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Ethanol Determination
Name: Will
Status: student
Grade: 6-8
Location: IL
Country: USA
Date: September 2008
Question:
Is there a way to measure the amount of alcohol in the
fermented crop without
distilling it?
Replies:
Will,
If you have given your correct age, the following submitted by Dr.
Zimmerman may be a little beyond your math education. However, this
is the best way of calculating the amount of ethanol you have after
fermentation. If you are taking algebra, what a great example of why
you need to study the subject.
If you were asking the amount of ethanol a crop will yield, this is
not possible because there are too many variables that make exact
determinations quantitatively unreliable.
Steve Sample
Hi Will,
The easiest way to measure the ethanol content in a dilute liquid is
by measuring its density. All you have to know is the solution's
volume and mass. However, that means that you can't have very much
else in the sample other than ethanol and water. If you have a small
amount of ethanol and lots of other stuff (such as bubbles / CO2 or
solids), then this method won't work well. There are specific tools
for measuring the alcohol content of beverages (such as beer). These
can be purchases at home brew supply stores.
Before I go too much farther, I want to point out that distillation is
a means of concentrating the ethanol (separating water out), but
distillation does not produce ethanol. Ethanol is produced by
microorganisms that eat sugar in a crop to product ethanol; this is
called fermentation. Typically there is very little (almost zero)
ethanol in crops when they are harvested (e.g. before fermentation).
To find the percent by volume of ethanol, you weigh a known volume of
water-ethanol mixture, and calculate its mass based on its weight.
Then, based on its volume and mass, you calculate its density. Since
we're assuming the sample contains only water and ethanol (which is a
good assumption for most non-carbonated beverages), you can calculate
how the ratio of ethanol to water. For specific gravity (SG) of pure
ethanol use 0.789 and for SG of water use 1.
For example, if you have 1 liter of a mixture of ethanol and water,
and you find its mass is 0.99 kilograms, then you can use the
following equation to find how much ethanol and water you have:
((a)*(sga) + ((v-a)*(sgb))) = m
where
a is your volume of ethanol (that's what you're trying to calculate)
(v-a) = b = your volume of water (also what you're trying to calculate)
sga = 0.789 is the specific gravity of the ethanol
sgb = 1 = the specific gravity of water
m = the mass of your mixture
v = the volume of your mixture
and % ethanol is (a/(v))!
A little algebra gives you
((a)*(sga) + ((v-a)*(sgb))) = m
a*sga +v*sgb-a*sgb = m
a*(sga-sgb)+v*sgb = m
a=(m-v*sgb)/(sga-sgb)
a/v = (m-v*sgb)/(sga-sgb)/v
So in the example I give, with 1000ml and 990grams, a/v =
(990-1000*1)/(0.789-1)/1000 = ~5% (4.7) alcohol (which is a typical
level for beer).
Hope this helps,
Burr
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