4.4: Energy profiles
It can be observed experimentally that the rate of a reaction varies with temperature, even at the same concentration. This must be hiding in the rate constant (k) somewhere; it turns out that it's not quite so constant.
In fact, it varies with temperature, but as can be seen from the example data on the right, it is most definitely not linear.
A little experimentation can determine that the rate constant depends on two main factors, plus one minor one:
1. The activation energy (Ea).
2. The temperature.
3. Assorted other stuff (A)
The equation that relates these is the Arrhenius Equation:
k = Ae-Ea/RT
Activation energy is the "hill" that the reactants have to get over to get to products. There is always some activation energy, though it may be very very small. It does not affect the enthalpy of the reaction--any extra heat you put in comes back out as you go down the other side of the hill.
Looking at the equation above:
* Big activation energies lead to small rate constants and slow reactions (because it's a negative exponent)
* Small activation energies lead to large rate constants and fast reactions
* High temperatures speed up reactions, but not linearly (doubling the temperature doesn't double the rate constant).
You will often see the explanation that a catalyst works by lowering the activation energy, with the following diagram:
This is basically true, and good enough for College Board and the AP exam. However, the better explanation is that usually the catalyst lowers the activation energy by breaking the reaction into two steps with smaller activation energies:
(a) is the activation energy for the forward reaction (Ea)
(b) is the activation energy if you were to run the reaction backwards
(c) is the ΔH of the reaction
The 'activated complex'--also known as the 'transition state'--is the very very top of the hill where the bonds are partially broken or partially made, and the compounds have a 50/50 chance of continuing on to products, or going back to reactants.
Here's the same graph, but for an exothermic reaction profile: