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.

Let's take the reaction $\ce{2A + B -> C}$ 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?

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

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-zeroth rate law behavior), but I just want to know if there's a way to derive these rate laws given just the elementary reaction.

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 rate law from scratch?

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

Also, does this rate law assume high relative concentrations of reactants so we can neglect the back reaction? $(\frac{dC}{dt} = k[A]^2 [B] - k'[C]$ would be a more difficult form to analyze).

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.

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.