Contribution of Ethanol to Brix Measurements and

Measurement of %ABV Using Brix Refractometry

  James M. Gossett (March 25, 2012)                Questions/Comments?    Description: http://www.ithacoin.com/brewing/stoichiometry_files/image002.gif

 

     Overview

     Stoichiometry of Ethanol Production From Maltose

     Contribution of EtOH to Apparent Brix   

     Measurement of %ABV Using Brix Refractometry

     Derivation of Calculator Equations

     Evaluation of The Method:  Comparing Estimated and Measured %ABV




Consideration of two factors is required to estimate ethanol (EtOH) production from initial and final refractometer (Brix) measurements:

 

         (i)  the stoichiometry of maltose fermentation to EtOH;  and

 

         (ii) the contribution that the resulting EtOH makes to Brix.

 

In this section, the effect of EtOH on Brix measurements is considered.  Quantifying this effect is not only integral to the Brix-based calculator for estimating %ABV from pre- and post-fermentation refractometer readings;  it also enables an analytical method for measuring %ABV from Brix refractometry.  Such a method is described and evaluated below, using standard additions of EtOH to two different background matrices:  an aqueous solution of sucrose;  and a commercial beer.

 

Like sugars, EtOH in solution will give an apparent Brix value that is dependent upon its concentration.   Thus, while Brix is expected to decline through fermentation as sugar is consumed, the effect is mitigated by the positive contributions to Brix measurements from the resulting EtOH produced in fermentation.   Though Brix superficially reports % (w/w) sugar in wort, the difference between initial and final Brix readings will underestimate the quantity of sugar consumed by yeast, since the final readings will be elevated by the presence of EtOH.

 

This is the opposite problem one encounters using hydrometers to measure specific gravity (SG).  In that case, the difference between initial SG (or original gravity, OG) and final SG (or final gravity, FG) will overestimate the quantity of sugar consumed by yeast, since the final SG reading will be depressed by the presence of EtOH, since it is less dense than water.

 

I experimentally measured the contribution that EtOH makes to Brix measurements by creating EtOH standards of  known % alcohol by volume (%ABV) – both in distilled water and in water with a constant background of 5 g sucrose/100 mL.  I also looked at incremental contributions to apparent Brix from standard additions of EtOH to a commercial beer (Budweiser).

 

Materials and Methods

 

EtOH used was ACS grade, 99.5% pure (Sigma-Aldrich).  It, and the distilled water used in these experiments, were stored at 15C (59F), the standard temperature at which %ABV is referenced and at which hydrometer readings are normally reported.  Standards were prepared in 100-mL glass volumetric flasks at 15C.  Ordinary cane sugar was used; it was neither oven-dried nor stored in a desiccator.  Therefore, its purity was not assured.  However, all that was required in these experiments is that the volumetric concentration of sucrose be uniform among standards that contained sucrose.   Sucrose masses were weighed to the nearest 0.01 g with a calibrated, electronic balance (Dillon D-Terminator, Dillon Precision Products, Inc.).

 

Two refractometers were employed:  (1) a hand-held, analog, optical model (RHB-32ATC, Huake Instrument Co.);  and (2) a bench-top, digital model (HI-96811, Hanna Instruments).   Both nominally report to 0.1 Brix;  both are automatically temperature-compensated (ATC) to report Brix at 20C, the standard temperature at which Brix is usually reported/referenced.   [This difference in standard reference temperatures (15C for %ABV & hydrometer measurements, versus 20C for Brix refractometry) is not a problem, so long as reference temperatures are clearly reported.  Since the refractometers were at approximately the same temperature as the samples, virtually no time-lag ensued between sample addition to either instrument and stable, ATC readings.]  Both refractometers were zeroed against distilled water, and this was checked frequently throughout the analytical period. Both refractometers gave indistinguishable readings;  therefore, in later studies I chose to employ only the analog refractometer because I found it quicker and easier to use.   



A background, 5 g sucrose/100 mL concentration was chosen to mimic the residual extract expected at the end of fermentation in brewing.  Samples were prepared by delivering 5.00 g of sucrose to a volumetric flask;  adding distilled water to dissolve the sucrose;  adding the desired volume of EtOH (15C);  and diluting to 100 mL (15C) with additional water.  To address concerns that the background sucrose solution might not adequately mimic wort, I also performed standard additions of EtOH to a commercial beer (Budweiser).  To keep the background concentration of beer constant (on a % volume basis) in the presence of different volumes of added EtOH, I used the beer at 80% strength (by volume).  Thus, the samples were constructed by measuring out 80 mL of beer in a graduated cylinder;  adding the desired volume of EtOH;  then diluting to 100 mL with distilled water in a volumetric flask.  All components were at 15C when delivered.



Results

 

Figure 1.   Apparent Brix (20C) vs. added %ABV (15C) under three conditions:   in water;  in an aqueous, constant background of 5 g sucrose/100 mL; and in a constant background of 80% (v/v) Budweiser beer.

