Carbonation differences in bottles with varying temps

This is a carryover from another thread that had started to take a vastly different course than the OP's intention. Not necessarily off topic, but focused on just this one issue. So this is a space for us to follow up on the topic while not bothering that thread.

I'm going to summarize our assumptions and questions, and I hope others can provide the scientific take on them. For anyone involved in the last thread, please correct me if I've failed to describe our conversation properly, or if I've missed anything.

Assuming a fully carbonated bottle of beer, we discussed a few things:

-Does the temperature of the bottle (assuming consistent temp of everything inside, too) affect the ratio of CO2 in the beer versus the headspace, and if so how much?

-Do changes in temp over time have any noticeable affect on carbonation ratios, such that a beer stored for a significant time at one temp will behave differently from one brought to that same temp from a very different one?


Assuming two identical bottles of beer, one stored cold (say 45F or whatever) and one stored warm and then quickly chilled over less than a minute to 45F:

-Many observe differences in the way beers like this will behave when opened. What factors account for these differences, if there are in fact differences?

I think that covers everything. Did I miss anything?

I posted this which I started and didn't finish before I saw the new thread:

unionrdr said:

But in brewing,not the lab,time is relavent. Putting a beer in the freezer for an hour or a bit less will not give the same carbonation in a bottle of beer as it would during a week in the fridge. That's what I was talking about before regarding time vs sheer temp.

Click to expand...

So are there two different sets of scientific laws, one that applies to breweries and one to laboratories?

If there's a difference in time, why is that? What is going on in the fridge that makes the carbonation better, if this is the case?

I think JZ mentioned in an old podcast that during the lager phase, certain particles drop out that act as nucleation sites which decrease carbonation stability. This might also work in the bottle as these would be left in the bottom cake. (Chill haze dropping out has been mentioned).

I don't know enough of the science, but could time be a potential factor? Solubility change with temp, but the CO2 distribution doesn't instantly reach equilibrium. How long does it take to reach equilibrium, if there is a noticeable difference in how much CO2 will dissolve at different temps (maybe it is a small difference that really is negligible).

-Does the temperature of the bottle (assuming consistent temp of everything inside, too) affect the ratio of CO2 in the beer versus the headspace, and if so how much?

Yes, as temperature increases, vapor pressure also increases (meaning we get more CO2 in the headspace and less in the beer **edit: ignore this, it isn't true**).
http://www.kentchemistry.com/links/GasLaws/dalton.htm has a nice graph of this with water.
http://en.wikipedia.org/wiki/Carbon_dioxide_data#Liquid.2Fvapor_equilibrium_thermodynamic_data has a table specifically about CO2 vapor pressure at different temperatures.

-Do changes in temp over time have any noticeable affect on carbonation ratios, such that a beer stored for a significant time at one temp will behave differently from one brought to that same temp from a very different one?

assuming 2 identical bottles of beer:
The bottle stored at a given temp for a long period of time will have reached equilibrium in terms of dissolved CO2 whereas the beer that has changed temperature will need some time to reach equilibrium. If this second bottle is left at the temperature for sufficient time, the two bottles should be indistinguishable.Ignore most of this as well, the beer that changed temperature quickly does not 'need time to reach equilibrium' since it is already at equilibrium.


Assuming two identical bottles of beer, one stored cold (say 45F or whatever) and one stored warm and then quickly chilled over less than a minute to 45F:

-Many observe differences in the way beers like this will behave when opened. What factors account for these differences, if there are in fact differences?

Same principle as above.

jro238 said:

Yes, as temperature increases, vapor pressure also increases (meaning we get more CO2 in the headspace and less in the beer).
http://www.kentchemistry.com/links/GasLaws/dalton.htm has a nice graph of this with water.

Click to expand...

Yes, I'm with you that far. But as temperature increases, the solubility of gasses in the liquid portion of the bottle decreases. So the question becomes something to the effect of, for a closed system changing temperature, which force is able to overcome the other, the increased vapor pressure, or the decreased solubility of gasses in the liquid phase? Or is the difference negligible? I don't know enough to know how to model the process via standard equations.

