I think that Lefaucheux10 has the best idea, but 10 square feet!? That's a lot. However, the liquid reagents needed to do an efficient extraction will
also be huge, and still leave any reduced metal behind. And, without a rotary evaporator, a huge task to process.
I doubt if significant Pd would leave in the smoke. I'd do a number of ignitions of smaller pieces at night. Maybe in whatever local spot is not
teeming with people?
A number of decantations of the burnt slurry in water should allow you to separate much of the burnt organics. Then a total ashing of the remainder,
more decantations.
Finally, treat residue with aqua regia. Concenrtate to drive off most of the HCl and all of the HNO3. Dilute. Treat with aq. NH3, followed by HCL to
precipitate Pd (NH3)2Cl2. Re-dissolve in excess NH3 soln, ppt. with HCl, ignite to give Pd sponge.
You won't get pure Pd without excessive work. Oxyacetylene with an oxidizing flame will melt it. Or just sell the Pd sponge to a refiner
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