# Dose Carbing: CO_{2} generation from sugar sources

In last issue’s column we went over the factors to consider when force carbonating beer. This month I would like to expand that knowledge by adding sugar as a tool to use for carbonation. While reading this upcoming column it may seem more difficult, but many brewers find the flavor changes natural carbonation creates make the effort to learn these processes worthwhile. Mastering your math will help you master your CO_{2}.

We have many sources of sugar we can use. We can buy glucose (dextrose or corn sugar), maltose, sucrose, and dried malt extract, to name just a few sources of sugar. We can save some wort from our brew day and freeze it till needed, brew a wort specifically to add for priming, we can simply repurpose a little wort on a brew day, we can take a beer that is still in active fermentation and add it to the beer we want to carbonate, or we can cap the beer at just the right time to hit our desired CO_{2}. No matter which method you choose, all of these methods use yeast to convert sugars to CO_{2}.

Many readers will see an equation and skip reading it to get to the conclusion. As a reader I have been guilty of this. As an author I struggle as to whether to include an equation or not. In “Advanced Brewing” the equations are important. In calculating how much sugar to add we need to understand how chemistry equations and the concept of molar mass work. If you’re already well-versed in chemistry, feel free to skip to the end of this next section.

#### Periodic Primer

The periodic chart of elements hung in every science class I ever took, but it wasn’t until I needed chemistry that I bothered to learn how it worked. To work through this missive we only will need to understand two key concepts of the chemistry world: Atomic mass and molar mass.

. . . many brewers find the flavor changes natural carbonation creates make the effort to learn these processes worthwhile.

The atomic mass is the number of protons and neutrons in an atom. If all isotopes of elements had the same number of neutrons this number would always be a whole number. Here we are going to use the actual atomic mass of the natural blend isotopes found on planet Earth. As an example, most carbon (C) has 6 protons and 6 neutrons (written as ^{12}C because 6 + 6 = 12) and we can use the atomic weight of 12. However, ^{13}C (6 protons and 7 neutrons) is also stable and is present, as well as other isotopes that decay over time (carbon dating sound familiar?), the actual value of the atomic weight of C to be precise is 12.011 and accounts for the extra isotopes found in any given Earth-bound samples.

The molar mass is defined as the weight of 1 mole of molecules of the molecule in question. The number that defines what a mole is is fairly abstract and a very large number. But a mole is defined as the number of ^{12}C molecules in 12.011 grams. This turns out to be 6.022×10^{23}, also known as Avogadro’s number. When we see the molecule H_{2}O it means that it takes a ratio of 2 moles of hydrogen to bind with 1 mole of oxygen to make water. Or, restated, 2.016 grams of hydrogen and 15.999 grams of oxygen combine to make 18.015 grams of water.

In terms of brewing and creating carbonation we are talking about CO_{2} and sugars. So let’s look at a few relevant “molar mass” examples. Molar mass is the weight, in grams, of a specific atom or molecule to get one mole. Let’s start with CO_{2} and glucose, we will expand this to other sugars later.

CO_{2} is one carbon and two oxygens, looking at a periodic chart we find that carbon’s atomic mass is 12.011 and oxygen is 15.999. So the molar mass of CO_{2} is (12.011 + 2 x 15.999 = 44.009). Glucose is C_{6}H_{12}O_{6}. (12.011 x 6 + 1.008 x 12 + 15.999 x 6 = 180.156). We don’t get to see glucose as pure glucose because it rapidly picks up water from the air and clumps. So when we purchase a bag of corn sugar, what we are actually getting is called glucose monohydrate or more precisely C_{6}H_{12}O_{6} • H_{2}O.

We are also going to need these:

Molar mass of sucrose C_{12}H_{22}O_{11} = 342.3

Molar mass of maltose C_{12}H_{22}O_{11} = 342.3 (Note, this is made from the same atoms but simply structured differently than sucrose)

Molar mass of ethanol C_{2}H_{6}O = 46.1

For all you chemistry geeks out there: Why was the mole of oxygen molecules excited when he left the singles bar? He got Avogadro’s number! If you don’t get it, don’t worry. Moving on . . .

#### Sugar Dose Rates

Now that we know enough chemistry to be dangerous we can look at carbonating a beer. The first thing we must remember is the CO_{2} level of a fermented beer is not 0. It is lower than we typically want, but if we know the exact CO_{2} level then we can make a precise sugar addition to bump the CO_{2} up to our desired level. The easiest way to measure the CO_{2} level in homebrewing is take the fermentation temperature and look it up on a residual CO_{2} chart. This is a rough estimate at best and the actual value is often a little higher because the beer likely has not had time to reach equilibrium with atmospheric pressure. Another approach to read residual sugar is to transfer the beer into a keg then hook a pressure gauge to the beverage-out fitting and shake the keg. While a beer is fermenting, solution becomes super saturated with CO_{2}. If you measure the CO_{2} at the end of gravity change, it will still be supersaturated. This CO_{2} will off-gas over the next few days. The reason this is important is you can over-carbonate if you simply use the residual CO_{2} chart without measuring if you are pushing close to the end of fermentation.