So I had a very nice little writeup and then reread your post and realized that most of it wasn't really applicable. Oh well

What you are describing is the equilibrium state. At a given temperature, equilibrium is reached when the vapor pressure of the gas in solution equals the "atmospheric" pressure in the headspace of the bottle. The only points where one force will really 'overwhelm' the other is at the freezing point and at the boiling point.

So the question that remains in my mind (if the answer is above then I apologize for my ignorance and will go sit in a corner wearing a dunce cap) is this:

I understand there would probably be a differential equation based on the rate of temperature change and rate of change in CO2 solubility to give an accurate idea of how long it will take the 12oz bottle system to reach equilibrium, but to keep things simple, is there a way for us to determine the length of time until equilibrium is reached in an ideal situation like a bottle being instantly cooled from 70F to 45F? We could probably assume from that point that a bottle cooled reasonably quickly would reach that equilibrium state reasonably close to the calculated ideal, right?

jro238 said:

What you are describing is the equilibrium state. At a given temperature, equilibrium is reached when the vapor pressure of the gas in solution equals the "atmospheric" pressure in the headspace of the bottle. The only points where one force will really 'overwhelm' the other is at the freezing point and at the boiling point.

Click to expand...

Overwhelm is clearly the wrong word. What I'm getting at is this, and please correct me if I'm wrong:

1 - As temperature goes down, solubility of CO2 in water/beer goes up, so all things equal, in a bottled state, more CO2 will go into the beer.

2 - As temperature goes down, the pressure the CO2 in the gas phase exerts on the beer does down, hence more CO2 is likely to move to the headspace, all things equal.

3 - So as temperature goes down, these two forces work against one another (increased solubility, decreased gas pressure). So what is the net effect on the amount of CO2 in the beer versus the headspace?

I hope that clarifies my concern, or at least makes clear where my analysis does not fit reality. Does that make sense?

So if we determine there is an interesting difference in where the CO2 goes, then the question of time to reach equilibrium becomes interesting, as well.

The partial pressure of CO2 in a bottle is proportional to the absolute temperature. At equilibrium, the partial pressure in the headspace will be equal to the partial pressure in the beer.

When you put a beer in the fridge it cools and the pressure goes down. If it cools evenly then CO2 will not go from the beer to the headspace or vice versa.

I think any perceived difference in the head is due to cold crashing in the bottle. Small particles that would provide nucleation sites fall out of solution. The bubbles are smaller and the head retention is better when the beer has been cold for a while.

Wynne-R said:

The partial pressure of CO2 in a bottle is proportional to the absolute temperature. At equilibrium, the partial pressure in the headspace will be equal to the partial pressure in the beer.

Click to expand...

Right. I think I understand that. So far, so good.

Wynne-R said:

When you put a beer in the fridge it cools and the pressure goes down. If it cools evenly then CO2 will not go from the beer to the headspace or vice versa.

Click to expand...

That's what I thought, there would be little to no movement in CO2 from one phase to the other, but everyone outside of the Science forum seems to be saying otherwise. I thought this was true, but didn't have the ability to demonstrate it.

Wynne-R said:

I think any perceived difference in the head is due to cold crashing in the bottle. Small particles that would provide nucleation sites fall out of solution. The bubbles are smaller and the head retention is better when the beer has been cold for a while.

Click to expand...

This makes sense. I figured any perceived differences in behavior would be caused by something other than amount of CO2 in each phase. So would the size of the bubbles change over time once the beer is chilled, or if the difference due strictly to what encourages the change of phase (nucleation sites, etc.)?

Wynne-R said:

When you put a beer in the fridge it cools and the pressure goes down. If it cools evenly then CO2 will not go from the beer to the headspace or vice versa.

Click to expand...

Granted there are opposing forces - increased solubility tends to increase the CO2 in solution, and decreased head space pressure tends to decrease CO2 in solution. But how can we know that these two opposing forces are equal? It seems like it would be an amazing coincidence for these forces to exactly cancel each other, resulting in no more or less CO2 in solution.
Thoughts?

In physics, Henry's law is one of the gas laws formulated by William Henry in 1803. It states:

"At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid."

An equivalent way of stating the law is that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

Click to expand...

I kinda left that part out. Liquid/gas interactions are insanely complicated. Fortunately we don’t have to keep track of all that because we have Henry’s law.

Forget solubility. In a closed system it cancels out. As the temperature goes up, so does the pressure.

