Relating k-values to energy diagrams and rate-determining steps

[The Head]

TL;DR Summary

How a k value can be the higher of the k values, but still an Rate-Determining Step

I'm trying to understand a little bit more about how k-values relate to rate-determining steps and energy diagrams. I always assumed that the lowest value of k (in the forward direction) was the RDS saw something in a handout that indicated otherwise. It explained that even though k1 > k2, because k-1 was so low, k1 would have the highest energy transition and that k1 was the RDS. I would have thought that would only indicate that k1 was irreversible, not the RDS.

Further, it showed an energy diagram that then displayed the activation energy being higher for k2, which thoroughly confused me, because I would think the one with the greater activation energy would be the RDS.

Can someone clarify for me what is going on? I'm including the image below for clarity's sake, but really just want to learn how to think about the principles at hand, so any help would be greatly appreciated!

 

[jbsteele]

The key concept here is that the rate-determining step (RDS) is the slowest step in the reaction. In this case, the reaction is: A --> B --> C. The rate of the overall reaction is determined by the slowest step, and that is typically the step with the lowest activation energy (the energy difference between the transition state and the reactants). So, even though k1 > k2, if k1 has a lower activation energy than k2, then k1 will be the RDS. The energy diagram you have shown is showing the activation energies for each reaction step. As you can see, the activation energy for k1 is lower than k2, so k1 is the RDS. The fact that k1 is greater than k2 does not necessarily mean that k1 is irreversible, but it does mean that k2 is reversible. This means that k2 can proceed in either the forward or reverse direction, depending on the concentrations of the reactants and products.