal pressure contribution of each additional molecule of CO2 becomes less. At some point it will turn into carbonic acid and the pH will drop and that will affect the solubility. But then some of the carbonic acid will turn into bicarbonate and the solution will buffer itself. All in all you are talking about a very involved problem here.

If you use the combined gas law instead of Boyle's law and assume no solubility of CO2 and 1L of headspace:

P1*V1/T1=P2*V2/T2
or:
P2=P1*V1*T2/(V2*T1)=14.7 PSI*408 L*298.15 K/(1 L * 273.15 K)=~6500 PSI

so HairyDog was about right.