Density and %ABV

rangaz · Post by **rangaz** » Mon Sep 25, 2006 12:31 am

noticed a strange thing the other day. I was working a formula to find %ABV as i only have a hydrometer.
* times
/ divide
- subtract
+ plus

1) %A+%W=1
(percentage alcohol plus percentage water will equal 1. the percentage must be as a decimal ie. 50%=0.5, 45%=0.45)

2) %W=1-%A
(switch around equation to get %W as subject)

3) D=%A*0.78936 + %W*1
(density of the mixture will be equal to the percentage alcohol times density of alcohol (0.78936) plus percentage water times density of water (1))

4) D=%A*0.78936 + (1-%A)*1
(we substitute in the value from equation 2 for %water, leaving us with only density and %A, allowing one to be work out one from the other)

5) %A=(D-1)/(0.78936-1)
(rearrange to have %A as the subject so we can work out from desity of the solution)

This suggests a linear relationship between density and %ABV ie. the total volume of a mixture of alcohol and water will be the sum of the volumes of alcohol and water before they were mixed

Tried it by matching it against a program and noticed my results were out by as much as 5% at around 50%ABV but near perfect at high and low concentrations.

Then proceeded to graph the density and %ABV against each other and found that it was indeed a curve and not a straight line... hmm (i have images of the graphs but dont know how to post them)

This leads me to believe that when mixing alcohol and water, the ensuing volume will not be the sum of the volumes of the separate alcohol and water. Instead it will be slightly different, assuming that the program i found is indeed correct.

Ideas...? errors in my working or theory...? comments?

Miraculix · Post by **Miraculix** » Mon Sep 25, 2006 1:01 am

You're totally correct. Think of it like mixing "sugar and marbles".

With 0.5 liters of each, you're not getting 1 liters in total. The sugar is "hiding"
inbetween the marbles. But as you reach "each end", the volume is more
and more "correct".

Harry · Post by **Harry** » Mon Sep 25, 2006 1:25 am

Volume is not mass. The mass of the two substances, ethanol & water, will add together. That is, 200gms water + 200gms ethanol = 400gms mixture. However, the volumes do not add precisely. The reason is that
the sizes of the individual molecules are different enough that the smaller molecules can slip into the spaces between the larger molecules. Ethanol molecules are larger than water molecules.

As a demonstration of this, get some spheres that are two different sizes (e.g., marbles and golf balls, or gravel and sand).

Fill a container with the larger objects and then put some of the smaller objects on top and shake the container. The smaller particles will slip between the larger ones and will also fit in the container with little or no increase in volume (depending on how much you add).

Unfortunately there is no easy method of calculating the final volume of mixtures of different sized molecules, except for trial and error.

.

rangaz · Post by **rangaz** » Mon Sep 25, 2006 1:48 am

then dilution calcs on the parent site slightly wrong? i noticed the errors were more prominant towards 50%ABV, conveniently about drinking strength. are these just aproximations and then you're meant to use an alcometer?

hornedrhodent · Post by **hornedrhodent** » Mon Sep 25, 2006 2:22 am

="rangaz"
then dilution calcs on the parent site slightly wrong? i noticed the errors were more prominant towards 50%ABV, conveniently about drinking strength. are these just aproximations and then you're meant to use an alcometer?

If you do you dilutions measuring initial and final volumes you'll be correct. If you use initial volume and added volume you'll be wrong = but not enough to spoil the taste.