 


Figure 1 shows that the incremental contribution of EtOH to apparent Brix was independent of the background matrix – i.e., all three regression lines have virtually the same slope.  This is important, because it demonstrates that we are operating in a range where refractive index contributions are predictably additive among components.

 

At high concentrations of EtOH (and presumably of sugars or wort extract), non-linear behavior is expected.  For example, Figure 2 shows how refractive index is affected by %ABW in water.  At levels of EtOH expected in brewing, linearity exists; at levels of EtOH expected in distilled spirits, a non-linear relationship commences between refractive index and %ABW.

 

AppleMark

 

Figure 2.   Effect of EtOH concentration (in water) on index of refraction.  [Data from Taschenbuch fr Chemiker und Physiker (D'Ans-Lax ), Band 2: Organische Verbindungen.  Springer (1983).  ISBN 978-3-540-12263-0, Geb.].

 

The experiment depicted in Figure 1 was replicated four times with both analog and digital Brix refractometers.  The grand mean slope from all trials gives a conversion factor:

 

         0.353  Brix (20C) per %ABV (15C)

 

Or, expressed per %ABW:

 

         0.445 Brix (20C) per %ABW

 

This latter conversion factor was obtained from the former by:   0.353*(1.000)/0.794, where a SG of 1.000 was assumed (as not atypical for the end of fermentation in brewing) and 0.794 is the density of EtOH at 15C.

 

Measuring %ABV Using Brix Refractometry

 

The reliable contribution that %ABV makes to apparent Brix suggests a method to measure %ABV in fermenting wort or finished beers.  A Brix reading is taken on a sample;  the EtOH is then driven off by boiling a known volume of sample down to 20 – 25% of its initial volume;  the residue is reconstituted to its original volume with distilled water;  and a final Brix reading is made.  The difference in Brix (pre-boil vs. post-boil, reconstituted) is divided by the previously determined conversion factor of 0.353 to determine %ABV in the original sample.


 

For a first test of this method, the EtOH standards in aqueous solutions of 5 g sucrose/100 mL were used.  A sample of 100 mL was obtained in a 100-mL volumetric flask at 15C.  This was transferred to a small, stainless-steel saucepan, with excess distilled water used (via squirt bottle) to thoroughly rinse the sample from the volumetric flask into the pan.  The sample in the pan was boiled until only 20 - 25 mL remained (see image above-left -- but note that this shows boiling beer, not EtOH/sucrose standards).  This remnant was transferred back to the volumetric flask, with distilled water rinses of the pan (via squirt bottle) to insure complete transfer back to the flask (see image above-right).  The liquid in the flask was then diluted to 100 mL with additional distilled water.  The flask contents were mixed by repeated inversion.  The flask was placed in a 15C water bath to equilibrate.  The drop in temperature caused the fluid level in the flask to drop below the 100-mL line;  therefore distilled water was added to bring it back up to the mark, insuring that the boiled sample was reconstituted to 100 mL at 15C.  The liquid in the flask was mixed again, and Brix was measured on this reconstituted sample.

 

                  %ABVoriginal sample = (Brixoriginal sample –  Brixreconsttd aftr boil) / 0.353

 

Results are shown in Figure 3 for EtOH standards in a background of 5 g sucrose/100 mL.


AppleMark

        

Figure 3.  Test of Brix-based method for measuring %ABV.

 

The method appears to work quite well.  It is, of course, limited by the precision of Brix measurements (among other factors).  The method uses the computed difference (Brix) between two Brix measurements, and the typical Brix refractometer reports only to the nearest 0.1 Brix.  A 0.1 deviation in Brix propagates to a deviation of 0.1/0.353 = 0.28 %ABV.  We can look at this Brix-reading problem in a more statistically sophisticated way.  Assume measurements of original (pre-boil) and final (reconstituted) Brix could each have potential deviations from their means of +0.1, 0.0, or 0.1 Brix due to reading imprecision.  If each of these three possibilities is equally likely,  then there would be 5 possible outcomes, in terms of deviation from "true mean " Brix reading:  +0.2 (1/9th probability);  +0.1 (2/9ths probability);  0.0 (3/9ths probability);  0.1 (2/9ths probability); and 0.2 (1/9th probability).  The population mean deviation in Brix would, of course, be zero.  The population standard deviation would be 0.115 Brix, for an expected population standard deviation in %ABV of 0.115/0.353 = 0.33 %ABV.   This, however, considers only reading imprecision from using instruments that report to the nearest 0.1 Brix.   And "precision" is not the same thing as accuracy:  any systematic error in Brix reading or in the conversion factor (0.353) systematically affects estimated %ABV.

 

The data in Figure 3 suggest a precision higher than expected:  mean error is 0.05 %ABV and sample standard deviation (n=14) is 0.16 %ABV.

