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Assume that somebody wants to measure the sugar content of a liqueur. It seems that there are two types of Brix meters for it, ones which use the solution density and ones which use refraction of light.

If we have a meter intended for measuring the content of a sugar-in-water solution (and assume that we are talking pure sucrose here, not other sugars), but are using it for measuring a solution which has, beside sugar and water, also 15 to 35 percent alcohol and also unknown organic (colored or transparent) substances dissolved:

  1. which type will give less error, refractional or density-based?
  2. how large will the error be? For example, if the true value is 20 g sugar per 100 ml solution, how far are the values delivered by the meter likely to stray from those 20 grams (I am looking for a back of an envelope estimation, not for an exact interval)?
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  • $\begingroup$ This was prompted by a question on Cooking, cooking.stackexchange.com/questions/41757/…, where we had to tell the poor OP that doing the measurement won't help him much anyway. But it sparked this interesting side discussion. $\endgroup$
    – rumtscho
    Feb 5, 2014 at 20:07
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    $\begingroup$ My first guess would be that both methods are likely to be heavily affected by ethanol content, which would make them useless. The simplest method I would guess to have a chance would be to measure optical rotation of polarized light, ethanol is not visible there. $\endgroup$
    – Mad Scientist
    Feb 6, 2014 at 6:48
  • $\begingroup$ @MadScientist are there commercial kits for measuring polarized light rotation which are as cheap, cabinet-space-economical and easy to use for a chemistry noob as a candymaker/brewer's Brix meter? $\endgroup$
    – rumtscho
    Feb 10, 2014 at 16:32

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Once I got going, this turned out to be a lengthy answer. So here's the summary: the alcohol will introduce a significant error in both methods. The density measurement will probably be closer to the actual sugar content. Th density measurement will underestimate the sugar, and the refractive index will overestimate the sugar.

Both the refractive index and the density-based methods work for measuring sugar content because adding sugar to water raises the refractive index and the density in amounts proportional to the concentration of the added sugar. As you and others noted in that thread, ethanol interferes with that measurement because it also affects the density and refractive index of the resulting solution. So how large is that effect?

To estimate this effect, I am going to restrict myself to the 15-35% alcohol (by volume) range you suggested. The charts I found for the density and refractive index of water/ethanol mixtures gives the ratio by weight; your range converts to 12-28% by weight. Pure water has a density of 0.99823 g/mL, and a refractive index of 1.3330. 12% ethanol has a density of 0.97910 g/mL, and a refractive index of 1.3410. 28% ethanol has a density of 0.95710 and a refractive index of 1.3524. Note that adding ethanol increases the refractive index, but decreases the density. I'll come back to that at the end.

This page gives a table of the index of refraction and density of sucrose solutions in water, as a function of the sucrose weight fraction. The 20 g sucrose per 100 mL solution is approximately 20% by weight, so that will have a refractive index of 1.3639, and a density of 1.0810 g/mL.

The density and refractive index changes for both sucrose and ethanol are pretty linear over the range you're interested in, if you take them independently. Assuming that the sucrose effects and the ethanol effects are independent (NB: this may not be a good assumption), the refractive index measurement will be higher by 0.01-0.02, which corresponds to an overestimate of 7-14% sucrose. The density measurement will be lower by an amount 0.02-0.04 g/mL, which corresponds to an underestimate of 5-10% sucrose. So it looks like the hydrometer measurement will be a bit better, but the two methods will be off in different directions. It's a noticeable effect: depending on the method and the alcohol content, you might be off by somewhere between a quarter and half of your intended sugar content.

There is one neat thing you could do to take advantage of the fact that the alcohol moves the density in the opposite direction to the sugar. If you had a bottle of liquor with unknown alcohol content and unknown sugar content, you could take both the density and the refractive index measurement. Again, assuming the four effects are linear, and the sugar effects are independent of the alcohol, you could write two equations for the refractive index $RI$ and density $\rho$ as functions of the alcohol and sugar: $RI = Ax + By, \rho = Cx + Dy$. $x$ and $y$ are your alcohol and sugar content in whatever units you prefer, and $A, B, C,$ and $D$ are the empirical parameters describing each of the four effects. If you take a measurement for $RI$ and for $\rho$, you can solve for $x$ and $y$.