As an example, if we measure (or guess) 1.1 volumes of CO_{2} left over from fermentation and we want 2.8 volumes in the final packaged beer, that means we need enough sugar to create 1.7 volumes of CO_{2}. Now, this math is easier to do in grams/liter — there is a reason science uses metrics. So we will work in grams per liter and then you can convert from there if you so desire.

1 volume of CO_{2} = 1.97 grams per liter (The weight of gaseous CO_{2} at 1 bar of pressure in 1 liter of space.)

Since we need 1.7 volumes of CO_{2} to move from 1.1 to 2.8 volumes in our beer, we first need to convert the volumes to g/L based on the numbers above. Once we are in g/L we then solve for the total grams needed based on the volume of beer we are carbonated. So let’s say we’re carbonating a beer in a standard corny keg, which is 5 gallons or 18.9 liters.

18.9 L x 1.7 volumes x 1.97 g/L = 63.4 g of CO_{2}

There are many ways we can use yeast to create CO_{2}. The simplest is to add some glucose to the beer, hold it at room temperature and let it do its magic. How do we sort out how much sugar to add? Back to the first section we go.

As we found out earlier, one mole of glucose is 198 grams [molar mass of glucose = 180 g/mol + molar mass of water = 18 g/mol]. Yeast will ferment the glucose and store energy in the form of ATP leaving ethyl alcohol (ethanol) and CO_{2}. It does so following this equation

C_{6}H_{12}O_{6} • H_{2}O → 2(C_{2}H_{6}O) + 2(CO_{2}) + 2ATP + H_{2}O

The key with this equation is that one mole of glucose when fermented will create 2 moles of ethanol and 2 moles of CO_{2}. In other words, 198 grams of glucose makes 88 grams of CO_{2}. Another way to look at this is that 51% of the weight of glucose will be fermented into CO_{2} (88 / 198 = 0.51). Since we only need 63.4 grams of CO_{2} for our example we don’t need a full mole of glucose monohydrate. Instead we calculate the following:

63.4 g / 92.12 g/mol = 0.72 moles of CO_{2} needed for 1.7 volumes

0.72 moles x 198 g/mol = 142 grams of glucose monohydrate to carbonate our keg.

If we use sucrose (table sugar) or maltose (good luck finding it), we simply need to follow the same logic to generate our new numbers. Creating a spreadsheet can be handy device to perform these calculations for you.

Total Fermentable Sugars in an average wort (83.5%)

Maltose (40.43%) C_{12}H_{22}O_{11}[aq]→ 4(C_{2}H_{6}O) + 4(CO_{2}) + ATP

Glucose (20.6%) C_{6}H_{12}O_{6}[aq]→ 2(C_{2}H_{6}O) + 2(CO_{2}) + ATP

Maltotriose (16.6%) C_{18}H_{32}O_{16}[aq]→ 6(C_{2}H_{6}O) + 6(CO_{2}) + ATP (*Not all yeasts can ferment maltotriose)

Fructose (1.7%) C_{6}H_{12}O_{6}[aq]→ 2(C_{2}H_{6}O) + 2(CO_{2}) + ATP

Sucrose (1.5%) C_{12}H_{22}O_{11}[aq]→ 4(C_{2}H_{6}O) + 4(CO_{2}) + ATP

Isomaltos (1.3%) C_{12}H_{22}O_{11}[aq]→ 4(C_{2}H_{6}O) + 4(CO_{2}) + ATP

We can also use dried malt extract (DME). Briess Pilsner DME is cited to be 75% fermentable by standard brewer’s yeast as an example. If we divide the molar mass of CO_{2} by the molar mass of fermentable sugars in wort and weight the answers by wort composition we find that 51% of wort sugars added are converted to CO_{2}. Removing maltotriose from our average only changes the result by 0.002% so we can use one constant for every yeast. So the equation for using DME comes out to look like:

1 g DME x 0.51 x 0.75 = 0.375 grams of CO_{2} produced

Comparing this to the glucose monohydrate above, a given weight of DME will end up as 37.5% CO_{2} while a given weight of glucose ends up as 51% CO_{2}. This implies you need about 1.36 times more DME than if you were using corn sugar for priming.

