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08-24-2010, 08:55 PM   #11
ajdelange
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As I like things simple I calculated a polynomial which approximates the freezing point of pure ethanol in pure water solutions it is:

Fp = ((0.0075275*ABV + 0.054922)*ABV + 31.947 °F

You can copy this and paste it into Excel. It's good from 0 to 25% ABV. As you can see it calls the freezing point of water 31.947 - an error of 0.053 °F and at 25% ABV the error is -0.065 °F. It's better away from the ends of the range. rms error is 0.02°

It is assumed that ABV is specified at 20 °C and this temperature was used in conversion from ABV to ABW using the OIML polynomial. The water constant used to calculate the freezing point depression was 1.855.

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08-24-2010, 09:36 PM   #12
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Quote:
 Originally Posted by rayg I found an analysis of a stout in a book I have, the alcohol content of which was 6.37% by w, which is 7.96% by v. The amount of other material dissolved is pretty small, the most being protein 5.8g/L and glycerol 2 g/L. Other things include: K .468g/L P .227 g/L So4 .130 g/L Cl .250 g/L Pyruvate .128 g/L citrate .187 g/L Acetate .219 g/L Polyphenols .199 g/L
Those sum up to a TE of about 1°P. Noticeably missing from this list is sugar! HBS&Y have some limited data on sugar contents of beer. For a "Danish Lager" sugars contribute about 2.4 °P to the TE. For "German Lager" its 2.83 and even for "Diabetic Lager" it's 0.96.

My stouts (the only ones for which I have TE data) have TE's between 3.7 and 4. And these are dry stouts. They have the lowest TE's of anything I brew. Eighteen beers I've analyzed have an average TE of 5.2 with a standard deviation of 1. The stouts are the lowest, Kölschs next at 4.7 - 4.8, Pils and ales around 5, Fests 5-6 and Bocks 6 - 7.9. Remember that TE is everything in the beer except the alcohol (and any other volatile such as acetic acid) thus these figures would include the pyruvate and citrate to the extent that they behave like sucrose in terms of the way they effect density. But they are kind of in the noise relative to residual sugars. It's going to be alcohol, glycerol (makes great antifreeze), protein and sugars that are going to be responsible for most of the FP depression.

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08-25-2010, 06:05 PM   #13
rayg
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Quote:
 Originally Posted by ajdelange Those sum up to a TE of about 1°P. Noticeably missing from this list is sugar!
I'm sure I just overlooked it in the table. I'll have to check again
tonight when I get home.

Don't understand why you are using TE, it can't be converted to moles
so you can't use it for calculating a freezing point depression.

Ray
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08-25-2010, 07:50 PM   #14
ajdelange
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In order to compute molality I have to know both how much stuff is in solution and what it's average molecular weight is. TE answers the first question. The average molecular weight must be determined by experiment i.e. by measuring freezing point depression or boiling point elevation. As FP depression is 3.7 times more sensitive than boiling point elevation, I think the former is the way to go. The intent, of course, would be to measure average mol. wt on a couple of beers in the hopes that the grouping would be tight enough that one "average average" value could be used for general purpose estimation or that one could at least say the AMW is one thing for Pils and another for Bock, for example.

Another approach to getting AMW is to look at the spectrum of sugars and other things reported in beer in brewing texts and compute an average that way.

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08-25-2010, 08:28 PM   #15
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Quote:
 Originally Posted by ajdelange In order to compute molality I have to know both how much stuff is in solution and what it's average molecular weight is. TE answers the first question. The average molecular weight must be determined by experiment i.e. by measuring freezing point depression or boiling point elevation. As FP depression is 3.7 times more sensitive than boiling point elevation, I think the former is the way to go. The intent, of course, would be to measure average mol. wt on a couple of beers in the hopes that the grouping would be tight enough that one "average average" value could be used for general purpose estimation or that one could at least say the AMW is one thing for Pils and another for Bock, for example. Another approach to getting AMW is to look at the spectrum of sugars and other things reported in beer in brewing texts and compute an average that way.
It seems to me that calculating the mw from reported values of
dissolved substances is the way to go. If you are going to
go to the trouble of actually measuring the freezing point of the beer,
you don't need a table of freezing points. But I don't see how you
can accurately measure the freezing point. In a lab you use a capillary
melting point apparatus, but how are you going to get an accurate
melting point of something the freezes so low at home? Are you going
to put a container of beer in a cold room and watch it melt (and
do it several times to get an average)? You have be there right at
the instant it starts to melt, and you need a really small sample
to eliminate heat imbalance across the sample (that's why it's
done in a capillary tube and viewed with a magnifying glass).

Ray
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08-25-2010, 09:03 PM   #16
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I have some experience in using an ebulliometer to measure BP depression (for alcohol estimation) but none with FP depression. What I was thinking of doing is put the sample in a small tube and put that in the freezer and record the temperature as a function of time. The temperature should fall as the solution cools and then stay more or less constant while freezing is taking place until the tube is frozen solid at which time it should start to decline again. I'd probably grab the middle point of that flatish region and call that the freezing point. Yes, I understand the problems you mention but I'm not shooting for extreme accuracy here. Obviously I'd do this with calibrated strength solutions to see how close I could get.

In trying to estimate the molecular weight of sucrose by by boiling point elevation this afternoon I observed a 0.2° rise when I should have seen 0.1° so I'd estimate sucrose at 171 Daltons. It's clear that a thermometer readable to 0.1°C doesn't have enough precision.

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08-25-2010, 09:46 PM   #17
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While brushing the dog it occurred to me that I have a device in which a capillary tube is affixed to a Peltier attemperator with a PRT that reads to 0.001°C and a camera for monitoring what goes on it the tube. Perfect, right? Well, alas no. For one thing, it only goes down to 0° C. For another it's designed to measure density - not freezing point and I'd have to commit ceremonial sepuku if I burst that tube by letting something freeze in it.

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08-26-2010, 04:54 PM   #18
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The real extract of that beer was 6.6. If subtract the
~1 degree of extract that the other substances
contribute, that leaves 5.6. That's going to bring the
mass of water remaining to ~0.88 kg. But the sugars must
be at least as big as maltotriose (~504.5 daltons), which
means a further reduction in the freezing point of about
0.42F. But the average mol wt is probably closer to
maltoheptose (~1153 daltons), so that would mean
a reduction of only about 0.18 degree. The low mol
wt of the alchohol means it has a much larger effect.

Ray

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