
StoichiometryBased
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 boilingoff EtOH



Some use
this as a measure of residual, Real Extract.
I think it overestimates because it includes noncarbohydrate
contributors to refraction.



&
reconstituting volume)





%ABW before bottleconditioning




%ABV before bottleconditioning


at 15˚C.

ABV _{(15˚C)} = ABW*(final SG) / 0.794
where 0.794 = density of EtOH at 15˚C.



%ABV after bottleconditioning


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 solvedfor 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 oftenassumed
attenuation factor (reflecting relation between wort sugars and Brix). It accounts both for refractionproducing
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), 2733 (1980).






****

From Bonham, L. K., "The Use of
Handheld Refractometers by Homebrewers," Zymurgy, 4345, January/February (2001)




