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The simple/short version of the question:

What does a hydrometer gravity reading of 1.036 really mean? Does it mean the density of the liquid is 3.6% greater than that of distilled water (ignoring inaccuracies and errors in measurement)?

The context/long version of the question:

When creating a yeast starter, it is commonly advised to create a light wort in the range of 1.030 to 1.040 gravity by using 100g of dry malt extract (DME) per liter of water in the starter, or a 10-to-1 ratio of water to DME by weight.

According to wikipedia, gravity is "the ratio of the density of a sample to the density of water", or equivalently, the ratio of the mass of a given volume of a sample to the mass of an equal volume of pure water. By my math, 1L of water is ~1000g (with variation depending on temperature), and dissolving 100g of DME into that should result in a gravity of (1000g + 100g)/1000g = 1.100. This is very, very far off from the 1.030-1.040 range expected by common wisdom.

Thinking this common wisdom was perhaps just a commonly-repeated mistake, I checked the suggestions of 4 online yeast starter calculators, to see how much DME they each suggest should be added to 1 liter of water to achieve 1.036 gravity (apologies for the non-links, apparently I need more reputation to post more than 2):

  • 102.7g according to www.brewersfriend.com/yeast-pitch-rate-and-starter-calculator/
  • 103g according to www.captainbrew.com/yeast-pitch-rate-and-starter-calculator
  • 98.18g according to www.yeastcalculator.com/yeastcalc.html
  • 98g according to www.brewunited.com/yeast_calculator.php

Aside from rounding differences, there are 2 different values given here, within ~5% of each other, and essentially agreeing with commonly-repeated advice. In contrast, my straightforward calculation would suggest the value is 36g of DME per liter, barely more than a third of the values from the calculators.

So I checked experimentally (and very roughly) while creating a big starter. Using a kitchen scale, I took 3.1L of hot tap water (the extra 0.1L is to compensate a bit for boil-off), and added 300g of DME. I brought it to a rolling boil and held it there for ~5 minutes to sanitize, then used a larger pot to make an ice water bath, and cooled the starter wort to ~68F according to my floating thermometer. I checked the gravity with my hydrometer, and it read ~1.040. There's plenty of room for little errors here, but the fact is, I got results pretty much in line with the common advice and the online calculators.

I just don't understand how this can be. It seems like I should have seen a gravity reading close to 1.100. But when common wisdom, 4 online calculators using (apparently) at least 2 different equations, and my own experimental results all disagree with my abstract logic, I have to assume my abstract logic is incorrect. What's wrong with my calculation? How does adding 100g of DME to 1L of water result in a gravity of ~1.036 instead of ~1.100?

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Specific gravity measures density, which is mass/volume. If you measured the total mass of your system (3000g + 300g) you would have gotten 3300 grams, but the volume is not 3000 ml because you added the DME and it increases the volume of the solution. If the volume increased by 174 ml you would get 3300/3174 = 1.040 for the density.

In other words, the answer to your initial question is yes.

  • What you seem to be implying is that DME is not 100% soluble, but contains some proportion of insoluble solids which increase the volume of the sample. Is that what you mean? – zacronos Oct 6 '17 at 1:12
  • No, it can dissolve completely, but it still increases the volume. All of those molecules in the DME are still taking up space -- they can't just disappear. If you add 100 g of water to 1000 g of water you don't end up with a gravity of 1.100, you end up with a gravity of 1.000 because the total volume increased to 1100 ml and the mass increased to 1100 g. This is the perfect case where the water is completely "dissolved" in the water, but it still takes up volume. – GigaFemto Oct 6 '17 at 3:13
  • I don't think adding water to water is technically "dissolving". However, point taken; I had it in my head that when you dissolve a solid in a liquid, the volume of the resulting liquid doesn't change (I know the molecules don't "disappear", but there is plenty of "empty space" between them). After looking around, it seems I was just wrong. The resulting volume almost always increases; in some cases, it even increases by more than the volume of dissolved solids. It may also be theoretically possible for the volume to stay the same or decrease. – zacronos Oct 6 '17 at 14:49
  • Yup, it can decrease. Alcohol is less dense than water, which is why you can have a final gravity reading less than 1.0 for a beer with high alcohol and yeast with high attenuation. – ThisIsTheDave Oct 10 '17 at 16:30

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