Purging oxygen from headspace with sugar... check my maths

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passedpawn

call me satoshi
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I do pressure fermentation. However, for IPAs, I do open the fermentor and drop the hops in. Thus, I'd like to somehow purge the introduced O2. I know there's all sorts of methods and apparatus for this, but I have just been adding sugar and letting nature (yeast) do it for me. The question is, how much sugar should I add to ensure that the headspace is purged.

Here's my variables:
  • Pressure = 12psi over atmospheric (that's the cracking pressure of my spunging valve).
  • Volume = 3 gallons (I have a 8gal fermentor, and a 5g batch in it).
  • Temperature = 33F
Use ideal gas law to find the number of mols of CO2 in that headspace: PV=nRT

solving, I get n = 0.92 moles. That' how much CO2 I need for direct replacement of the headspace. Given the molecular weight of CO2 (22g per mol), I need 20 grams of CO2 created.

1 gram of sugar will result in about 0.5g of CO2. So, I need about 40 grams of sugar, or about 1/4 cup.

This is actually a dilution problem, with the associated differential equation. I could tackle that, but I don't remember diffEQ much. The number would be MUCH higher if I accepted the mixing issue. If anyone wants to do that and get me down under 1%, I'd be impressed.
 
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