calculating alcohol with mixed solutions

I couldn't find any equations or a calculator for this, so if anybody knows either, that'd be great.

I just added 160 ml of whiskey to a RIS (along with the wood that was soaking in it). This is 20.75 liters at 9.8% abv, for the stout, mixed with that 160 ml of whiskey that is 45% abv.

Naturally, I want to calculate the new alcohol content for the RIS. Help?

MattHollingsworth said:

I couldn't find any equations or a calculator for this, so if anybody knows either, that'd be great.

I just added 160 ml of whiskey to a RIS (along with the wood that was soaking in it). This is 20.75 liters at 9.8% abv, for the stout, mixed with that 160 ml of whiskey that is 45% abv.
Naturally, I want to calculate the new alcohol content for the RIS. Help?

Click to expand...

Well I would do it like this
20.75*.098=2.0335 L alcohol in beer
.16*.45=.072L alcohol in whisky
Then do ((total alcohol)/(total volume))*100
(2.1055/20.822)*100=10.11%

45% ABV whiskey has density 0.93954 g/cc. A volume of 160mL of such whiskey contains 0.45*160 = 72 mL of alcohol which, at 20 °C has density 0.78924 g/cc. So this 160 mL of whiskey weighs 160*0.93954 = 150.326 grams and contains 72* 0.7894 = 56.825 grams of alcohol and thus 150.326-56.825=93.50 grams of water.

20.75 liters of beer at 9.8% abv contains 0.098*20.75 = 2.033 L of alcohol which weighs 2.033*0.7894 = 1605.2 grams. The beer weighs 20.75*.998203*SG so I need to know the specific gravity of the beer to go forward. I'll assume that SG is 1.015 in order to complete the calculation. As I'm laying out all the steps you should be able to go back through it with the correct SG. Thus 20.75*1.0131 = 21.023kg. You are adding 150.32 grams of whiskey to this and the alcohol from that, 56.82 grams, is added to the alcohol from the beer, 1605.2 grams. Thus the alcohol by weight is
(1605.2 + 56.82)/(21023 + 150.32) = 7.849%
Convert this to ABV by dividing by the SG of ethanol and multiplying by the specific gravity of the post addition beer.
7.849*1.014/.79066 = 10.07%
I used 1.014 to represent the decrease in the apparent specific gravity caused by the addition of the alcohol which is going to be very small because you are adding very little whiskey. Were you adding appreciably more you would need to measure the specific gravity after you did the addition.

You guys are awesome! Thanks!