# Co2 Formulae



## Aidan2727 (12/9/10)

Hello, 

Im after a fairly specific formulae; Ive had a good look on the internet but I cant find one, so was hoping someone in here could help me out. 

Basically, Im putting together a spreadsheet that will give me a very accurate calculation on how much of various sugars to use for priming beer in bottles. I found a table which displays the amount of CO2 left in the fermented beer after primary (green beer) and formulae to calculate how much sugar to add for priming. The formula takes in to account the amount of CO2 which is already present in the green beer after primary fermentation. The table and formulae can be found at the following website: http://www.brewery.org/library/YPrimerMH.html

Formulae = Subtract initial volume of CO2 in the green beer from desired CO2 level, then multiply this by 4 to give you the amount of cane sugar in grams per litre. You then add 15% if you are using corn sugar. 

Now this is all well and good; however, I would like to know what formulae is used here to calculate how much CO2 is present per litre of fermented beer according to fermentation temperature so that I can calculate how much priming sugar to use if I am fermenting at higher temps than 22 C. 

So apart from the formulae, I'm also hoping someone can answer this question as well; I understand that the volume of CO2 per litre is determined by the fermentation temp as this has something to do with how much the beer can hold at that temp. Im just wondering if the level of alcohol in the green beer would have any affect on this. What I mean is, I would assume that a higher alcohol beer would have produced more CO2 during fermentation, or is this irrelevant due to the fact that the beer can only hold a certain amount of CO2 at a given temperature and therefore amount of alcohol produced during fermentation would be irrelevant? 

Cheers, 
Aidan


----------



## MHB (12/9/10)

It's an interesting concept is carbonation. It's come up here regularly over the years and there have even been several spreadsheets that do pretty much what you're talking about.

Have a read of this: - Carbonation Tables and there is more information there on other pages.

Professional brewing has pretty much given up on the concept of "Volumes" and talks about g/L of CO2 which makes measuring easy. Degas the beer, lost weight is grams of CO2...

Now this is dredging up from deep in the memory banks so IIRC the definition of "1 Volume" is the amount of CO2 that stays in solution (equilibrium) at given temperature again IIFR it's the old version of STP around 15oC

Commercial draught beer is carbonated to something like 4.75 g/L, which can be very handy if you want to gas a keg (assuming that it's flat) 19.6 L at 4.75 g/L means 93 g of CO2. Lots of scales out there with the capacity and resolution to make it a matter of taring the scales then measuring the gas you put into the beer, I think its 1.97 g/L = one volume

Anyway have fun

MHB


----------



## MaltyHops (12/9/10)

Aidan2727 said:


> ...
> Now this is all well and good; however, I would like to know what formulae is used here to calculate how much CO2 is present per litre of fermented beer according to fermentation temperature so that I can calculate how much priming sugar to use if I am fermenting at higher temps than 22 C.
> 
> So apart from the formulae, I'm also hoping someone can answer this question as well; I understand that the volume of CO2 per litre is determined by the fermentation temp as this has something to do with how much the beer can hold at that temp. Im just wondering if the level of alcohol in the green beer would have any affect on this. What I mean is, I would assume that a higher alcohol beer would have produced more CO2 during fermentation, or is this irrelevant due to the fact that the beer can only hold a certain amount of CO2 at a given temperature and therefore amount of alcohol produced during fermentation would be irrelevant?
> ...


I'm not a boffin and assuming there's no chemical reason why alcohol helps to retain
CO2 in a liquid, the amount of dissolved CO2 doesn't depend on how much is produced
by ferment since CO2 is almost always allowed to escape pretty much freely through
an airlock so the main factor is the temperature the wort/beer is subject to.

What would also be good is to be able to provide a safety margin to allow for any
fermentable sugar that might be left in the beer - because the yeast has slowed right
down for instance. For example, if the beer calculators indicate that the final gravity
should be 1010 and the primary/secondary ferment seems to not want to get any lower
than 1015, then it would be good to know how much (in CO2 volume) that remaining 5
gravity units could generate and take this into account when figuring how much sugar
to prime with.

I guess a study of the various maths and chemical formulas could figure this out but
I'm worried about the migraine that might be caused by doing that.

This is probably only an issue for those who bottle in glass - and then only minor - but
anything that improves safety is good.

Tom


----------



## Aidan2727 (12/9/10)

Im not actually after the carbonation formulae for working out the carbonation level in bottled beer; Im trying to find the equation that tells you what the carbonation level of beer that has just finished fermenting, but not yet primed or kegged (green beer). The carbonation level depends on the temperature of the beer when it was fermenting. 

Anyone know the formulae?


