# Multiplication of the reaction and Equilibrium constant

\begin{align}\ce{2A + 2B &-> 2C }\\ \ce{A + B &-> C}\end{align}

Why does the equilibrium constant change?

And why the rate of the first reaction square the rate of the second? I understand it mathematically, but logically and scientifically I can't understand it at all.

• A simple(?) thought experiment: A+B involves a 2-body interaction (i.e. 2 molecules are interacting at one common location). 2A+2B involves a 4-body interaction. That's (MUCH) less than half as likely to occur than 2x 2-body interactions. So there's not much reason to believe that the distribution of reactants and products (i.e. the equilibrium constant) will be in a 1:2 ratio because you doubled the number the particles involved in the reaction, right? – rch Apr 22 '14 at 5:44
• If you consider collisions at hard sphere model, even three bodies hitting each other is highly unlikely. Four however is virtually almost impossible. So the basic question is more likely to be, if there are two of A and B necessary. Upscaling reactions and therefore the change in the kinetics is most likely connected to concentrations. – Martin - マーチン Apr 22 '14 at 6:31
• Thanks @Martin I had meant to make those changes earlier. :) – jonsca Apr 22 '14 at 7:48
• Related question: chemistry.stackexchange.com/questions/6641/… – mic Dec 19 '18 at 2:36

Rate will not be square in most of the cases and who said so? The equilibrium constant scientifically changes because Gibb's free energy is extensive quantity and it is related to equilibrium constant through relation that you might know $\Delta G=\Delta G^\circ +\mathcal{R}T\ln Q$. Where $Q$ is reaction quotient which at equilibrium becomes equilibrium constant and then it gives $\Delta G^\circ = -\mathcal{R}T\ln K$