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Why can't we apply law of mass action for non-elementary reaction? Why does is vary with the rate law in case of non-elementary reactions?

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The Law of Mass action states:

The rate of a reaction is directly proportional to the concentration of reactants raised to powers equal to their stoichometric coefficients

This is only valid for elementary reactions since they happen in a single step. As a result, such simple relations hold good.

But what about the more complicated ones. Certain reactions, like the oxidation of ethylbenzene to benzoic acid using hot $\ce{KMnO4}$ don't happen in a single magical step. They involve lots of reactive intermediates and transition states, so it's basically a bunch of several elementary reactions. You can't consider the whole reaction as an elementary reaction.

But you can formulate a rate equation for non elementary reactions by considering them as a bunch of elementary ones. However such formulations involve knowing the mechanism of the reaction in question, along with other data.

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  • $\begingroup$ //This is only valid for elementary reactions since they happen in a single step. As a result, such simple relations hold good.// Why does such simple relations hold good only when a reaction happens in a single step? Why is the 'single step' so necessary for this law? $\endgroup$ – Hisab Jul 4 '17 at 16:24
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    $\begingroup$ @Hisab For example, consider an arbitrary reaction: $$\ce{A + 2B -> C}$$ If this was a single step reaction, a molecule of $\ce{A}$ and two molecules of $\ce{B}$ should simultaneously collide and form $\ce{C}$. The concentration of $\ce{B}$ is more important than $\ce{A}$ (since two of it are needed in a single collision), and hence the $^2$ is attributed to it. For other single step reactions this isn't the case, not all reactants collide simultaneously. $\endgroup$ – Pritt says Reinstate Monica Jul 4 '17 at 16:25
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If I ever knew why the tLoMA held for elementary reactions, I've forgotten. I can, however, give an example of a situation applicable to your question illustrating why it doesn't necessarily hold for complex reaction systems. Consider the two elementary reactions A+B→ C+D and A+C→E the first thing I'd ask you to do is express the equation for the total equilibrium constant. The second thing I'd ask you to consider is if the first reaction had an extremely high rate and the second had an extremely low one (on the order of years-1). The overall reaction will be dependent almost exclusively (except for the very very start) on the rate of the second reaction, tLoMA will (and must) fail.

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