# How are reaction rate laws derived?

Let's take the reaction $2A + B \rightarrow C$, with the assumption that this is an elementary reaction. If I'm only given this information, how would I derive the following forward rate law from scratch?

$$\frac{dC}{dt} = k[A]^2 [B]$$

I tried to find an answer online but most sources jump straight to the above format for a rate law. I also understand that there are many experimental considerations which can affect what is actually observed (e.g. pseudo $0^{th}$rate law behavior) but I just want to know if there's a way to derive these rate laws given just the reaction. Thank you.

• They're found experimentally. – Mithoron Jan 12 '18 at 1:41
• I just read online that the form for an elementary rate equation can be derived from collision theory. Can anyone confirm that this is a common theoretical approach? – Cain Jan 12 '18 at 1:49
• I think you may need to be more precise in wording your question. You're trying to ask whether or not the law of mass action can be derived, not whether reaction mechanisms can be derived, correct? I think a lot of these comments are talking about the latter. – a-cyclohexane-molecule Jan 12 '18 at 5:56
• I mostly agree @a-cyclohexane-molecule's preceeding comment. The question has been misinterpreted; OP does say to assume an elementary reaction. The classical ways of deriving rate laws are collision theory (Trautz–Lewis), and Eyring transition state theory (also Evans–Polanyi). The question is quite broad, though. You (@OP) might include more of your background after following up on these two approaches. – Linear Christmas Jan 12 '18 at 15:36
• I see! Thank you for your answers. I'm sorry if I worded my question poorly. – Cain Jan 12 '18 at 19:27