Integrated rate equation for association

I have been trying to understand how we can get the first order integrated equation from the differential rate equation to no avail

I have attached a screenshot. It be great if someone can show the actual steps to ge to the final integrated equation

 

I don't know much about integrating but in short this is it.



The [A] in your formule is C since it is constant in flow based systems.

Arnoud

Thank you Arnoud. I got the steps before and after integration but not the actual integration step.

I was keen to how the variables were separated from the previous step and the subsuequent integration to end up with Ka.C.Rmax / (kaC+Kd)x(1-e*(kaC+Kd)t Just couldn't figure.. yet

Thank you as always for the quick repsonse and amazing contirbution!!

cheers

When discussing the integrated rate equation for association, it’s essential to understand that it describes the time-dependent formation of a complex between two molecules (like a ligand and a receptor). The equation relates the concentration of the complex to the rate constants for association and dissociation. [Deleted]



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I've tried to go through this derivation myself and it is not straight forward. There is a lot of strange algebraic manipulation to get there. I was only able to solve it by starting with the integrated rate equation and working backwards toward the differential equation.

Here, I drew out the differentiation from the integrated form to the differential form.