What is the Correct Pressure of CO2 Gas Required to Carbonate 5 Gallons of Beer?

[Gremlyn1]

Hi all, I'm a home brewer and microbiologist by training, so I have taken a fair amount of physics and chemistry (wasn't sure if gas laws were more physics or chemistry related, so hopefully this is in the right section) but my memory of dealing with gases is not the clearest, so I'd like some help checking my math.

A fellow home brewer recently proposed carbonating the beer by adding all the CO2 we would need to carbonate 5 gallons of beer in one concentrated shot of gas to the keg and what was curious what the pressure of CO2 gas required to do so would be. We use 'volumes of CO2' when talking about how much CO2 we want in the beer, and 1 volume of CO2 is defined as 1 L of CO2 per 1L of beer at STP.

Say I have a keg with an internal volume of 5.5 gal (20.82 L) and it contains 5 gal (18.93 L) of beer. This leaves 0.5 gal (1.89 L) of head space above the beer to be filled by the requisite amount of CO2. I started out trying to determine the needed amount of gas by figuring out that 2.25 vol of CO2 for 5 gal of beer is 42.59 L of CO2 at STP. Given that I need to cram 42.59 L of CO2 into half a gallon's worth of space, I went to the old standby, P1V1 = P2V2. This resulted in 331 psi, and this is most assuredly greater than the max pressure our kegs can hold (something like 120 psi). Luckily, we don't store and server from the kegs at room temp, we chill the kegs into the upper 30's or 40's before carbonating. But this is where my math and theory get fuzzy...

The gas itself is kept at room temp, but the beer is not. When we determine the pressure needed, we consult a chart such as this one. This chart uses the temperature of the beer cross referenced with a pressure to give you the appropriate volumes you will achieve once equilibrium is reached, which makes me believe when trying to figure out my problem above that I should use the temperature of the beer. I used this assumption and tried setting two ideal gas law equations equal to each other, and initially got a result that seemed reasonable when I plugged in something like 43F (got about 85 psi), but then if I plugged in 33F I got only about 7 psi so I decided I must have done it wrong. I'm not entirely sure if setting the two ideal gas laws equal to each other is a legit method or not, so I came here to ask for some help.

PS: Sorry that was kind of long, but I couldn't pare it down any more and get all the info across!

 

[Curl]

For the ideal gas relation you need to use absolute temperature. Degrees fahrenheit are an abomination.

If you want to know how much CO2 you dissolve in the water, look up Henry's Law (not really a law just a result). It's all about the partial pressure of CO2 and the change Gibbs free energy in going from gas to aqueous.

 

[Gremlyn1]

Oh, right how could I forget about using K. I dislike Fahrenheit as well, but all the US based brewer use it :( I did convert everything to Celsius when doing my calculations, but that still wouldn't have been right!

I wasn't sure if I would need to get into partial pressure, but I thinking more about t I guess so. Calculating the amount of gas needed to fit into the head space doesn't necessarily require it, but if I put the amount of CO2 into the headspace that would yield 2.25 vol of CO2 when dissolved in the liquid, I guess I am not account for the CO2 not absorbed and remains in the head space once equilibrium is achieved. So I will have to figure out the total gas needed by finding the partial pressure of the amount I want dissolved and see what's left above... thanks!

 

[kfh]

Funny you mention this, I have the same hobby and contemplated the same problem. I wanted to carbonate some beverages, but I did not want to buy expensive equipment to do so. Thinking on this for a short while, it came to me that dry ice is just solid CO2 and I could add a piece of dry ice to a sealed bottle, it would sublimate to a gas and create the necessary pressure to carbonate the liquid.

After toiling with PV=nRT, various charts, etc I arrived at a way to figure how much dry ice, in grams, I would need for a specified volume. As mentioned above, you need to use Kelvin or the equation will not work. Also as mentioned above, you will ONLY be working with partial pressure of co2. You could pressurize your vessel to 10,000psi with air and it would not change how much CO2 is dissolved in it at all.

I was working with 1/2 gallon growlers and I came to the conclusion I would need 5 grams of dry ice to produce about 3 volumes of carbonation when the liquid was refrigerated.

