Calculations over blending alcohol with water..

[NeoPTLD]

In some reading materials for teachers online, I recall a demonstration of mixing equal parts water and rubbing alcohol into a graduated cylinder to demonstrate that the volume do not add up, because alcohol and water interacts on molecular level and shrinks in volume.

100ml of alcohol + 100ml of water mixed and stirred yields something like 190ml of water/alcohol solution.

http://answers.yahoo.com/question/index?qid=20080124082949AAGrjJ5

In the beverage industry, the expression used is the percent absolute alcohol per volume, or ABV.

So, if one was to take 500ml of pure alcohol, 500ml of water and blend the two they'll shrink. Since we know the amount of absolute alcohol that was in it, would the new solution be higher than 50%, because it is 500ml alcohol/970ml =51.5% or would it be 500/(500+500)=50% based on original volumes?

So to yield a liter of 50.0% alcohol=by-volume solution, does one have to add 500ml of pure alcohol and add 500ml, THEN add water until you hit the 1000ml line on the volumetric flask?

 

[Paperdoc]

Your understanding appears to be correct. ABV appears to be calculated as ABV (&#37 = 100 x (ml of pure alcohol) / (ml of solution). And "proof" is simply twice the ABV number. In practice, and for easy measurement, a series of experiments is carried out in which known volumes of pure ethanol and water are mixed, and their total volumes measured to give known ABV values, and then each has its specific gravity measured at a common reference temperature. An interpolated curve of ABV versus Specific Gravity is constructed, and then a simple Specific Gravity test can tell you the ABV number. Now, obviously this technique needs to be altered for situations in which there is more than just ethanol and water in the beverage - beer is a fine example. But the principle is the same.

 

[CycloWizard]

Paperdoc is right on the money as usual. Not much to add but a summary: ABV should be based on the final volume.

 

[jimhsu]

I'm doing instrumental analysis work, and it is a major PITA when a percentage can have so many meanings (mass/volume, volume/volume of solution, volume/volume of initial, mass/mass, moles/volumes, etc). A 50% Ethanol in water solution can have at least 5 possible meanings. Things like ppm are also ambiguous (mg stuff in L solvent? in kg solvent? Micromoles of stuff in moles of solvent?) If the molecular weights are very different, these numbers can vary dramatically (>1 order of magnitude).

 

[Paperdoc]

jimhsu is right - it is ALWAYS necessary to specify (and ask if it's not given) the EXACT units being quoted. Reminds me of my old rule: when someone tells me an answer as a "percent", I ask immediately, "of what?" I find it amazing how often people misuse percent calculations and get the wrong answer.

 

[NeoPTLD]

Paperdoc, how useful is a hydrometer in determining alcohol content in anything other than vodka that contains sugars and such that alters the density measurably?

I'm doing instrumental analysis work, and it is a major PITA when a percentage can have so many meanings (mass/volume, volume/volume of solution, volume/volume of initial, mass/mass, moles/volumes, etc). A 50% Ethanol in water solution can have at least 5 possible meanings. Things like ppm are also ambiguous (mg stuff in L solvent? in kg solvent? Micromoles of stuff in moles of solvent?) If the molecular weights are very different, these numbers can vary dramatically (>1 order of magnitude).

Good example is chloroform( the only significant trihalomethane in water contamination in places that do not use brominated or fluorinated treatment chemicals).

Its density is 1.5g/ml, so municipalities would have more favorable report if they use ppm on volumetric scale rather than graviometric. 3ppm on w/w scale would turn into 2ppm on v/v scale, which is more favorable for reporting purposes.

 

[Paperdoc]

Your are right, OP. You can construct a graph of solution specific gravity versus its contents of a specific component, but EVERY other component must remain unchanged. For example, that's why I said the principle can be applied, but the specific graph built from ethanol plus water only (a 2-component system) cannot be used for beer, which is much more complex. You would have to start again. And some of these things have to be done from known real-world samples because they cannot be done from theory. For example, wine and beer makers often "measure" the alcohol content of their brews with hydrometers. But the truth is they are just ESTIMATING, which is OK. I've done it. It starts with a hydrometer reading of specific gravity of the original solution before fermentation which has water, sugar, and a whole bunch of minor ingredients. This yields an estimate of the sugar content, based on a graph for solutions of sugar in water with a few "contaminants" typical of grape juice (in the case of wine makers). After almost all sugar has been fermented, you re-measure the specific gravity of a solution which now contains water, very little sugar, a bunch of new ethanol, and most of the same minor ingredients. Using a different reference curve constructed from similar solutions, you can estimate the remaining sugar content, and hence estimate how much ethanol must have been made from the sugar that disappeared. But simply measuring the specific gravity of the final wine cannot tell you its ethanol content because there are so many unknown components in the wine besides water and ethanol. In fact, a very significant source of error in this procedure is the second reference graph. It is constructed ASSUMING that the ethanol content of the final wine is about 12%, and in a synthetic solution like that you can use specific gravity to measure the sugar content. But if you were making a very different wine, that last estimate is going to be off. Professional winemaking is done differently, of course, I'm just talking about the simple tools available to home brewers.