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Recently, I was taught that the coefficients of the reactants in an elementary step of a reaction indicates that reactant's order. Why is this the case? I thought that the order of a reactant was not related to its coefficient.

For example, in the following termolecular reaction mechanism

$$\ce{A + 2B -> C + 2D}$$

the rate law is $k[\ce{A}][\ce{B}]^2$. Why is this the case?

EDIT: Also, for equilibrium reactions, do we always assume the coefficients of the reactants to provide the order for those reactants? What about for equilibrium reactions involving multiple steps?

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    $\begingroup$ "I thought that the order of a reactant" - do you mean order of the reactant or order of the reaction? $\endgroup$ – Dissenter Jan 12 '15 at 5:54
  • $\begingroup$ I mean the order of the reactant. Is this an incorrect assumption? From the ChemWiki, it states that for chemical reactions involving multiple elementary steps, the orders of the reactants are not necessarily the coefficients of the reactants. $\endgroup$ – Kootling Jan 12 '15 at 6:11
  • $\begingroup$ That's for reactions involving multiple elementary steps. $\endgroup$ – Dissenter Jan 12 '15 at 6:27
  • $\begingroup$ For reactions involving multiple steps, do we use the coefficients of the slowest step of that reaction to write the rate law? Or is the order of each reactant (in multiple step rxns) unrelated to its coefficient? Also, does this multiple step rule apply to equilibrium reactions as well, or do the coefficients always provide the order for equilibrium reactions? $\endgroup$ – Kootling Jan 12 '15 at 6:36
  • $\begingroup$ I'll have to leave that question for someone else; it's late and I can't think it through atm. Good question though. $\endgroup$ – Dissenter Jan 12 '15 at 6:37
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If a reaction has just one step, it's named an elementary reaction. In this reaction all of reactant directly participate on reaction and effectively collide with each other. So, the order of reaction corresponds to its coefficient, but if a reaction is not a elementary reaction, there isn't any reason for colliding all reactants with each other. For example, consider the following overall reaction:

$$\ce{A + B + D -> F}$$

Assume the corresponding mechanism is constituted of two elementary reactions:

$$\ce{A + B -> C}$$ $$\ce{C + D -> F}$$

As shown above, there is no need to collide A with D or A with C ... Then, in these type of reactions coefficients are not corresponded to order of reaction .

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    $\begingroup$ In these multiple step type reactions, would the coefficient of the slowest step be used to determine the order of the reactants? $\endgroup$ – Kootling Jan 12 '15 at 17:41
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    $\begingroup$ yes ,it is correct in a reaction with multiple steps,the coefficient of the slowest step would be used to determine the order of the reactants. $\endgroup$ – Fatima Sajadi Jan 12 '15 at 18:10

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