Alcohol Dilution
Calculates how much stock alcohol and water you need to prepare a given amount of alcohol at the strength you want. Because the volume shrinks on mixing, more water is needed than simple proportion suggests.
What it does
- Dilution recipe: how much stock alcohol and water are needed to prepare a given amount at a given strength, as volumes and as weights.
- Density from strength: the density of a water–ethanol mixture at a given temperature and its strength on the other basis (% v/v ↔ % w/w).
- Strength from density: % w/w and % v/v from a measured density.
Why the water is more than simple proportion suggests
Ethanol and water contract on mixing: 72.92 mL of 96 % alcohol and 27.08 mL of water give about 97.5 mL, not 100 mL, and the mixture is slightly stronger than 70 %. The tool therefore works with masses: the ethanol mass is conserved (mstock·wstock = mfinal·wfinal), and the water is the mass difference. For 100 mL of 70 % from 96 % at 20 °C this is 29.74 mL of water.
Why the volume shrinks
The hydroxyl group of ethanol forms hydrogen bonds with water, and in water-rich mixtures the non-polar ethyl group is accommodated in the open, void-rich hydrogen-bond network of water, which rearranges around it (hydrophobic hydration). At higher alcohol contents the molecules do not mix randomly: water forms small clusters among closely packed ethyl groups. Together these effects make the mixture denser than the average of the pure liquids. Mixing also releases heat. For small volumes the effect is negligible, but when preparing large volumes read the final volume only after the mixture has cooled. More in the guide.
Method
- Densities from the OIML R 22 (1975) formula, valid from −20 to 40 °C; the tool reproduces the printed OIML tables (compared on 6 889 cells).
- Strength by volume is defined at 20 °C. Converting % v/v to % w/w has no closed-form solution and is solved iteratively; strength from density is solved by bisection.
- Volumes in the recipe are volumes at the preparation temperature; weighing is independent of temperature and is the more accurate way to prepare.
Limitations
- Pure water–ethanol mixtures only. Dissolved solids (tinctures, extracts) and other volatiles change the density.
- The density must be a true density; alcoholometer and hydrometer readings need a glass-expansion correction that is not applied here.
- Dilute ethanol-containing injections with 0.9 % sodium chloride, not water.
Detailed guide: formula, tables, iterative solution, worked examples and references