 

One hypothetical concern is that, unlike with the EtOH/sucrose solutions depicted in Figure 3, authentic wort might have non-EtOH constituents whose contributions to apparent Brix could undergo change during the boiling step used with the analytical method.  The method relies on a premise that the Brix between original and boiled/reconstituted samples is solely due to the loss of EtOH from the boil.  To address this concern, a second test of the analytical method was performed, using standard additions of EtOH to an 80%(v/v)-strength sample of a commercial beer (Budweiser).  The resulting Brix values (original boiled/reconstituted) were then divided by the previously determined conversion factor [0.353 Brix (20C) per %ABV (15C)] to provide an analytical estimate of the %ABV in the samples.  Results are shown in Figure 4.

Figure 4.  Brix-based analytical method for %ABV applied to standard additons of EtOH in 80%(v/v) Budweiser beer.

 

That the slope of the regression line in Figure 4 is essentially 1.000 means that the 0.353 conversion factor between incremental Brix and incremental %ABV is valid which is unsurprising since the regression slope in Figure 1 for these standards in 80%(v/v) beer was 0.353.  It also reflects that I observed the same Brix (2.8) in all six samples after boil/reconstitution, regardless of the amount of standard EtOH addition to the original.  This demonstrates that the boiling step successfully removed EtOH from all.  The only evidence to be found, here, that this after-boil/reconstitution Brix (2.8) is a good measure of non-EtOH constituents in the unboiled beer is that the method provides a reasonable measure of the %ABV for the Budweiser sample: the 80%(v/v) dilution without added EtOH gave a Brix of 4.2, which computes to a measured %ABV = (4.2 2.8)/0.353 = 4.0 %ABV, meaning that the original, undiluted sample is 5.0 %ABV.  This agrees with the reported %ABV for this beer. 


In a final application of the method, I applied it to the measurement of %ABV in samples of two distilled spirits:  Gordon's Vodka and Jim Beam Kentucky Bourbon, both of which report "80 Proof" on the bottle, which is 40 %ABV.  I diluted each four-fold before analysis, to get the EtOH content down into the range within which method evaluations had been performed.  Results for both gave 40.8% as the ABV of the undiluted spirits.  It's interesting to note that after boiling and reconstitution of samples during analysis, both gave Brix readings of zero.  There's very little in the spirits besides EtOH and water.   

 

 

Finally, a comment about the refractometers used:  In all respects, the hand-held, analog refractometer performed as well as the bench-top, digital refractometer.  The hand-held model uses smaller samples (an advantage) but is more difficult to read (a disadvantage).  On the other hand, the hand-held, analog model tends to provide the user with feedback when problems develop that limit precision.  For example, some dark and turbid samples will give rather fuzzy lines of demarcation when one tries to read the analog scale.  Often this fuzziness gets worse with time as the sample sits on the glass slide, presumably as solids settle or gas bubbles form.  The fuzziness of the demarcation line serves as a kind of warning to the user. The digital instrument gives the user no such feedback:  a button is pressed, and Brix numerals appear on an LCD screen;  the instrument is doing the optical reading, not the user.   I rather like knowing when I am encountering difficult samples.  To be sure, if the user presses the "read" button of the digital refractometer repeatedly over time, with the same sample loaded, the Brix readings will be observed to change as solids settle or bubbles form.  But since the user is not observing the sample as closely as is necessary when using a hand-held, analog refractometer, the cause of drifting Brix is not apparent.  The user might presume the cause is merely time delay in the ATC mechanism;  and the user would be mistaken, in many instances. 


Tips for Application of This Analytical Method to Beers


The major difference between application of this Brix-based, %ABV analysis method to beers, versus its application to EtOH/sucrose/water samples (or, likely, to wines), is the production of foam in working with beers.  The initial sample volume must be precisely fixed, and the after-boil sample must be accurately reconstituted to this initial volume (Note: knowledge of that volume is not important;  it is sufficient merely to have restored the boiled sample back to whatever was the intial sample volume.  In that regard, any container that allows precision in volume may be used.  A volumetric flask, with its bulbous body and narrow neck, is designed for this purpose.)  Foam presents problems in both steps.  It is advisable to thoroughly degas the initial sample before attempting to pour it into a volumetric flask.  Degassing may be reasonably accomplished by stirring, but this is best done at a temperature above the temperature at which volume is to be fixed (15C or 59F).  If degassing is done on a cold bottle of beer, more gas will evolve as it is warmed to 15C.    In the boiling step, much foam and "skin" will develop.  Boiling should be done gently, minimizing caramelization.  Care must be taken in transferring the boiled residue back to the volumetric flask.  I recommend reconstituting the boiled sample in the flask back up to just below the desired, final level.  Incubate this warm, diluted sample at length in a 15C bath, not only to reach this desired temperature, but also to allow the foam to subside.  Occasional rotation of the flask back and forth can help move entrained bubbles to the top surface.  When you are confident that the sample has reached 15C and the foam has subsided, add the last few mL of water to bring the level up to the desired starting mark.  Then invert the stoppered flask a few times, gently, to mix;  and place the flask back in the bath to wait for foam to subside again.  This can be a lengthy process, but the reward is precision.


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