PS: to answer one question suggested by the comments of the [cooking.se] question you linked, density-based brix meters (I'm used to seeing them called hydrometers) are typically used for home brewing beer and wine because the only source of alcohol is the fermenting sugar. You take a density measurement before fermentation begins to get a baseline. Then, at any point after fermentation begins, the difference between the current density and the baseline density is directly proportional to the alcohol content. I'm sure the same reasoning applies to the refractive index method, but I've never used that for beer-brewing (I've only used it for my real research). See Cutaia, A.J., Reid, A-J. and R.A. Speers, 2009. Examination of the relationships between Original, Real and Apparent Extracts, and Alcohol in Pilot Plant and Commercially Produced Beers. J. Inst. Brew. 115:318-327.

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  • $\begingroup$ Wow, this is even more detailed than I expected. But something you didn't mention: there are also other organic substances in a liqueur, which give aroma and sometimes color, and whose effect we can't correct for. Do you think that they will generally have a higher effect on density, or on refraction, or is it impossible to tell? $\endgroup$
    – rumtscho
    Feb 9, 2014 at 21:23
  • $\begingroup$ @rumtscho: For clear liquors such as amaretto, Kirschwasser, absinth, pernot and the like we have water, ethanol and sugar as main constitutents (each usually > 10%) - other constituents have much lower concentrations so at the end of the day they don't introduce that much error. The flavor-carrying compounds like the extracted stuff from the herbs or the benzaldehyde are usually in the ppm to maximum 1 permil range. Things will be different e.g. with advocaat but I don't think refractive index measurements will be much fun with that, anyways... $\endgroup$
    – cbeleites unhappy with SX
    Feb 10, 2014 at 16:07
  • $\begingroup$ @cbeleites so even when the additional compounds are enough to change the color of a liqueur (such as in absinth or grand marnier), you think they are not enough to change the refractive index? I am not a chemist, so I don't know if the change of one optical quality (color) is indicative of the change of another optical quality (refractive index), or if the color changes at much lower concentration which are not enough to have a practically noticeable effect on the refractive index. $\endgroup$
    – rumtscho
    Feb 10, 2014 at 16:30
  • $\begingroup$ @rumtscho: Of course it always depends. But we're talking about kitchen chemistry, not about high-precision measurements. There are certain things that can disturb the measurements: turbidity is a bad sign. The advocaat also has a high protein content which makes it very different from other kinds of liqueur. But there are very colorful compounds that don't disturb. Consider that the alcohol content of both white and dark red wines can be measured without any problem with the same instrument. Caramel color (and its "natural" counterpart) should also be at most in the permil range, I guess. $\endgroup$
    – cbeleites unhappy with SX
    Feb 10, 2014 at 17:11
  • $\begingroup$ @cbeleites thank you. I was aware that the content of the pigments, essential oils and waxes is in a very low range, I didn't know that this is low enough to not matter. As for white and red wine, I have only seen density meters used in wine making. $\endgroup$
    – rumtscho
    Feb 10, 2014 at 17:59
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Consider density vs. a Pousse-café. Refractive index might do less galloping overall - but whoa! for things like Benedictine and absinthe loaded with refractive organic essences. You need calibration tables either way.

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Brewers are interested in both the sugar content and alcohol content of their products. The way they get both is by distilling a known volume of beer and measuring the density of the distillate (made up to the original volume of the beer). As it is assumed that all the alcohol has been recovered, the alcohol content of the distillate is the alcohol content of the beer.

The same is done for the sugars with the residue. It is made up to original volume and its density measured using a digital density meter. Correction for the specific gravity of the beer and distillate give the percent sugar in the original beer.

When it comes to liquers, the concern is usually more with the alcohol that what TTB calls the 'obscuration' (sugars). If the obscuration is less than 100 mg/L (not really sure I remember that right) then the same basic method as used by brewers must be used i.e. distillation for the EtOH determination and I suppose that the same method could be used to estimate the obscuration itself but I do not recall the accepted TTB procedure for this.

In any case the only time refractometers are used in the brewing industry is where they have been calibrated against a digital density meter.

To illustrate the point about other substances interfering: a fellow once asked me to proof a limoncello. The distillate was murky with suspended droplets of lemon oil. I had one conversation with the TTB lab about what to do about this but the guy dropped the project before I ever got an answer.

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