How is Alcohol-by-Volume (abv) Calculated?

[slkinsey]

I was talking about this with my father the other day, who is a chemist of some repute. He mentioned that it's not necessarily a no-brainer to say what percentage of a given liquor is alcohol. This is because when two liquids (or two solids, or a liquid and a solid, etc.) are mixed together, it does not necessarily follow that the volume of the resultant mixture will be equal to the sum of the volumes of the two liquids. It might be more than the sum of the two volumes, or it might be less.

In the case of alcohol, for example, if you mix together a half-liter of pure ethanol and a half-liter of pure water, you do not get a liter of alcohol-and-water. No, you get 956 ml of alcohol-and-water. This is because equal volumes of ethanol and water will have only 95.6% of the volume of the equal parts of ethanol and water when unmixed. So... is that 956 ml of water 100 proof (aka 50% abv) or not? It is comprised of 500 ml of water and 500 ml of ethanol for a total of 956 ml. In the most literal sense, it does not add up.

This is pretty easy to figure out when we mix the alcohol ourselves, but it seems like it would be quite a bit more difficult to back-calculate if you're staring at a 956 ml bottle of booze. If you correctly say that the 956 ml of booze contains 500 ml of alcohol, does that make it 104 proof (52% abv)? Or if you correctly say that the 956 ml of booze contains 500 ml of water, does that make it 96 proof (48% abv)?

As you may imagine, when the bottle starts to contain things other than just ethanol and water (i.e., everything but vodka), and when the amount of alohol deviates from the 50/50 example I gave above, it becomes even more complicated.

So? How is it done?

[Soren Nielsen]

Intesting point!

In my view:

Given 956ml of a liquid made from 500ml water and 500ml ethanol, which decreased in volume when mixed.

I assume that this decrease is caused by dissolving of ethanol molecules.

No alcohol (or water) disappears when mixing, it just becomes tighter packed. Additionally, assuming perfect distillation, you could still seperate the mixture to 500ml water and 500ml ethanol. Thus, the mixture remains 50% abv.

Keeping the fact that the mixture decreases in volume in mind, a statement like

"this mixture contains 500ml of water"

is misleading. It was made with 500ml of water, but that's not the same.

Volume also varies with temperature (different variations for alcohol and water), adding more to the confusion.

If anyone knows of a generally accepted standard for measuring abv in spirits I'd like to know too!

[slkinsey]

No alcohol (or water) disappears when mixing, it just becomes tighter packed. Additionally, assuming perfect distillation, you could still seperate the mixture to 500ml water and 500ml ethanol. Thus, the mixture remains 50% abv.

Yes, this is how it works. Ethanol and water together can pack tighter than either one can on its own. I should add that the same thing can happen in the other direction, depending on the substances involved: two volumes mixed together can result in a volume that is greater than the sum of the original volumes.

The question of alcohol by volume is a difficult one to answer, however. What, exactly, constitutes "volume" in the context of a 1:1 solution of alcohol and water? More to the point, how is this determined? Are we looking at a hypothetical idea where all the various constituents of a bottle of liquor are separated out, measured as to volume and then the percentage of alcohol by volume is calculated on this basis? What basis are we using to determine abv when it's got more than just water and ethanol? What about something like Drambuie, which is comprised of alcohol, water, sugar and various other dissolved substances?

[Soren Nielsen]

After digging around a bit I found the following:

Temperature when measuring abv is standardized (but varies in EU and US of course)

Reading this page you can see that in beer production, they measure the change in specific gravity caused by fermentation and use that as a basis for calculating abv. Since it is based on percentage of alcohol by mass I guess it is unaffected by molecular changes as result of mixing?

It also seems that a variance of 1-2% is allowed, depending on product.

[Fat Guy]

If you correctly say that the 956 ml of booze contains 500 ml of alcohol, does that make it 104 proof (52% abv)?  Or if you correctly say that the 956 ml of booze contains 500 ml of water, does that make it 96 proof (48% abv)?

←

If I remember correctly from chemistry: when you're calculating alcohol by volume, the volume of water isn't part of the equation at all. The only two variables are volume of alcohol and volume of total solution: it's just volume of alcohol over volume of total solution times 100, right?

[JohnL]

After digging around a bit I found the following:

Temperature when measuring abv is standardized (but varies in EU and US of    course)

Reading this page you can see that in beer production, they measure the change in specific gravity caused by fermentation and use that as a basis for calculating abv. Since it is based on percentage of alcohol by mass I guess it is unaffected by molecular changes as result of mixing?

It also seems that a variance of 1-2% is allowed, depending on product.

←

From the textbook used by the Wine and Spirits Education Trust (WSET)

"Potable alcohol as contained in alcoholic drinks is ethanol, sometimes called ethyl alcohol. Actual alcohol is the amount of ethanol present in a wine, measured as a percentage of the total volume at 20 degrees centigrade as shown on the label."

These folks follow the EU to a tee!

[slkinsey]

Dude. You remember anything from chemistry class? Whoa.

Okay... I have been able to determine that the legal definition of ABV in the US specifies a temperature of 60F.

[thirtyoneknots]

It does seem that by logic since you are measuring alcohol by volume and not water by volume then it would be 104* or whatever.

Of course this is nothing but a thought experiment on my part, I managed to weasel my way through high school without taking any chemistry (2 years of physics though) and dropped the one college chem class I enrolled in within the first week. heh

-Andy

[jsolomon]

Usually you plot the response of a set of standards of ethanol/water mixtures on a Near Infrared spectrometer. Then, you find the response of your mixture, and read it off of the plot.

But, 50% abv, in my lab, would mean for each liter, you would add first 500 ml of alcohol. Then, you would add to the 1 liter mark of water, meaning that you would add 500 ml of water to get 956 ml, and then keep adding water to 1 liter.

Typically, 50% by volume means that you measure 50% of the desired final volume, then don't measure what you're topping up with.

However, there are other more precise methods. When you are talking about ABV you are allowing yourself certain wiggle rooms due to volume not being a conserved property.

[Fat Guy]

Dude.  You remember anything from chemistry class?  Whoa.

←

I remembered that one thing, knowing some day it would come up. Now I plan to forget it.

I found this online source, sort of a general chemistry reference:

http://antoine.frostburg.edu/chem/senese/1...by-volume.shtml

If I understand it correctly, it agrees with me. In answering the question, "How do I calculate percentage by volume of a solution containing alcohol or any other liquid?" it says:

Vol/vol percentage is calculated as

    Volume % =

  volume of substance

-----------------

    volume of total solution 

×100 %

    For example, to prepare 100 mL of 5% (v/v) solution of ethanol, pipette 5 mL of ethanol into the bottom of a 100 mL flask and dilute to the mark with water.

    Careful, though. The denominator specifically says volume of total solution and NOT volume of solvent. This makes a difference, because volumes are not additive. 5 mL ethanol plus 95 mL of water does NOT equal 100 mL of solution!

I never realized that temperature would make a difference to this sort of computation, so long as everything is liquid -- I'd have thought the ratio would remain constant throughout the phase, but I guess the 60-degree regulation says otherwise.

[jsolomon]

I never realized that temperature would make a difference to this sort of computation, so long as everything is liquid -- I'd have thought the ratio would remain constant throughout the phase, but I guess the 60-degree regulation says otherwise.

←

Yep. If you ever want to show that to yourself, grab a CRC handbook of organic chemistry and look at the different expansion coefficients of different liquids.

On the other side of the coin, most densities only differ in the second decimal point, so you're not going to have a terrific amount of variance, but when you look at the sheer volume of ethanol produced in the world, it makes for a large second decimal!