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I was wondering as to why in 15.3, we divide by the number of moles from the equation (such as part c where we divide by 2 for the moles of NO2), whereas in 15.5 we multiply by the number of moles (such as part a where we multiply by 3 for the moles of O2)?
Part c of 15.3 asks for the the unique rate of reaction, which is the rate of change of the reactant(s)/stoichiometric coefficient. So you divide the rate of change of 2NO2(g), -6.5, by the stoichiometric coefficient of 2NO2(g), which is 2. Part a of 15.5 asks for something different, which is simply the rate of reaction (notice how it's not the unique rate of reaction).
Just remember that the rate of the reaction (unique rate of the reaction) is always the rate of either formation of a product or consumption of a reactant divided by the coefficient of that product or reactant in the balanced chemical equation. For calculating the rate of a formation, you simply divide concentration change by change in time. Coefficients are only used when relating rates of one reactant or product to another reactant or product, such as when calculating the unique rate of the reaction.
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