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Part science, part arithmetic question.

For alcohol with proof x what volume constitutes a single drink?

Defining a standard drink as 14 grams of alcohol:

https://en.wikipedia.org/wiki/Standard_drink

although it seems to be the wrong units. I vaguely remember something about moles but wouldn't recall how to apply this here.

Actually, not sure where I got the 14 grams from, but a unit of alcohol looks to be perhaps a better measure:

https://en.wikipedia.org/wiki/Unit_of_alcohol

see also:

How to determine the alcohol content of a mixed-drink?

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The question provided a link to "How to determine the alcohol content of a mixed-drink?", so I'll assume you want a simpler, easier to understand answer.

Consider some common drinks:

  • 12 US fl.oz. (355 mL) bottle of 5% beer = 355×5/100 = 17.75 mL alcohol.
  • 1½ US fl.oz (44.4 mL) shot of 40% bourbon = 44.4×40/100 = 17.76 mL alcohol.
  • 5 US fl.oz (148 mL) glass of 12% wine = 148×12/100 = 17.76 mL alcohol.

Your other link defines an American standard drink as 18 mL of pure alcohol, so it's no coincidence that the examples they gave matched so closely.

Basically all you need is the volume of the alcoholic product in mL and the strength as a percentage, and simply multiply them and divide by 18 to get the equivalent number of standard drinks.

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It is easier to define the standard drink by volume as you won't have to switch between concentrations by volume (as is normal in most drinks) and grams.

This is probably where your recollection of moles comes in as somewhere in this morass of units they get involved.

14 grams of alcohol is 17.7 ml

so 30% alcohol (many spirits) to get to a 100% you need to add another 70/100 ths of volume.

(17.7/30)*100 = 59 ml of drink which just so happens to be two fluid ounces for our american viewers.

or, slightly less intuitive but easier to use:

the volume of your drink = 17.7 / (the concentration or your drink /100)

Now if you want to use the "proof" of your drink as a unit of volume I'll need a drink first.

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    Note that this calculation by volume is slightly imprecise, because mixtures of alcohol and water don't retain their volume exactly - if you mix 100 g of water with 17.7 g of ethanol, you don't get 117.7 ml liquid, but somewhat less, so 117.7 ml of your new drink will have slightly more than the 14 g of alcohol your calculation suggests. It is up to the OP to decide whether this is relevant for their situation though, for practical purposes people may decide to just go with the formula you suggest. – rumtscho Jan 2 at 16:35
  • You meant to write "100 ml of water with 17.7 ml of ethanol", I presume, not grams? – Federico Poloni Jan 2 at 21:08
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    @rumtscho, alcoholic content is usually indicated as "v/v" (volume per volume) and takes this factor into account. For instance, a 40% alcohol rating would mean that there are 400mL of alcohol in 1L of product (which as you indicated, will contain more than 600mL of water). – Ray Butterworth Jan 3 at 0:49
  • @RayButterworth: Yes, that's how it works, though non-chemists may perhaps recognize the volume percentage definition as ABV. – Athanasius Jan 3 at 1:17
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There is an "easy" way to do this if you are drinking somewhere that uses fluid ounces instead of mL. I call it the "divide by 60" method.

A US "standard drink" is 12 fl oz of 5%. Multiplying 12 * 0.05 gives us 0.6 fl oz of alcohol as a "standard drink". However, since we are going to be using % alcohol over and over, I find it easiest to not do the conversion from % to decimal and just work with the % number. Then a "pseudo-standard" drink is 12 fl oz * 5 = 60.

Now you can calculate the "standard drinks" in your drink by taking the volume (in fl oz) multiplying by the alcohol percentage, then divide by 60. For example, a 20 fl oz glass of 6.7% IPA works out to 20 * 6.7 = 134. 134 divided by 60 is a little more than 2 (2.23 actually) and so your big glass of IPA is equivalent to a little more than two standard drinks.

Another example: a mixed drink with 3 "shots" of hard alcohol. In the US, a "shot" is roughly 1 - 1.25 fl oz. A lot of hard alcohol (vodka, gin, etc.) is around 40% alcohol. We can then calculate 3 fl oz * 40 = 120. Dividing by 60 gives us 2 "standard drinks" in your mixed drink. If you want to be on the safe side, you could round up: 3 shots * 1.25 fl oz = 3.75 fl oz round up to 4 fl oz. Then 4 fl oz * 40 = 160, divide by 60 to get 2 2/3 standard drinks.

I like this method because I find it somewhat easy (with a little rounding sometimes). I would probably need a calculator to use the other (good) methods that people have outlined in answers to this question, but I can do the "divide by 60" method in my head.

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  • Welcome to Seasoned Advice! I like this method: very practical if you like to do the math in your head. – Athanasius Jan 3 at 14:20

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