# Calculating volume ethanol in an fermented aqueous solution of sucrose, water, and ethanol

I've been working on a biology experiment where I calculate the fermentation yield of yeast under various light induced stress responses inhibiting the translation of various fermentation enzymes. My solution initially contained 12.5g of sucrose, and 50g of water, resulting in 20% by mass sucrose.

Initially, I expected to measure this value before and after using a refractometer that measures in brix, which is a measure of percent mass of sucrose in a solution. I figured that the difference between these two values would represent the percent by mass ethanol in the final solution.

I failed to consider though that the yeast produced ethanol as the experiment progressed changing the mass of the solvent and therefore the percent mass of sucrose of the solution.

Primarily, my goal is to calculate the volume of ethanol in the solution. In order to do this though, I would need to be able to calculate the volume of the whole solution based on the change in the percent by mass sucrose in the solution, and the volume of the sucrose in the solution. With these values I could subtract the volume sucrose and the constant volume water from the solution and obtain the volume of ethanol.

Based on some internet searching, I've gathered that this is possible but it involves a knowledge of intermolecular interactions paired with a knowledge of the molarity of particular molecules. This is beyond my scope of knowledge for chemestry. Overall, I'm trying to develop a generalized equation for determining volume ethanol based on change in brix of the solution. This has been baffling me for a while now and I figured there may be other amateur researchers with the same questions I have so I figured I'd pose the question to the community at large. Thanks for the help!

• It seems to me that your experimental design fails on several points. First yeast is inhibited by alcohol. I think about 16% (vol %) is the concentration that kills yeast. So I think your sugar content is beyond that. Second I'd expect the conversion to be non-linear. At first yeast is multiplying rapidly and hence converting rapidly. But as the alcohol % increases I think conversion would slow. Third I'd wonder about conversion of sucrose into glucose and fructose. I know that brix is used in wine and beer industries so this may not be a problem. – MaxW Dec 20 '15 at 23:25
• @MaxW I can get the yield with an online calculator so I know it's possible but since I'm writing a paper on this I have to demonstrate the underlying calculations. Also I don't think it should matter that the yeast dies because it's a constant strain of yeast so it would all be inhibited at the same levels of ethanol exposure – Mikey G Dec 20 '15 at 23:27
• I'm not sure if the data in the link can be adjusted to your sugar content, but boiling the solution to remove ethanol, then diluting to some constant volume would be a way to generate your own calibration curve. ithacoin.com/brewing/EtOH_to_Brix.htm#Measure_ABV – MaxW Dec 21 '15 at 0:18
• Some of the fundamental calculations are detailed here. web2.airmail.net/sgross/fermcalc/… Google search for additional references: google.com/… – MaxW Dec 21 '15 at 5:20
• @user2985955 Would you mind summarizing the chemically relevant portion here in an answer? I think this might be useful to future readers over here as well. – jonsca Feb 11 '16 at 23:47