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When making any kind of tea, I understand that water temperature can make a big difference with flavor. I'm wondering if we can also use precise water temperatures to selectively brew for specific compounds in herbal teas.

Is it possible to calculate an optimal water temperature for extracting a chemical compound in a plant/herb based on other chemical information; like density, melting point, etc? If so, how?

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No, calculating is practically impossible, there are too many variables. It's not about density and melting point, it's about tons more.

The way you'd go about it is like everything else in biology: empirically. You'll have to brew your herbs with different temperatures (and ratios of herb to water! These are very important) and use some method for measuring the resulting solute. Sadly, you'll likely need expensive lab equipment for that, although some specific compounds may have characteristic reactions which allow for easy analytical chemistry.

If your compound is very interesting, there is a chance research on it has already been made. You can search Pubmed and Google scholar for phrases like "Extraction of X from Y" where X is the compound and Y the plant. Try doing it with an account which has access to scientific journals' paywalls, for example by becoming a subscriber to your nearest university's library - many will allow this for citizens who are not immatriculated.

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