Determining Percent Alcohol

Whenever I've talked to people about homebrewing beer and hand them one of my own, a lot of the time I'll give fair warning if the percent alcohol is above 7% Alcohol by Volume (ABV).  They usually say, "Oh", then wait a second, and finally ask, "How exactly do you know that?".  Most of the time it's someone saying "Really?  You're that much of a nerd that you calculate the percent alchohol of your beer?"  And to them I respond a firm "YES I DO", and I also calculate the percent Alcohol by Weight (ABW), which we'll talk about soon.

In the last post, I wrote about BU:GU ratios and had to briefly explain OG, but I didn't get into very much detail other than to inform you that it tells the homebrewer the concentration of sugar before the yeast is thrown in.  You might wonder how we get such a number as 1.048 for the Original Gravity, and the answer lies in a small homebrewing tool we call a hydrometer (see picture). 

It's basically like a floating thermometer except instead of measuring temperature, it measures the density of a liquid.  To use a hydrometer, you toss it in the liquid and the hydrometer will float to a certain numerical value on the skinny part of it that is flush with the surface of the liquid.  When a well calibrated hydrometer is placed in deionized water at 59 degrees F, it reads 1.000, and this makes sense because the density of water is roughly 1 kilogram per Liter (kg/L) or 1 gram per milliliter (g/mL), they mean the same thing.  When the hydrometer is placed in a solution that contains water mixed with a certain amount of sugar, like the sugars brewers extract from the grains, it will always read higher than 1.000 g/mL because sugar makes the solution denser.  So the OG on the hydrometer for a beer could read a number of ranges from 1.030 (not much sugar) to 1.120 (a hell of a lot of sugar).

You can check the concentration of sugar at any time you wish during the brewing/fermenting process and with the exception of two readings we typically refer to these readings as Specific Gravity or SG readings.  The two exceptions, which are essential to calculating the percent alcohol in your beer are the OG (Original Gravity) and the FG (Final Gravity) readings.  As explained earlier, the OG is the sugar concentration before the yeast is added, and as you can guess, the FG is the sugar concentration after the yeast is done converting the sugar into alcohol.  OG is measured when the wort is cooled and ready for the yeast and the FG is measured just before you bottle the beer.  The time between the two measurements depends on the type of beer, the higher the OG, the longer it takes to reach the FG.  Since you now know those two values I could just give you the formula for calculating %ABV, but where's the fun in that... to the chemistry!

Simplistically, here's what happens to sugar when yeast is added:


C­₆H₁₂O₆ (one glucose sugar molecule) -------> 2 CO₂ (gas) + 2 CH₃CH₂OH (ethanol, *this gets you drunk*)

There's much much more going on when yeast is added, but understand that roughly for every 1 glucose sugar molecule, it yields 2 carbon dioxide molecules and 2 ethanol molecules.  Depending on the type of yeast, most of the time not all the sugar is converted to ethanol and CO₂, which is why some beers can taste sweeter than others.  Let's assume that we just got done fermenting a pale ale and it's ready for bottling, we take a hydrometer reading and record a FG=1.010, and the OG recorded weeks earlier was 1.055.  This may not be the most accurate way to calculate percent alcohol, but let's assume that all of the CO₂ gas produced left out the airlock and all the ethanol produced remained in the beer.  By subtracting the FG from the OG, it tells us the concentration of CO₂ that left.

In our example: 1.055 - 1.010 = 0.045 g/mL CO₂


Since we know the balanced equation for converting sugar to alcohol and gas, we can use stoichiometry (bet you never thought you'd see this again) to determine the concentration of ethanol from the concentration of CO₂ that left the beer.  Looking at a periodic table, we can obtain the molecular weights for ethanol (46.069 g/mol) and CO₂ (44.009 g/mol), and starting with the concentration of CO₂:

Alright, now that we know how much ethanol is in 1 milliliter of our beer and we also know the total weight of everything in 1 milliliter of our beer (from FG=1.010), we can take a ratio of these two values and what you end up with is a percentage of ethanol by weight in the final beer, which is referred to as percent Alcohol by Weight (%ABW):

But the fun doesn't stop there.  If you're from the U.S. like I am you'll notice most breweries report their alcohol percentages as Alcohol by Volume (%ABV).  The difference between ABW and ABV values has to do with ethanol being less dense than water, and because of this the ethanol occupies more volume.  The ABW is basing its value on just the weight of ethanol in say a 12oz bottle of beer, not the space it takes up in the 12oz bottle.  Since the final beer is usually made up of >90% water and some unfermented sugar, that percent of the beer has a density close to water's, which is 1.000 g/mL, telling us that roughly every gram occupies 1 millilers of volume.  Since the other percent has a the density of ethanol we must divide by the density of ethanol to see how much volume it occupies, so every 1 gram of ethanol would actually occupy 1.27 mL of volume.  Here's how percent Alcohol by Volume is calculated:

 

 OR

So our final beer is 5.9% ABV.  If you think about this logically, it falls apart when you get into high percent alcohol beers simply because if you had a 100% ethanol beverage it would be 100% ABW and 127% ABV, which isn't possible.  However, since most beers are within the 2-10% ABW range this method for ABV works quite well.

This can come in handy if you're ever in Europe where they express there percent alcohol by weight, and as an American you might be so used to judging your alcohol intake based on the %ABV that you might make the grave mistake of assuming they're close in value, or worse, the same.  So if you walk into a pub and order a pint that is 5.0% ABW you'll be quick to realize that your beer is actually 6.3% ABV.  If you'd like a quick and dirty way to calculate in your head (because god forbid that you bust out a calculator in a pub), I take a quarter of the %ABW value and add it back to the %ABW:

5.0/4 = 1.25 ---> 5.0 + 1.25 = 6.25% ABV  (I know... sig figs are wrong)

Not exact, but close enough for a quick answer.  Enjoy!