Solution to Weird Science

To solve this reaction traditionally, observe that the state change N−3 → N+4 loses 7 electrons, while the state change Cl+7 → Cl−1 gains 8 electrons. So the reaction must involve 8 nitrogen atoms for every 7 chlorine atoms. The alternative method is to treat the coefficients of the 8 compounds as unknowns in a system of 7 simultaneous equations, one for each element. Specify one coefficient arbitrarily and the other 7 will be uniquely determined.

The solution:

21 Sb(ClO4)5 + 40 (NH4)3PO4 + 120 NaOH → 7 Sb3(PO4)5↓ + 120 NO2↑ + 5 Na3PO4 + 105 NaCl + 300 H2O

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