#### Delving Deep

Most brewers stop after here and don’t look at other sugar sources. However, the advanced brewer will want to understand how to use any wort-derived sugar source. Many brewers perceive there to be a flavor advantage in using wort or partially fermented beer as a source of sugar to generate CO_{2}. This is where our math can really come in handy. We are going to run through some examples, the first is if we were to store wort from our brew day in the freezer or use fresh wort from the brewhouse on the day we need to carbonate and use it at end of fermentation to carbonate.

We are going to work in °Plato. If you only measure in standard gravity (SG) I will provide two equations to convert over to Plato (where most brewing equations are derived from since it is measuring the ratio of water-to-sugar). The first conversion formula is for normal day-to-day use. The second conversion equation is slightly more precise at high-gravity readings:

°P = [(SG – 1) x 1000] / 4 or °P = Gravity Points / 4

°P = (-1 x 616.868) + (1111.14 x SG) – (630.272 x SG^{2}) + (135.997 x SG^{3})

We always measure the original gravity (OG) and the final gravity (FG) of our batches of beer (I hope). Again, despite being called OG and FG, these readings are in °Plato.

Apparent Extract (AE) = OG – FG

This gives us an idea of how much sugar was consumed by the yeast but the numbers we really need for our calculations are the Real Extract (RE) and the Real Degree of Fermentation (RDF). Developing a spreadsheet to generate these numbers for you is simple and helpful.

Accounting for the weight of alcohol to differentiate it from AE, the Real Extract can be solved for using the common equation:

RE = (0.1808 x OG) + (0.8192 x FG)

The Apparent Degree of Fermentation (ADF) is also known as apparent attenuation in some circles. Note this will often be found in percent.

ADF = OG x AE/OG

This is useful to compare different fermentations, like when performing yeast trials or during recipe adjustments. However, the RDF is what we really need when calculating out more exact numbers (like for kräusening), and is sometimes referred to as real attenuation in some circles.

RDF = [100 x (OG – RE) / OG] x [1 / (1 – 0.001561 x RE)]

The correction of 0.001561 was created to allow for the creation of CO_{2}. These equations tell us everything we need to understand how much CO_{2} we can create with our wort (among other things).

#### Advanced Dose Rates

In order to use wort to carbonate your beer, the equation we need looks a lot like the DME equation from page 99, but we have to account for the water dilution factor in wort.

CO_{2} from a gram of wort = 0.5055 x RDF x (OG / 100)

Since Plato is simply a measure of percent sugar by weight dissolved in water, we can easily solve for CO_{2} evolution from almost any given wort with the gravity reading. When we merge all of these equations we get wort needed.

Liters_{wort} = [(CO_{2desired} – CO_{2measured}) x 1.969 x Liters_{beer}] / [0.5055 x RDF x (OG / 100)].

We have other options as well! What if we want to add a different wort that is fermenting (kräusening)? We logged the OG (of course!), we’ll have to estimate the FG and we need the current gravity. With this information we can calculate how much sugar we have left in the fermentation. We should know the expected final gravity from having brewed before or we can estimate from what data we have on the yeast like the typical RDF and the OG. So if we swap out the RDF x (OG / 100) part of our equation with (Current Gravity – FG_{expected}) / 100, then we have adapted the unfermented wort equation to a fermenting wort or kräusening formula.

Liters_{kräusen} = [(CO_{2desired} – CO_{2measured}) x 1.969 x Liters_{beer}] / 0.5055 x [(CG – FG_{expected}) / 100].

Now this equation is looking interesting!

What if we want to cap off or bottle the fermentation early? (Before you try this without a spunding valve, become very familiar with the process. You don’t want bottle bombs.) We can rearrange this equation with a little effort. Remember that now the Liters_{kräusen} / Liters_{beer} = 1.

FG_{capping} = [100 / (CO_{2desired} – CO_{2measured}) x 1.969 x 0.5055] + FG

It should be noted that this entire math exercise assumes that no CO_{2} is lost to headspace and if you have a large head-space you will need to account for the CO_{2} lost to pressurize it. (Hint: We have assumed the volume of beer = the volume of the tank.)

I hope this gives you some ideas and tools to work out the perfect carbonation level and method for dose carbing your beer. Again, spreadsheets/calculators can be your friend. I do a lot of tasting before I am happy with my CO_{2} levels and I hope you will take the time to study your CO_{2} as well.

**References:**

https://chme.nmsu.edu/files/2017/03/FeatAug15.pdf

https://onlinelibrary.wiley.com/doi/pdf/10.1002/j.2050-0416.2009.tb00387.x

http://braukaiser.com/blog/blog/2010/01/11/differences -in-efficiency-calculations/

https://www.tandfonline.com/doi/abs/10.1094/ASBCJ-36-0107?journalCode=ujbc20