Caleb with info given
NO + O3 ---- NO2 + O2 -198.9 KJ/mole
3/2 O2 ---- O3 +142.3 KJ/mole
O ---- 1/2 O2 -247.5 KJ/mole
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NO + O ---- NO2 -304.1 KJ/mole
when a reactant and a product are the same, they (in a sense) can be eliminated from the equation. Both ozone and oxygen gas were not part of the final equation, so they needed to be "canceled". That is why you had to switch the 2nd equation and why you needed half of the final equation.