Both Cr2O3 and Al2O3 are very inert when they are calcined. Cr2O3 and Al2O3 are absolutely insoluble in acids when they are calcined, they are more
like SiO2.
Only freshly precipitated and non-calcined material can be dissolved in acid.
Separating the two will be very difficult. The only thing I can imagine is dissolving in strong base (or molten base if the material is calcined) and
then oxidizing the chromium to the +6 oxidation state. Then by adding excess acid and then adding ammonia you can precipitate the Al as Al(OH)3 while
the hexavalent chromium remains in solution.
Then you need to add acid and reduce the chromium to trivalent again and then add ammonia to precipitate the Cr as Cr(OH)3.
It's a long way and involves a lot of steps and other chemicals. Probably it's not worth the hassle when done on a small scale.
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