According to the Brewer's Friend yeast starter calculator, it takes 114g of DME to create a 1L 1.040 starter wort.
Is it correct to assume that 1L of 1.040 starter wort made from grain also contains 114g of sugar?
A liter of wort made from any source of 'extract' weighs 1.040*998.203 = 1038.1 grams. A sucrose solution of that density contains 9.993 grams sucrose per 100 grams i.e. it is 9.993 °P or very close to 9.993 Brix (the scales are very close to one another) or, in other words 9.993% w/w sucrose.
0.09993*1038.1 = 103.7 sucrose. So to make 1.040 sucrose solution one dissolves 103.7 grams sucrose in 3/4 L of water and then makes up to 1 L.
DME contains mostly maltose but other sugars as well. The fact that these are not sucrose doesn't effect the weight/density relationship appreciably but maltose does carry 1 water of hydration which means that a gram of maltose is only about 950 mg maltose and 50 mg water. Thus 103.7/.95 = 109 grams of maltose from the Spectrum Chemical Maltose jar would be needed to make a 1.040 SG solution. So the 114 grams number is either in error or assumes a higher moisture content for the particular DME who ever came up with that number was working with. As anyone who has opened a bag of DME on a humid day or dumped one into a steaming kettle knows it is very hygroscopic.
Also, how does Brix factor into this? 1 degree Brix is 1g of sugar dissolved in 100g solution. 1.040 wort is 10 degrees Brix. I don't understand how one extrapolates how much sugar is contained in a given amount of solution per degrees Brix. Can anyone explain?
I've kind of sketched out how it is done but here it is step by step.
1. Determine the density of the wort by multiplying the specific gravity by the density of water, 998.203 g/L (at 20 °C)
2. Determine the °P either by looking it up it the ASBC table or using the ASBC polynomial (which I'll get to in a minute)
3. Multiply the density (grams/L) but the Plato value (percent) and divide by 100 (to convert °P to a fraction). The result is the number of grams of sugar in 1L of wort.
4. Subtract that from the density from Step 1. That is the weight of the water in 1 liter of wort in grams.
5. Divide the weight of the water by .998203 to get the number of mL of water.
6. Measure out sugar and water and mix. If the sugar contains water, either as water of hydration or adsorbed moisture, be sure to allow for that (or dessicate the sugar before weighing out).
ASBC Polynomial:
To calculate °P from 20°C/20°C apparent specific gravity use
°P = ((135.997*S - 630.272)*S +1111.14)*S - 616.868
You can copy and paste that into an excel spreadsheet
