Ideal Gas Law help

I'm trying to design a micro kegging serving/carbonator system that uses 2L soda bottles. I want it to have a onboard CO2 gas reservoir that'll be refilled from a bulk tank w/ regulator, when you change/refill the soda bottle. I need a little help understanding/applying the Ideal Gas Law (or other if its the wrong one) to this situation.

Worst case, to carbonate:
So to carbonate water I need upto 4 volumes of CO2, meaning 8 liters
How many extra to completely serve the 2L of soda at upto 30 psi? another 8 liters?
Thinking 28in of 1in Sch 80 PVC (rated to 378psi max operating pressure, burst pressure is an insane 1440psi) in a U shape as my CO2 gas reservoir, meaning about 1/3 of a liter.
Filling reservoir will be done at say 78deg F ambient, then the whole thing will go into a (lets say) 38deg F fridge to do its thing.
How do I figure out the PSI to charge the reservoir to, to provide enough gas to carbonate & serve 2L at a regulated 30psi?

 

I'm think I understand what you're asking, but my knowledge on this is limited.

I would think you only need enough gas to charge(8L), serve(?), and have exactly 30psi left over(?) once it is empty.

The serve amount is, in my estimation, 4L at 30PSI @38dF. Boyles law tells us that to get that into .3L of space (assuming the same temp) we would need 400PSI. Since on an absolute scale 78dF is ~8% hotter than 38dF, it would take 432PSI? I'm guessing?

So 432PSI + (8L would be 864PSI then?) 864PSI = 1296PSI in .3L space? That seems like a lot... but you are only dealing with .3L. Plus you still need to add the 30PSI left over, so 30PSI at 38dF is 32PSI at 78dF.

Grand total of 1328 PSI. Thats nearly bursting your PVC! I admit that I could be WAAAY off, but it SEEMS correct... Sorry, wish I could be more help. It is an interesting question. I hope someone else can answer this with authority.

 

Actually now that I think about this more, my last post is probably wrong.

I think the fact that the water is absorbing CO2 changes the equations, plus I probably misapplied them.

Let's figure you are at your theoretical burst pressure of 1440PSI. 0.3L of space @78dF is the same as 40PSI in 10L (4 volumes of 2L plus 2L to push) of space at 38dF. We already know you want 30PSI, so... yeah I don't know. I still think it changes based on what the water absorbs.

I am pretty sure you will need a bigger reservoir, but I don't know how to calculate the ideal size.

 

Okay... one more idea.

1 ATM is 14.7 PSI.
We know you will need 8L at 14.7 PSI at 38dF. Plus 2L at 30 PSI at 38dF.
Adding these gives 5.92 L at 30 PSI (@ 38dF).
@78dF it is 5.92L at 32.4 PSI.
@.36L it is 532 PSI.

I don't know. No matter how I do the math you are still above your operating pressure for that volume of PVC. I think you would at least need to double it.

 

You have 8 L at STP, (that's how volumes of carbonation are defined), + 2L at 30 PSI and 38F.

Get everything into moles, it's easier:
There are 22.4 liters of gas per mole at STP. You need 8, so that's 8/22.4 = 0.36 moles. You need 2L at 30 PSI and 38F, (note, that's 30PSIG, not PSIA, so really 44.7 PSIA!!). 2L * 44.7 PSIA / 38°F / R = 0.27 moles more. A total of 0.63 moles.

Now you need to fit those moles into your 1/3 liter reservoir. When filling at 78*F:
0.63 moles * R * 78*F / 0.3333 liters = 46.3 atms, or 681 PSI.

When you cool it down, pressure will drop accordingly.

Why not just use a paintball CO2 tank? Fill with liquid from your bulk tank, don't worry about getting it exact, just have more than enough. You need 0.63 moles, or 27.7 grams, of CO2. Get a 7 or 9 oz paintball CO2 tank and you'll have MORE than enough for multiple carb/dispensing operations.

 

Interesting info here about CO2 physics - note the warnings about overfilling your tank.

http://www.warpig.com/paintball/technical/gasses/co2dynamics.shtml

 

Very cool! This was news to me:

 

THATS where I went wrong! (that and a couple... other... things...)

 

OP, I understand your design choices and applaud your efforts. However, I really have to discourage you in using PVC as a pressure vessel, regardless of the safety factors involved. Yes, you have a high theoretical burst pressure, but that's theoretical. joints, connections, and fittings all combine to reduce the strength of the vessel, and PVC had a tendency to make sharp-edged shrapnel when it ruptures -- not something you want to be standing next to.

Also, as PVC ages, it becomes more brittle (due mostly to oxidation of the polymer), so as your system ages and you get more confident (and complacent) in its use, it becomes more likely to suddenly rupture.

Have you considered something safer, like a copper or stainless steel tube?

 

I'm trying to understand the math but I'm just not getting your answer...
Temp should be in K, so 38F = 276.4833
According to DoomLabs - Science of CO2, R = 0.082 liter*atm/K, so 0.082 * 1 / 276.5 = 0.000296564
So 2 * 44.7 / 276.5 / 0.0003 = 1077.7577
Ya, I'm getting something or multiple somethings very wrong here.

1, was hoping to avoid putting a whole tank & HP Reg/Gauge setup in the fridge & to let my device use a cheap air compressor reg vs high $ HP reg.
2, don't like the higher cost of getting a PB tank refilled at sporting good store vs a bulk tank at welding supply (per unit of CO2) & especially don't want to make a family member (read mom) refill a PB tank from a bulk tank (I'm disabled, DMD w/vent or I would).

 

Yes, all those thoughts occurred to me (perfect joints required yet practically impossible for amateurs & no way to know what ya got and the aging / brittleness issues). Just thought I'd throw it out for comment.
Copper I haven't delved into yet
Black Pipe I found to be rated to only 150psi
Stainless = to expensive, like $22/ft for threaded 1in
Think best option for the gas reservoir is actually a PB tank, if I continue down the LowPressure gas only path.