[galpinj]

A catalyst can help create proper orientation for reactants, thus decreasing activation energy.

Based off this information, does Eα factor in orientation as well as the average KE of the reactants? Otherwise, how is "orientation" measured?

 I've found that orientation is measured by the steric factor (P), as seen in the attached photo. Can this relate to Eα in reaction coordinate diagrams? I still don't know why a catalyst (which affects steric factor) would cause the activation energy to decrease.

[mjc123]

E_a is the energy barrier for reaction with the reactants in the most favourable orientation - if they collide in an unfavourable orientation, the barrier is much higher and reaction usually doesn't occur at all. Orientation is not factored into E_a - as your equation shows, it is factored into the pre-exponential term (A in the Arrhenius equation). It can be regarded as a factor in the entropy of activation; the more stringent the steric requirements, the more the reduction in entropy on forming the transition state, and the lower the pre-exponential term. If we write
k = Zexp(-ΔG_a/RT) = Zexp(-ΔH_a/RT)exp(ΔS_a/R)
we can identify A with Zexp(ΔS_a/R)
If a catalyst only "helped create proper orientation for reactants" it would increase A, but not decrease E_a. In fact there are many mechanisms of catalysis, and many of them involve creating or facilitating a reaction mechanism of lower E_a not available to the reactants alone. For example, the disproportionation of hydrogen peroxide
2H₂O₂  2H₂O + O₂
has a high activation energy; catalysts for this reaction involve species like Fe²⁺/Fe³⁺ or I^-/I₂ that can undergo facile conversion between different oxidation states, for which electron transfer reactions between them and H₂O₂ have much lower E_a than for H₂O₂ reacting with itself.

[galpinj]

E_a is the energy barrier for reaction with the reactants in the most favourable orientation - if they collide in an unfavourable orientation, the barrier is much higher and reaction usually doesn't occur at all. Orientation is not factored into E_a - as your equation shows, it is factored into the pre-exponential term (A in the Arrhenius equation). It can be regarded as a factor in the entropy of activation; the more stringent the steric requirements, the more the reduction in entropy on forming the transition state, and the lower the pre-exponential term. If we write
k = Zexp(-ΔG_a/RT) = Zexp(-ΔH_a/RT)exp(ΔS_a/R)
we can identify A with Zexp(ΔS_a/R)
If a catalyst only "helped create proper orientation for reactants" it would increase A, but not decrease E_a. In fact there are many mechanisms of catalysis, and many of them involve creating or facilitating a reaction mechanism of lower E_a not available to the reactants alone. For example, the disproportionation of hydrogen peroxide
2H₂O₂  2H₂O + O₂

has a high activation energy; catalysts for this reaction involve species like Fe²⁺/Fe³⁺ or I^-/I₂ that can undergo facile conversion between different oxidation states, for which electron transfer reactions between them and H₂O₂ have much lower E_a than for H₂O₂ reacting with itself.

Thank you MJC! So, although many catalysts can provide alternative pathways (as you noted), would a catalyst that only ensures proper orientation still lower Eα?

I also found an old post about this exact same question, but it didn't really get answered. It was basically asking whether Eα includes the steric factor or whether it is just a representation of the energy needed by two molecules to reach the products.

link: http://www.chemicalforums.com/index.php?topic=58891.0

[mjc123]

So, although many catalysts can provide alternative pathways (as you noted), would a catalyst that only ensures proper orientation still lower Eα?

Let me say it again, slowly, and watch my lips. "If a catalyst only "helped create proper orientation for reactants" it would increase A, but not decrease Ea."
The diagram you posted can be generalised to 3 dimensions (or more of course, but that gets very complicated). Consider a reaction AB + C  A + BC. We can make a plot with r_AB as the x-axis and r_{AC as the y-axis}, and potential energy as the z-axis. This gives us a potential energy surface, as illustrated in the attached diagram. You see there are two "valleys" linked by a "pass", which is the easiest way between reactants and products. The reaction coordinate (the x-axis in your diagram) is the lowest-energy trajectory from reactants to products; the transition state is the summit of the pass and E_a is the energy of the TS above reactants. E_a is the energy barrier for the most favourable orientation for reaction. A different collision orientation means a different trajectory over the energy surface, climbing the slopes above the top of the pass, and having a higher energy barrier (generally much higher, so reaction doesn't happen). The steric factor p reflects the probability of a collision being on the right trajectory to take it over TS if it has enough energy. A catalyst that "ensures proper orientation" would increase p but not decrease E_a.
The old post you refer to discusses two types of "steric factor"; the one we have just discussed, and a steric hindrance factor that increases E_a due to the presence of e.g. bulky groups. But if I understand what they're getting at, this has nothing to do with catalysis, i.e. speeding up the reaction for a particular reagent. It is relevant in comparing different reagents, e.g. phenol and 2,6-di-t-butylphenol.