Difference between intermediates and transition states?

Question

Can someone please explain what exactly the difference between an intermediate and a transition state is? I understand that they are formed as part of the process in converting the reactants to products in a chemical reaction. Other than that, all I know is that usually a transition state exists very briefly (if at all) whereas an intermediate can be isolated. But why?

Answer 1

Chemical intermediates are stable species on the potential energy surface, unlike activated complexes that are fictitious transitory species formed somewhere between bond forming and bond breaking.

Intermediates can be isolated and are associated with the specific steps in a chemical kinetic mechanism of reaction. As such, they represent a local minimum energy on the potential energy surface of the system.

Activated complexes found in transition state theory are hypothetical models of activated complexes giving a maximum energy along the potential energy surface of the reaction coordinate. These are not stable molecules, but imaginary hypothetical transitory states. The transition state activated complex is between bond breaking and bond forming that only exists to illustrate the energy barrier involved in the reaction coordinate.

A transition state is associated with an activation energy during reaction, typically along some reaction coordinate. (i.e., along the bond forming - bond breaking vibrational mode associated with the reaction). That is is good and all, and for a single reaction step (elementary process) it makes sense. For this ideal case, it has been worked out in detail and forms the basis for more advanced theories.This picture of transition state theory and activated complexes says nothing about the mechanism of the reaction other than that there is a single bond being broken - formed. Your question comes down to kinetics. The fictitious transition state cannot be isolated.

When people measure rate constants, they are typically not measuring an elementary process like that described by an activated complex (transition state theory). Instead, they measure a combination of processes such as chemical reactions and physical processes, i.e., bond breaking and forming along with a reversible mass transfer process. That experimental measurement of the rate constant gives the "apparent" activation energy. And is something not directly related to any single specific transition state. Chemists try to explain their measured activation energy (and pre-factors) with a mechanism involving a collection of specific elementary steps for chemical conversion (these should be elementary processes like those in transition state theory). This mechanistic "explanation" of a reaction can never be proven, but only supported through experimental rates and measurements of the chemical intermediates along their way to products (where slick ways of measuring elementary processes becomes important). That is why people are always always coming up with new methods to measure chemical intermediates.

An illustrative example is that of a non-Arrhenius "negative" activation energy. That is, the reaction rate increases with lower temperatures. This is only the case if one has at least one reversible step involved in the reaction. (we are not considering weird potentially energy surfaces, or barrier-less reactions)

A ↔ X → B

where X is some low concentration intermediate. It is formed in a reversible process by step 1 and goes on to products B in step 2. The first step is reversible, the second in not.

You could isolate species X if you wanted, and you will see below how its formation rate constant affects the activation energy.

The rate expressions are...

d[A]/dt = -k₁[A] + k_-1[X]

d[X]/dt = k₁[A] - k_-1[X] -k₂[X] ,

where you can apply the steady stead approximation for d[X]/dt, its concentration isn't changing as a function of time, so its derivative wrt time is zero. -d[X]/dt = 0, so k₁[A] - k_-1[X] -k₂[X] = 0, solve for [X].

k_-1[X] +k₂[X] = k₁[A]

(k_-1 + k₂) [X]= k₁[A]

[X]= k₁[A]/(k_-1 + k₂)

where k₁ and k_-1 are the forward and reverse rate constants of the first step.

d[B]/dt = k₂[X], where k₂ is the forward rate for second step.

So the rate of product formation d[B]/dt = {k₂k₁/(k_-1 + k₂)}[A]. You can lump all of the reaction rate constants into an "apparent" activation energy, k_app.

d[B]/dt = {k₂k₁/(k_-1 + k₂)}[A] = k_app[A]

Now it all comes down to the math and what the rate constants have for their activation energies and pre-factors. For the rate to decrease with increasing temperature at least one of the denominator terms has to increase more than the the numerator. While this isn't true for all values of the rate constants, it depends on just how much one rate constant (numerator) changes with temperature versus the other. Negative activation energies are typically found in heterogeneous processes (i.e., gas-surface processes like film growth) where adsorption is a necessary part of the process.