----------



## MHB (12/9/10)

It's on the link I posted

Cbeer = (Phead+1.013)*(2.71828182845904^(-10.73797+(2617.25/(Tbeer+273.15))))*10

Just write the equation in excel and set the Phead to 0

MHB


----------



## Aidan2727 (12/9/10)

Thanks for the formulae, but now I am confused. These numbers don't match up to the table results from the website I posted earlier. If you compare the results, for instance, at 20 celcius with the table it says the CO2 volume is 0.88 where as the formulae says its 1.66. Thats a huge difference; so who's right???


----------



## MHB (13/9/10)

Have you got the units right?

Are you comparing Volumes and g/L by any chance, in which case the answers are pretty close.

MHB


----------



## MHB (13/9/10)

Yep just went and had a look, if you follow my link and look at the table for CO2 content in Volumes based on Fahrenheit and Psi, at 32oF it says 1.6 Vols, on the table you posted 1.7 Vols, most likely just a rounding discrepancy, at 60oF they both say 1 Vol
M


----------



## pcmfisher (13/9/10)

I thought the residual co2 is determined by the maximum temperature of your beer after fermentation has finished.


----------



## Aidan2727 (13/9/10)

We are getting close, I can feel it. You are correct regarding the two tables; however, I still can't get this formulae to work. I've punched in the following formulae into excel:

= ( 0 + 1.013 ) * ( 2.71828182845904 ^ ( -10.73797+ (2617.25/ ( 32 + 273.15)))) * 10

So Im testing at temperature 32 Fahrenheit, but it gives me 1.17 not 1.7

Can you see what I'm doing wrong?


----------



## MHB (13/9/10)

Do you mean apart from trying to work in irrational units.

The equation is in SI units, do it in metric then convert the answer to pounds, shillings and pennies or pecks and bushels if you like but FFS why would you want to work in anything but metric?

MHB

View attachment 40740

View attachment 40742


----------



## Aidan2727 (13/9/10)

I cant see how Im using irrational units. If I work at 20 C, using C units, I get this:

= ( 0 + 1.013 ) * ( 2.71828182845904 ^ ( -10.73797+ (2617.25/ ( 20 + 273.15)))) * 10

Which results in an answer of: 0.88

If I plug in Fahrenheit at 20 C, which equates to 68 F:

= ( 0 + 1.013 ) * ( 2.71828182845904 ^ ( -10.73797+ (2617.25/ ( 68 + 273.15)))) * 10

I get this:

0.47

Your calculation at 20 C works out basically the same as what Ive calculated using the formulae that you pointed me to. At 20 C Im getting 1.66. In the excel spreadsheet that you have linked to, you are getting 1.7 which is basically the same thing with a slight difference in rounding. 

The point that I am trying to make, is that the results from this formulae do not seem to match the results from the table at the website I posted earlier: http://www.brewery.org/library/YPrimerMH.html

This table says that the Volume of CO2 in green beer at 20 C should be 0.88. 

So, as I said earlier, which is right, the formulae or the table???


----------



## np1962 (13/9/10)

Just changing your Tbeer variable from C to F will not work.
The constants in the formula relate ONLY to temps in celcius therefore it won't work the way you are doing it.
The result is g/l not volumes.
I can see this and I am a humble builder. :lol: 
Cheers
Nige


----------



## MaltyHops (13/9/10)

MHB said:


> ]It's on the link I posted
> Cbeer = (Phead+1.013)*(2.71828182845904^(-10.73797+(2617.25/(Tbeer+273.15))))*10
> Just write the equation in excel and set the Phead to 0





Aidan2727 said:


> I cant see how Im using irrational units. If I work at 20 C, using C units, I get this:


Yes, I don't think simply changing the temp from C to F will work - the 273.15 value
relates to the 0 Celcius value in the Kelvin range (which has the same scale as Celcius,
ie. 1 C = 1 K in size, 0 C = +273.15 K and -273.15 C = 0 K ).

Fahrenheit however has a different scale to C and K hence the F to C conversion formula
is F = (9/5)C + 32 (ie. 1 F = (9/5) x 1 C)

Also the 1.013 value is probably a pressure constant in atmospheres or kilopascals
(SI unit) whereas the imperial pressure unit is psi (pounds per square inch).

So to do the calculations in imperial units, the formula would probably have different
values instead of the 1.013 and 273.15.


----------



## Aidan2727 (14/9/10)

I think theres been some confusion here; maybe I didnt explain myself properly. In any case, I wasnt reading the titles of those charts properly; not getting enough sleep lately. In any case, I worked out that if you just divide the results of the formula by 2.06 you will get the required results in volume. 

Cheers fellers


----------



## Newbiebrewer (14/9/10)

as for the last half of your post aidan, concentration of gas is directly proportional to pressure (double pressure= double concentration). With ethanol I am not exactly sure on how it affects water (very tired atm to lazy to research) but if it can effect the pressure of water then can effect the ability of water to saturate with Co2.


----------

