# How does alcoholic proof relate to molarity? **URL:** \ **Category:** Factual Questions\ **Created:** [June 24, 2007, 6:31am UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198 "2007-06-24T06:31:14Z")\ **Posts on this page:** 17\ **Page:** 1
**Author:** ![Strinka](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/strinka/32/512_2.png) [@Strinka](https://boards.straightdope.com/u/Strinka)\ **Post date:** [June 24, 2007, 6:31am UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/1 "2007-06-24T06:31:14Z")
Alcoholic proof is a unit of concentration of alcohol by volume. 2 proof is about 1% volume of ethanol. Can that be converted into molarity? ---
**Author:** ![Harmonix](https://avatars.discourse-cdn.com/v4/letter/h/3ec8ea/32.png) [@Harmonix](https://boards.straightdope.com/u/Harmonix)\ **Post date:** [June 24, 2007, 7:01am UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/2 "2007-06-24T07:01:42Z")
Seeing as you are a student i’m going to assume this is HW. I will not do the HW for you but I will give you a hint. I think you need 1 more piece of information. It’s contained on this webpage. [http://homedistiller.org/calc.htm](http://homedistiller.org/calc.htm) - edit Actually you need a periodic table too… and the chemical structure of ethanol. ---
**Author:** ![WarmNPrickly](https://avatars.discourse-cdn.com/v4/letter/w/d78d45/32.png) [@WarmNPrickly](https://boards.straightdope.com/u/WarmNPrickly)\ **Post date:** [June 24, 2007, 8:13pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/3 "2007-06-24T20:13:57Z")
Can you tell me what the density of a 50:50 mixture of ethanol:water is from that data? I think the answer is no as you cannot make the assumption that density is a linear function of consentration. ---
**Author:** ![WarmNPrickly](https://avatars.discourse-cdn.com/v4/letter/w/d78d45/32.png) [@WarmNPrickly](https://boards.straightdope.com/u/WarmNPrickly)\ **Post date:** [June 24, 2007, 8:30pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/4 "2007-06-24T20:30:49Z")
or concentration even. ---
**Author:** ![WoodenTaco](https://avatars.discourse-cdn.com/v4/letter/w/45deac/32.png) [@WoodenTaco](https://boards.straightdope.com/u/WoodenTaco)\ **Post date:** [June 24, 2007, 8:57pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/5 "2007-06-24T20:57:00Z")
[QUOTE=Harmonix] Seeing as you are a student i’m going to assume this is HW. I will not do the HW for you but I will give you a hint. [/QUOTE] It’s summer. School would be out. ---
**Author:** ![Harmonix](https://avatars.discourse-cdn.com/v4/letter/h/3ec8ea/32.png) [@Harmonix](https://boards.straightdope.com/u/Harmonix)\ **Post date:** [June 24, 2007, 8:59pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/6 "2007-06-24T20:59:43Z")
_shrugs_ I went to summer school. I’ll let strinka make his case. > [@](#): > > Can you tell me what the density of a 50:50 mixture of ethanol:water is from that data? I think the answer is no as you cannot make the assumption that density is a linear function of consentration. I’ll respond again in a day or so with my answer, but i’m pretty sure I don’t need to know it because of the definition of proof. ---
**Author:** ![Squink](https://avatars.discourse-cdn.com/v4/letter/s/b5e925/32.png) [@Squink](https://boards.straightdope.com/u/Squink)\ **Post date:** [June 24, 2007, 9:03pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/7 "2007-06-24T21:03:02Z")
A 50% ethanol/water mix, by mass, has a density of 0.9139 kg/L at 20°C. It contains 9.919 moles ethanol per liter. -CRC Handbook of Chemistry and Physics. ---
**Author:** ![Harmonix](https://avatars.discourse-cdn.com/v4/letter/h/3ec8ea/32.png) [@Harmonix](https://boards.straightdope.com/u/Harmonix)\ **Post date:** [June 24, 2007, 9:09pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/8 "2007-06-24T21:09:42Z")
By mass does not equal by volume. ---
**Author:** ![WarmNPrickly](https://avatars.discourse-cdn.com/v4/letter/w/d78d45/32.png) [@WarmNPrickly](https://boards.straightdope.com/u/WarmNPrickly)\ **Post date:** [June 24, 2007, 9:13pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/9 "2007-06-24T21:13:08Z")
Of course I could have looked it up that way too **Squink**. The point I was making was that it might be a more complicated problem than it appears. This does depend on the definition of proof though so perhaps it can be solved simply. My instinct would be to calculate the mass of ethanol in a particular volume of solution using the density multiplied by the % volume. Then again I think that assumes that %mass = %volume. Something is wrong with my solution. …does somebody have a synthetic problem I can solve? ---
**Author:** ![Bob55](https://avatars.discourse-cdn.com/v4/letter/b/e9c0ed/32.png) [@Bob55](https://boards.straightdope.com/u/Bob55)\ **Post date:** [June 24, 2007, 9:31pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/10 "2007-06-24T21:31:33Z")
From the page linked above, the density of ethanol is 0.789g/mL, or 789g/L, and a molecular weight of 46 g/mol. 789g x 1 mole = 17.1 mol/L or 17.1 Molar for 200 proof ethanol. 1 Liter 46 grams That equates to an increase of 0.0855 M per proof. ---
