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No, that is not always the case. A good example is homework problem 7A.15. The given reaction is 2A(g) + 2B(g) + C(g) ---> 2G(g) + 4F(g). Even though A has a coefficient of 2, the data shows that reactant A is first order.
According to the book, the rate law (which can tell us the order of reaction) cannot in general be inferred from the chemical equation for the reaction. Thus, looking at stoichiometric coefficients are not a reliable way to determine the order of reactions.
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