That is tricky! A pH test won’t work- calcium would increase the pH of pure water, but its pH-changing effects will probably be negligible in a solution of acidic vinegar. I don’t think there is a way to definitively prove that calcium has come out of the bone without some sophisticated laboratory set ups, but I have one idea…
It involves reacting the dissolved calcium in the vinegar with sodium hydroxide (a strong base, commonly found in drain cleaner) to form an insoluble salt: calcium hydroxide. Calcium hydroxide is relatively insoluble in water (at room temperature, no more than 0.16 grams can be dissolved in 100 grams of water, according to chem.libretexts.org ).
I don’t know how well this will work, and it will probably take a bit of optimization, but here’s what I would try first…
1. Set up two jars of vinegar, one with chicken bones and one without. Leave for the designated amount of time (a couple weeks?)
2. Remove the bones from the jar and observe how they have changed.
3. Add sodium hydroxide to both jars of vinegar (add enough to raise the pH above neutral- you could verify this with pH paper). Be careful adding it- the reaction gives off heat, so add a little bit at a time. And make sure to wear safety goggles and gloves when working with sodium hydroxide!
4. Observe: If calcium is present in the solution, it should precipitate out to form a white-ish solid at the bottom of the jar. This should happen right after you add it.
Theoretically, the vinegar in the jar that once held the bones will have a lot of dissolved calcium, and should form an insoluble precipitate. [Relevant science joke: If you’re not part of the solution, you’re part of the precipitate!] The solution in the other jar, which has vinegar with no dissolved calcium, should not visibly change when sodium hydroxide is added (no precipitate will form).
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