# Can I determine the rate law order from stoichiometric coefficients?

I've read in two books, and seen in three separate videos courses, that you cannot determine the rate law order from stoichiometric coefficients.

Then, I have seen homework and "practice" problems that ask you to do exactly that.

Needless to say, I am confused.

This is how I am presently making sense of the issue: Given a balanced equation, and absent any other information, you can (and must) use the stoichiometric coefficients to determine the rate law. So, for example, given the equation $$2A+B \rightarrow C + 3D$$, the rate law would be $$rate = k[A]^2[B]$$.

But, this would only hold true if this were an "elementary reaction" (i.e., no equilibrium).

So, I wonder why the books and videos emphasize that you can only determine order by experiment and not from the stoichiometric coefficients. I am guessing that they do so because, in practice, you do not know if the reaction is an elementary reaction or not and therefore experiment is the only way to make that determination. And, because you don't really know if it is an elementary reaction, you can only determine the rate law experimentally.

The bottom line:

• as a practitioner, determine rate law experimentally;
• as a student, given no information other than the balanced equation, determine the rate law from the stoichiometric coefficients;
• as a student, given rate and concentration data, determine the order (and rate law) from the data.

That is a pragmatic, but unsatisfying, solution to the problem but I would prefer a clearer explanation of what is going on.

• In general, three body collisions are rare, so 2A + B will not be reacting via a three body collision and, therefore, it is not an elementary step reaction. Coincidences aside, and there are plenty, rate law orders are determined experimentally unless the reaction is an elementary step reaction. And this cannot just be assumed. – Ed V Feb 13 '20 at 17:18
• The stoichiometry indicates only how many moles of A and B etc react to give products and nothing about the mechanism of the reaction, even for apparently simple reactions. The mechanism can only be determined by experiment. – porphyrin Feb 13 '20 at 19:19
• Thanks for the comment. I understand that "multi-body" collisions become rarer as the required number increases, but I had not yet "put two and two together" that the third order reaction [A]^2[B] would not be very probable as a practical matter. That is important to understand, obviously. But, it really does not change my position that the student is in no position to do anything but use the stoichiometric coefficients if no other information is given (assuming the student is not supposed to break the reaction into its intermediate states) (see my comment below to @Zhe's answer). – Randall Blake Feb 13 '20 at 21:25
• @RandallBlake if that is really the only information given, then the question is underspecified. – Tyberius Feb 14 '20 at 18:16

There are multiple issues here:

1. You should not assume that there is a simple rate law. Chemistry is complicated, and even simple reactions may proceed through multiple pathways in parallel.
2. More generally, you should not assume that you are given enough information to determine the solution. Just because the stoichiometric coefficients are there, does not mean that you can use them to determine the answer. So, if you just have a balanced reaction, you know nothing. If you want to become a scientist, you should learn to be comfortable with not having the answer.

So, I would say that your bottom line is incorrect.

The experimental rate law should be determined experimentally.

Given a putative mechanism with elementary steps and knowledge of rate constants for those steps, you can propose a rate law that for that mechanism. Do not assume it has any bearing on reality, since your putative mechanism may be wrong.

Frequently, the approach is to take the experimental rate law and see if the derived rate law for a proposed mechanism is consistent with the experimental result.

• thanks for the explanation. I think "I get it." But, I have a small "quibble." You say that my "bottom line is incorrect" but I disagree. I agree that the rate law MUST be determined experimentally. Everybody says that and I have no problem with that. BUT, as a student answering a homework question, if I am ONLY given the balanced equation and asked to determine the order, then the ONLY thing I can do is use the stoichiometric coefficients (unless I'm being quizzed on multi-step reaction mechanisms). A practitioner, on the other hand, would simply go with the experimental measurement. – Randall Blake Feb 13 '20 at 21:16
• @RandallBlake "the ONLY thing I can do"... no, you could say there is insufficient information to arrive at a specific answer. – Karsten Theis Feb 14 '20 at 4:39
• Oh, Karsten, if it were only so simple! Homework nowadays is served by heartless computers which demand specific answers of specific type. Non-conforming answers are judged by these inanimate tormentors as simply wrong. The student victim is left to "suffer the slings and arrows of outrageous fortune" wherein one MUST give the expected answer to the question that cannot be answered. So be it. There is some consolation in the knowledge that the experts here seem to agree that such questions are ill crafted and ill conceived (and that my computer oppressor will never know what it means to love). – Randall Blake Feb 15 '20 at 13:35
• @RandallBlake To be fair, it was always that way, except that that machines of old were just heartless people. On occasion, one was lucky to have a good teacher who understand that chemistry was a discipline filled with subtlety and nuance. I specifically remember getting 30% or the like on a quiz in eighth grade because I knew about orbitals, but I did not provide the "correct" answer. – Zhe Feb 26 '20 at 1:35

Nobody can determine the order of a reaction with just the stoichiometric coefficients.

For example look at the reaction $$I_2 + Acetone -> ICH_2COCH_3 + HI$$. It has a rate corresponding to the law : -$$d([I_2])/dt = k[H^+][Acetone]$$. The concentration $$[I_2]$$ does not appear in the rate law. It may seem incredible, unbelievable. Nobody can guess it. It is an experimental result.

On the other hand, if a reaction A + B --> ..... has a rate law like : - d[A]/dt = k[A][B], in this case one can say that the reaction is an elementary reaction.

• Just because the rate law matches the stoichiometry does not mean it is an elementary reaction. Lots of multi-step mechanisms would result in the same rate law. On the other hand, if you specify that a reaction is an elementary one, you can infer the rate law from the coefficients of the reaction as written. – Karsten Theis Feb 14 '20 at 4:37
• "[i]f you specify that a reaction is an elementary one, you can infer the rate law from the coefficients of the reaction as written." Karsten, if I had read your simple, concise statement in my chemistry book (or the many other sources I consulted), I would never have had to ask this question!! In hindsight, those sources suggested as much, but none, in my opinion, stated the matter so clearly and plainly. It would have saved me much heartache. – Randall Blake Feb 15 '20 at 14:19