Wynne-R said:

Forget solubility. In a closed system it cancels out. As the temperature goes up, so does the pressure.

Click to expand...

Hold on. So in a closed system like a bottle, with a constant number of moles of CO2, are you saying that as temperature goes up, there will be more moles of CO2 dissolved in the beer than at a lower temp?

It sounds like since the system is closed, the CO2 won't switch phases. The reduced solubility is offset by the higher pressure in the headspace. No?

edit for me being stupid...i'll explain when I have a few minutes to type

Hold on. So in a closed system like a bottle, with a constant number of moles of CO2, are you saying that as temperature goes up, there will be more moles of CO2 dissolved in the beer than at a lower temp?

Click to expand...

No. How could that happen? The CO2 won’t go from the beer to the headspace if the pressures are equal. It can’t.

It’s not like putting sugar in your coffee, where there’s some chemistry involved. Pressure has almost nothing to do with it. If you add too much sugar it simply remains a solid and go to the bottom of the cup.

With gas in solution, there’s no chemistry. It’s physics, you are forcing the molecules to share the same space. It’s all about the pressure.

That's a bit of an oversimplification, but it's pretty close. Gases and liquids don't mix much.

OK, I didn't think that's what you meant, but that's how I read your earlier statement. I didn't see how it could be possible, either.

I still think we haven't fully addressed my question, but I'm probably just phrasing it poorly. When I have more time tonight, I'll fix that.

Ok. so now that I actually have time to type...

I did a very poor job of explaining in my first post and managed to get a few points wrong (at least for this specific case). I made the mistake of not thinking of the bottle as a closed system which was already in equilibrium.
As such, my entire point of having to wait for the example bottle that was instantly chilled to reach equilibrium at the new temperature isn't really correct. The instantly chilled bottle will be pretty much the same (in terms of physics at least) as the slowly chilled bottle as soon as they are at the same temperature.


Wynne-R is definitely correct. Once the gas in the bottle reaches equilibrium (following the completion of bottle carbonation), there will be no net movement of CO2 between the head space and liquid. Molecules of CO2 will always be moving back and fourth between the two phases BUT they will always be moving in a 1:1 ratio. This fact is independent of temperature. For this reason, solubility isn't really an issue here.

So the upshot is there should be no difference (other things being equal) in carbonation level between a warm bottle, a bottle that was quickly chilled, and a bottle that has been chilled for a long time, correct?

If there is a perceived difference between, say, bottles of the same batch which have been cooled for a long time versus ones that have been cooled for a short time, it will be because of factors other than amount of CO2 dissolved within the beer. Is that also correct?

GuldTuborg said:

So the upshot is there should be no difference (other things being equal) in carbonation level between a warm bottle, a bottle that was quickly chilled, and a bottle that has been chilled for a long time, correct?

If there is a perceived difference between, say, bottles of the same batch which have been cooled for a long time versus ones that have been cooled for a short time, it will be because of factors other than amount of CO2 dissolved within the beer. Is that also correct?

Click to expand...

As long as the bottles remain a closed system, then yes (for the warm vs cold).

As soon as you pop that cap though, the answer is no. Because the partial pressure of the dissolved gas will be higher at higher temperatures, the second the cap is opened and the headspace pressure rapidly decreases, the higher temperature beer will lose more CO2 out of solution than would a cold beer (this is why you hear a much louder pffft sound when you open a warm beer and why you chill over carbonated bottles to reduce excessive foam when opening).

For the long-chilled bottle and the fast chilled bottle though, the answer should be yes.

I do think, however, that the true answer is a little more complex than this and probably does have to do with the setting of small particles or other minor changes that occur when the beer is kept cold for extended periods.

Good, I think that's what I was after. I'm glad we seem to have cleared it up, and I'm glad my suspicions were correct. While I'm sure there are differences in either case, it's also good to know to what we can attribute them. Or, at least we know one thing to which we can not attribute them.

Thanks, all.

This was informative. I also like the statement about everyone outside of the science forum being wrong. I can think of a few 'senior' posters/members whose words are taken as Gospel yet who don't seem to make much sense on these sorts of issues.

The lesson here seems to be that (assuming the effects of fridge time have to do with small particles) you can lager/cold crash in bulk and therefore not need to have bottles in thefridge for a week before drinking.