The figure you’ve linked plots concentration by weight (wt.%), while the alcohol content of drinks is usually given in volume percent (v/v). Ethanol is less dense than water, so a 30% concentration by weight is a higher concentration by volume.
Imagine a 100g solution of 30wt.% alcohol. That means that 30g are ethanol and 70g are water. the 70g of water translate to 70ml volume (density 1g/ml) and the 30g of ethanol translate to 30/0.789 = 38.02ml. So in total, you would have 108.02ml of liquid and the concentration of ethanol by volume would be 38.02/108.02 = 35.2%.
Why it gets wacky at the end: Ethanol freezes at -114°C, water freezes at 0°C, but at specific concentrations, the eutectic composition, the solution freezes at a lower point than either of its constituents. The eutectic point is the lowest possible freezing point of a solution. The formula I gave is not applicable to eutectic solutions and is an approximation based on perfect solutions (which in reality don’t really exist).
There is only one error in your equations (and that doesn’t change much about your point) is that the volume of that mixture is slightly lower than 108mL and should sit at about 107.1mL.
The figure you’ve linked plots concentration by weight (wt.%), while the alcohol content of drinks is usually given in volume percent (v/v). Ethanol is less dense than water, so a 30% concentration by weight is a higher concentration by volume.
Imagine a 100g solution of 30wt.% alcohol. That means that 30g are ethanol and 70g are water. the 70g of water translate to 70ml volume (density 1g/ml) and the 30g of ethanol translate to 30/0.789 = 38.02ml. So in total, you would have 108.02ml of liquid and the concentration of ethanol by volume would be 38.02/108.02 = 35.2%.
Why it gets wacky at the end: Ethanol freezes at -114°C, water freezes at 0°C, but at specific concentrations, the eutectic composition, the solution freezes at a lower point than either of its constituents. The eutectic point is the lowest possible freezing point of a solution. The formula I gave is not applicable to eutectic solutions and is an approximation based on perfect solutions (which in reality don’t really exist).
There is only one error in your equations (and that doesn’t change much about your point) is that the volume of that mixture is slightly lower than 108mL and should sit at about 107.1mL.
Volume reduction in water - ethanol mixtures
Amazing, thanks for the clarification!