**Author:** ![WarmNPrickly](https://avatars.discourse-cdn.com/v4/letter/w/d78d45/32.png) [@WarmNPrickly](https://boards.straightdope.com/u/WarmNPrickly)\ **Post date:** [June 24, 2007, 9:53pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/11 "2007-06-24T21:53:37Z")
Alright so if I have a 50 proof solution then that is 25% by volume. That could be mixed by adding 250 mL of ethanol to 750 mL water. From the density of ethanol I can calculate the number of moles of ethanol in solution. The problem is that after mixing I no longer have 1 L of solution. I need to know the resulting volume after mixing 250 mL of ethanol with 750 mL of water. ---
**Author:** ![Vlad\_Igor](https://avatars.discourse-cdn.com/v4/letter/v/7feea3/32.png) [@Vlad\_Igor](https://boards.straightdope.com/u/Vlad_Igor)\ **Post date:** [June 24, 2007, 10:10pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/12 "2007-06-24T22:10:09Z")
I know from personal experience that mixing acetonitrile or methanol with water will result in a volume slightly less than the volumes of the individual components added together. However, the law of conservation of mass will maintain that the molar ratio (and molarity) as well as the proof (% v/v) will remain the same regardless of what happens to the final volume of the solution. That is precisely why I measure out individual volumes and then combine them, as opposed to filling a 100 mL cylinder with 25 mL of ethanol and then q.s. to 100 mL with water. If I did it that way, I’d end up with a solution that was \<25% ethanol v/v. Vlad/Igor ---
**Author:** ![Busy\_Scissors](https://avatars.discourse-cdn.com/v4/letter/b/d78d45/32.png) [@Busy\_Scissors](https://boards.straightdope.com/u/Busy_Scissors)\ **Post date:** [June 24, 2007, 10:21pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/13 "2007-06-24T22:21:14Z")
I think **Christopher** has the nub of the problem - no simple way to know the density of an x% proof ethanol solution just going on the densities of pure ethanol and pure water, so no way to **accurately** quote the molarity. I think you need to know partial molar volumes of ethanol and water, which are empirical measurements IIRC. Ignore the above if its just a high school homework question. ---
**Author:** ![Vlad\_Igor](https://avatars.discourse-cdn.com/v4/letter/v/7feea3/32.png) [@Vlad\_Igor](https://boards.straightdope.com/u/Vlad_Igor)\ **Post date:** [June 24, 2007, 11:01pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/14 "2007-06-24T23:01:20Z")
Acutally you can measure density and come up with a % ethanol solution: a hygrometer calibrated to water/ethanol mixtures. Any given volume of the solution will have the same molarity, so the original volume isn’t needed. The hygrometer will give the density, the calibration curve will provide the %ages, and from there it’s plug-and-chug. Vlad/Igor ---
**Author:** ![WarmNPrickly](https://avatars.discourse-cdn.com/v4/letter/w/d78d45/32.png) [@WarmNPrickly](https://boards.straightdope.com/u/WarmNPrickly)\ **Post date:** [June 24, 2007, 11:18pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/15 "2007-06-24T23:18:40Z")
**Squink** apparently has a better CRC than I do. I couldn’t find a density vs. proof (or %vol) table in mine. ---
**Author:** ![Harmonix](https://avatars.discourse-cdn.com/v4/letter/h/3ec8ea/32.png) [@Harmonix](https://boards.straightdope.com/u/Harmonix)\ **Post date:** [June 24, 2007, 11:37pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/16 "2007-06-24T23:37:24Z")
[QUOTE=Christopher] Alright so if I have a 50 proof solution then that is 25% by volume. That could be mixed by adding 250 mL of ethanol to 750 mL water. From the density of ethanol I can calculate the number of moles of ethanol in solution. The problem is that after mixing I no longer have 1 L of solution. I need to know the resulting volume after mixing 250 mL of ethanol with 750 mL of water. [/QUOTE] O.o This is how I solved it. Now I realize that ethanol being the solute will stack between the water molecules in a slightly more efficient manner the more plentiful the solution is but I wrote it off as being negligible at best. (forgive me if my terminology is completely off. I did biology in school and my knowledge of chemistry is general and mostly intuitive). using vodka as an example 80 proof. I calculated 80 proof = 40% BY VOLUME = 400ml of 100% ethanol and 600 ml of H2O. 400 ml x 0.789 G/ml = 315.6g 315.6G / 46g/mole = 6.8608 Moles Thats the high school answer anyway I guess. ---
**Author:** ![Squink](https://avatars.discourse-cdn.com/v4/letter/s/b5e925/32.png) [@Squink](https://boards.straightdope.com/u/Squink)\ **Post date:** [June 24, 2007, 11:46pm UTC](https://boards.straightdope.com/t/how-does-alcoholic-proof-relate-to-molarity/409198/17 "2007-06-24T23:46:21Z")
[QUOTE=Christopher] **Squink** apparently has a better CRC than I do. I couldn’t find a density vs. proof (or %vol) table in mine. [/QUOTE] 55th edition, page D-202.