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10 g of (NH4)2Cr2O7 contains 0.0412 moles of (NH4)2Cr2O7. The balanced equation shows that 1 mole of (NH4)2Cr2O7 produces 1 mole of Cr2O3. Therefore, 0.0412 moles of (NH4)2Cr2O7 will produce 0.0412 moles of Cr2O3.
Number of molecules = 0.0412 mol * 6.022 * 10^23 molecules/mol = 2.48 * 10^23 molecules