I made up a pressure gauge that would fit the bottle, filled it with about an inch of headspace, measured the 5g of dry ice, dropped it in and capped it. Within a few seconds, pressure spiked to dangerous levels and I quickly uncapped it. What I had not taken into account was the time required for the CO2 to actually dissolve in the liquid. It will sublimate quickly, but dissolve slowly, so all of the gas simply rises to the headspace and creates a great deal of pressure, until it finally all dissolves and reaches equilibrium at a lower pressure (this would take several days).

I was stumped because I did not have a vessel capable of withstanding that amount of pressure. If you just increase headspace to decrease initial pressure, your final (equilibrium) pressure would be undesirably low (not enough volumes dissolved) so you would need more CO2 and you would be back to the start again. The trick was to find a way to increase the rate at which CO2 would dissolve, so it was back to research. I discovered (via Google) that the rate of dissolution was based (primarily) on surface area of the co2/liquid interface. In short, if you shake it up and make the CO2 become many many small bubbles you will have a tremendous surface area and it will dissolve quickly.

I tried it again, this time vigorously shaking the jug while the dry ice was sublimating, and astonishingly it worked quite well!

I am unsure if you will be doing it this way or obtaining the CO2 in some other way (compressed liquid in a tank, perhaps). If you elaborate a bit more perhaps I can help. Give me a few minutes and I will calculate some things for you based on your above numbers.

 

[Gremlyn1]

I am using compressed CO2 in a tank and cornelius (soda) kegs. From my revisited math, it's looking unlikely that this is even possible, as I'm getting a few hundred psi, which is well above the level of safety for the kegs.

 

[kfh]

Well I can't seem to find my notebook, sorry, but essentially you are on the right track with everything. Your calculation of the requisite number of volumes seems right, and your assumption to use the beer temperature is also correct (since the gas will quickly cool to that temperature and not affect the overall temp noticeably).

So you have a vessel of volume 20.82L, and will be introducing 42.59L of co2. _Before it dissolves_ (reaches equilibrium), you will have almost all of this 42.59L residing in the headspace of 1.89L, making an unacceptable amount of pressure. Once it reaches equilibrium (it is all dissolved), much of the CO2 will reside in the liquid with a small amount remaining in the headspace, giving you measurable pressure. This is determined by the chart, essentially.

The ability of a liquid to dissolve CO2 is determined by temperature and pressure. At a given temperature, the liquid will accept only so much carbonation, as you know. When you introduce _all_ of the co2, suddenly the pressure (partial pressure of co2) over the liquid is tremendous and its ability to dissolve it increases. As it dissolves so, the pressure over it drops until it eventually reaches a point where the pressure above can allow no more dissolution- you have reached equilibrium.

Essentially you are in the same boat as I was, the time it takes to dissolve the CO2 is too long and so you will have too much gaseous CO2 residing in the headspace, thus making too much pressure for the vessel. Your options are to introduce CO2 more slowly, obtain a vessel rated for this pressure, or increase the rate of CO2 dissolution (aka, shake it).

However, as I mentioned, I am not sure how you plan to measure and deliver the CO2 so this will affect your options. I'm always interested in other options and ways of doing things, so do let me know what you're up to and keep me posted ;) I'll try to help you out if i can.EDIT: Saw you just posted while I was writing this...

 

[Gremlyn1]

Yeah, I figured it wouldn't be easily feasible to do, but fun to figure out all the same :) I have a dual regulator setup connected to my CO2 tank. If I need to carb quickly, I crank the regulator up to 30 psi and shake it a bit, and drop the pressure down to serving and then check it over the course of a day or two to see if it has reached equilibrium with the serving pressure. Otherwise, I just set the keg in the fridge and forget about it for a few week...

 

[kfh]

Yeah from my experiences that's pretty much the best way to do it. But being scientifically minded and the DIY type, I like to figure it all out too ;) Fun stuff.

 

[Wera90]

i do know that it is much easier and faster to inject CO2. In order to properly keg beer in either case it's necessary at least inject enough CO2 to seat the lid to prevent leakage. Good luck)