New ABV Concentration, Extracted from Frozen Batch

[Sludge Brewer]

Somehow, in what I thought was a temp controlled fridge, a batch of beer mostly froze in the keg during carbonation. I didn't learn this until after the 11th bottle because the keg wasn't giving up anymore liquid. Had I reason to check the keg first I think the beer would have been fine if I let it thaw, but I figured the integrity was compromised after removing 1/5th the volume into individual bottles.

The beer that was extracted was definitely an "imperial" version of the original, many characteristic were dialed up including the alcohol presence. I'm wondering if the ABV of the salvaged beer can be determined.

Original Batch:
5 gallons
OG 1.055
FG 1.014
Measured before carbonation started.

Thawed Beer:
3.97 gallons
Gravity 1.006
The theory here is the salvaged beer took additional alcohol with it since the alcohol would be much harder to freeze. The gravity going back to nearly that of water presumably backs this theory up. This volume was allowed to de-carbonate before taking a hydrometer reading.

Imperial Salvaged Beer:
1.03 gallons
Gravity?
ABV?
Hydrometer reading would be affected by carbonation, therefore wondering if an ABV is able to be calculated from the other measurements.

Figured this would be a fun problem to try to solve. I don't remember enough about changes in concentration levels of solutions from school to know where to start attacking this one.

 

[rhys333]

I think you can estimate reasonably closely as long as you know the original volume and abv, and how much volume you lost to the freezing process.

For example, 5.0 gallons (18.9L) @ 5.4% abv starting, and 4.0 gallons (15.1L) after freezing. I'll work in litres, as its easier for me.

18.9 x 0.054 = 1.02L of alcohol. Close enough to your loss of volume. This suggests that you have pure alcohol, but I'm guessing I'm wrong on this...