[curiouscat]

Hmm - can the elementary rate laws for each step change?

Yes.

So, ideally, we will have rate laws that we know to pertain directly to our system and all the equilibria it contains. Failing this, it is usually a good guess (with no other information) that a rate law will stay the same, including its constant, when the equilibrium occurs in a system of multiple equilibria. Right?

Yes. AFAIK. I could be wrong.

[Big-Daddy]

Yes.

Well, not much we can do then - just use whichever rate laws we have available, be they system-specific or not. So we may as well assume they will work, after having tried to get system-specific ones.

There is no way to predict the rate law without experiment, is there?

[curiouscat]

There is no way to predict the rate law without experiment, is there?

Sure there is. Do a literature search.

[Big-Daddy]

Sure there is. Do a literature search.

I've done a search. All I could find is the fact that a mechanism can be used to predict the rate law, which I already knew.

Maybe I should respecify my question: can we predict theoretically what the new rate law for equilibrium A+B  C+D will be in the system of equilibria (e.g. A+B  C+D, A+D ::equil::C+E, B F) , given we know what the rate law for the equilibrium A+B  C+D is, through experimental measurement or deduction from the mechanism, when this equilibrium is on its own.

[curiouscat]

Maybe I should respecify my question: can we predict theoretically what the new rate law for equilibrium A+B  C+D will be in the system of equilibria (e.g. A+B  C+D, A+D ::equil::C+E, B F) , given we know what the rate law for the equilibrium A+B  C+D is,

through experimental measurement

Usually, Yes.

or deduction from the mechanism

Typically, No.

[Big-Daddy]

Usually, Yes.

This is by assuming the same rate law applies (or experimentally determining the new rate law for the multiple-equilibria system), right? Or is there an actual way to "correct" the experimentally determined law for the presence of various other equilibria, without actually doing the experiment with various other equilibria?

Typically, No.

What? So if we've worked out using a mechanism what the rate law should be for the A+B  C+D case on its own, is it a poor assumption that the same rate law will hold for the system where there are several equilibria (e.g. A+B  C+D, A+D ::equil::C+E, B F)?

[curiouscat]

This is by assuming the same rate law applies (or experimentally determining the new rate law for the multiple-equilibria system), right? Or is there an actual way to "correct" the experimentally determined law for the presence of various other equilibria, without actually doing the experiment with various other equilibria?

Dunno. All I had in mind was do a fresh experiment. Then you have the right constants.

What? So if we've worked out using a mechanism what the rate law should be for the A+B  C+D case on its own, is it a poor assumption that the same rate law will hold for the system where there are several equilibria (e.g. A+B  C+D, A+D ::equil::C+E, B F)?

Not a poor assumption. Mostly it will work.  For equilibrium constants it has to work.

[Big-Daddy]

Not a poor assumption. Mostly it will work.

OK, good to know. On the other hand there is no way of finding the rate constants except from experimental measurements?

[curiouscat]

On the other hand there is no way of finding the rate constants except from experimental measurements?

There. We turned a full circle.

Answer: Sure there is. Do a literature search.

[curiouscat]

e.g.

Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants

Ab Initio Evaluation of the Barrier Height. Theoretical Rate Constant of the NH3+ H  NH2+ H2 Reaction

Ab Initio and DFT Direct Dynamics Studies on the Reaction Path and Rate Constant of the Hydrogen Abstraction Reaction: SiH3F+ H→ SiH2F+ H2

etc.

[Big-Daddy]

Hmm not really. There was this:

There is no way to predict the rate law without experiment, is there?

To which the only answer I could find was by deducing the mechanism. But this finds the rate law in terms of k. k itself must still come from an experiment as far as this method teaches me.

And now there is rate constant k:

there is no way of finding the rate constants except from experimental measurements?

Thanks for the recommended articles. I will try to get a hold of some of them. How is this article: http://schwartzgroup1.arizona.edu/steve/files/book_chapter_2005.pdf?

[curiouscat]

Looks good. If you can understand it.

I skimmed. It seems pretty advanced.

[Big-Daddy]

Looks good. If you can understand it.

I skimmed. It seems pretty advanced.

I agree. It seems much too advanced for me right now. But it's just encouraging to know there are methods to do it out there.

One more thing to check. In our ODE system, we use concentrations, because rate laws depend on concentrations. But to be more precise, should we be using activities? Do rate laws depend finally on activities, or concentrations?

If it is concentrations, then even if we need activities as our final answer it's easy to just calculate all the concentrations at the given time and then use them to find the activities.

[curiouscat]

One more thing to check. In our ODE system, we use concentrations, because rate laws depend on concentrations. But to be more precise, should we be using activities? Do rate laws depend finally on activities, or concentrations?

If it is concentrations, then even if we need activities as our final answer it's easy to just calculate all the concentrations at the given time and then use them to find the activities.

We'll cross that river once we get to it.

[Big-Daddy]

We'll cross that river once we get to it.

When will we get to it? Anything else I need to do first...

An Internet search doesn't give anything suggesting we should actually be using activities. It would also require a modification from the R_A*V ODE if we use activities instead of concentrations (multiplying activity by volume does not reach number of moles). On the other hand it seems logical that rate laws should be based around activities instead of concentrations, but I wouldn't know.