Let me know if this problem should go to Chemistry SE.
So I've got a substrate complexing reaction that can be reversed before forming the product: $$2S + E \overset{k_+}{\longrightarrow} C \overset{k_{++}}{\longrightarrow} 2P + E, \quad C \overset{k_-}{\longrightarrow} 2S + E;$$
I'm a bit confused about the reaction rate coefficient given multiple same item reacted at the same time, so
- Is $\dfrac{dC}{dt} = 2k_+ES - (k_- + k_{++})C$ or $k_+ES^2 - (k_- + k_{++})C$?
- Is $\dfrac{dP}{dt} = k_{++}C/2$ or $k_{++}C$?
Thanks in advance.