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To get the reduction half-reaction for NO2-(aq) + Al(s) ----> NH3(g) + AlO2-(aq), first you get the skeletal equation (NO2-(aq) ----> NH3(g)). Then you balance O atoms by adding 2 H2O molecules. To balance the H atoms on each side add, for each H atom needed, one H2O molecule to the side of each equation that needs hydrogen and one OH- ion to the opposite side. Since there are seven H atoms on the left side, you add seven H2O molecules for each of the H atoms needed. Since the solution is basic, you would add seven OH- ions on the left side, resulting in 7H2O(l) + NO2-(aq) ----> NH3(g) + 2H2O(l) + 7OH-(aq). Finally, cancel the like species on opposite sides of the arrows and balance the charge by adding electrons to get, 5H2O(l) + NO2-(aq) + 6e- ----> NH3(g) + 7OH-(aq).
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