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What are the cases when we can use the molar coefficients in an equation as the order when writing the rate law, instead of the experimentally determined order? And what exactly allows us to assume that the coefficient is also the order?
You'll be doing this when dealing with reaction mechanisms. Because an elementary reaction shows how the step of a reaction occurs, we can write the rate law of elementary reactions (not the overall reaction) with each exponent being the number of molecules of a particular type participating in that step. Then the rate law of the slowest step should agree with the experimentally determined order.
Just adding on that with reaction mechanisms, the rate law will sometimes have the same exponents as the coefficients in the chemical equation by mere coincidence. We cannot assume that the coefficients will be the exponents. We must look at the elementary steps.
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