﻿ brewing calcs-jmg_(Brix_post-ferment)31July2012
 Stoichiometry-Based Alcohol Estimation © James M. Gossett (July 31, 2012) (from initial Brix and final Brix measured before bottling sugar added) Inputs Measured Initial Brix (20˚C) Measured Final Brix (20˚C) before bottling sugar added Bottling Sugar Added (oz per 5 gal) Outputs Pi (initial real extract, %) * Pi = measured initial Brix/1.04 Pf (final real extract, %) ** Pf =100*(Pi - C) / Wf Real Attenuation (%) 100*(Pi - Pf) / Pi Est. final Brix (after boiling-off EtOH Some use this as a measure of residual, Real Extract.  I think it over-estimates because it includes non-carbohydrate contributors to refraction. & reconstituting volume) %ABW before bottle-conditioning %ABV before bottle-conditioning at 15˚C. ABV (15˚C) = ABW*(final SG) / 0.794   where 0.794 = density of EtOH at 15˚C. %ABV after bottle-conditioning at 15˚C. g sugar consumed per 100 g original wort C = g sugar consumed per 100 g original wort g EtOH produced per 100 g original wort Eq [1] g EtOH = 0.484*C g wort remaining per 100 g original wort Eq [2] Wf = g wort = 100 – C*(0.494 + 0.088) Initial SG (15˚C) from initial Brix*** =1.000019 + 0.003865613*Pi + 0.00001296425*Pi^2 + 0.00000005701128*Pi^3 + 0.001 (to correct from 20˚C to 15˚C) Final SG (15˚C)  from initlal and final Brix**** =1.001843 – 0.002318474*Pi – 0.000007775*Pi^2 – 0.000000034*Pi^3 + 0.00574*Bf + 0.00003344*Bf^2 + 0.0000000*Bf^3 Assumptions: "extract" = maltose 342 g/mol Mass EtOH produced EtOH g = 0.484 per gram maltose consumed Mass CO2 produced CO2 g = 0.494 per gram maltose consumed Mass TSS produced TSS g = 0.088 per gram maltose consumed k 0.445 = contrib of EtOH to Brix at 20˚C  [ Brix units per 1%(w/w) EtOH] Final Brix= [Initial Brix – C + (g EtOH/100 g orig wort)*(k)]*(100/Wf) Eqs [1] and [2] can be subst into this one, and C can be explicitly solved-for as function of initial and final Brix values: C = 100*(Bi – Bf) / [100 – 0.484*k*100 – {0.494 + 0.088}*Bf] Notes: * Pi (initial real extract).  1.04 is often-assumed attenuation factor (reflecting relation between wort sugars and Brix).  It accounts both for refraction-producing agents in wort that are not carbohydrates, and also for wort carbohydrates not being sucrose (on which the Brix scale is defined). ** Pf (final real extract) relates to the sense of "body" and residual sweetness in a beer. *** From Siebert, K.J., "Routine Use of a Programmable Calculator for Computing Alcohol, Real Extract, Original Gravity, and Calories in Beer," J. Amer. Soc. Brewing Chemists., Vol 38 (1), 27-33 (1980). **** From Bonham, L. K., "The Use of Handheld Refractometers by Homebrewers," Zymurgy, 43-45, January/February (2001)