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?