## aaronq 2 years ago I got this inorganic exam coming up, I'm unsure how to answer these questions related to Kinetics, any suggestions?

1. aaronq

2. aaronq

3. aaronq

4. aaronq

@Carl_Pham could you take a look, id really appreciate it

5. Carl_Pham

OK, for the first one you need the Gibbs-Helmholtz equation, which relates changes in reaction free energy with temperature to reaction entropy:$\left(\frac{\partial \Delta G}{\partial T}\right)_p = - \Delta S$So if you extract the variation of activation energy (which is a free energy of reaction, for the reaction of the reactants to form the transition state) with temperature, and get something like a straight line, the slope will be the activation energy. Now to measure the change in activation energy with temperature, you would run kinetics experiments and measure the reaction rate at various temperatures, and then assume Arrhenius behaviour, which means you can use the Arrthenius equation to relate the reaction rate constant k to the activation (free) energy Ea:$k = A e^{-\frac{E_a}{R T}}$I guess you don't have the rate law, so you need to determine that along the way. So you will measure initial reaction rate as a function of the concentration of each reactant, plot it, find out what order it is in each reactant and what the rate constant k is. Then you'll do that at some other temperatures, to find how Ea varies with T, plot that, hope it's a straight line, and extract the slope, giving you dS_a.

6. Carl_Pham

For the second one, I would say any variation of rate with dG_rxn is not "surprising" because there is no necessary connection between the kinetics of a reaction and the thermodynamics. dG_rxn just tells you by how much the products are more stable than the reactants -- it says zip about how *fast* the reaction goes, i.e. the free energy barriers between reactants and products. (I am assuming the dG_reaction he mentions here is NOT the activation energy, of course.) So what could be going on? The interesting question is how changing dG_rxn is changing the activation energy barriers along the reaction path. Let us suppose that there are at least two barriers, i.e. there is at least one intermediate state, and let us suppose whatever is being done is pulling down one barrier and pushing up the other. If the first barrier starts off initially higher, it will be the rate-determining step, and pulling it down will increase the rate of reaction, regardless of what's happening to the other. But when it gets low enough it will no longer be the rate-determining step -- the other barrier will be. And since that one is going up, the rate will now start decreasing. So that's one way this could happen. But it's a little hard to answer, because I don't know if it's plausible that there might be more than one step in this reaction, nor do I know by what means dG_rxn is being changed. Another, simpler route would be to assume only one barrier, but that whatever is being changed initially pulls the free energy G of reactants, products, and the transition state down, but not at the same rate. Maybe initially the rate is dG_t > dG_p > dG_r, which means the barrier (G_t - G_r) falls as dG_rxn = G_p - G_r grows. But later on, maybe it is dG_r > dG_t > dG_p, which means now the barrier height *grows* as dG_rxn grows. That would work, too.

7. Carl_Pham

Not sure about the third. Sounds like you need to develop the kinetics of competitive mechanisms, presumably within an Arrthenius model for both.

8. aaronq

thanks a lot, it helped (Y)