# Enzymes provide alternative routes to product with a lower activation energy

An enzyme lowers the activation energy for a reaction

Like a previous post, the problem here is not so much that this idea is flat-out wrong, but that it’s very prone to misinterpretation.

Text-books often state that an enzyme, or any other catalyst, lowers the activation energy of a reaction.

The activation energy for a reaction (written ∆G or Ea in most texts) is supposed to be a measure of how energetically two molecules need to collide with one another to react. If the the molecules collide too slowly, the collision won’t be energetic enough to break bonds, and the molecules will leave the collision unchanged. If they collide into one another fast enough, the collision will be energetic enough for a reaction to occur and for product to form.

For example, if you put some hydrogen peroxide into a beaker, and observe how quickly it breaks down to oxygen and water at different temperatures, it is possible to calculate that the activation energy for this uncatalysed decomposition is about 75 kJ mol⁻¹. This reaction is very slow at room temperature.

However, in the presence of the enzyme catalase (minced liver or blood is a cheap source), the reaction is almost explosively fast, and the calculated activation energy drops all the way down to about 25 kJ mol⁻¹.

Hydrogen peroxide decomposition

When a reaction’s activation energy is low, then a greater proportion of the molecules zipping around in the beaker collide with enough energy to break down. The reason for this is usually shown using a diagram of the sort below (although generally with much more vaguely labelled axes):

Maxwell Boltzmann distribution: the area under the curve and to the right of a threshold speed gives the proportion of molecules moving fast enough to react

This diagram shows the speed distribution of molecules. Technically it’s only applicable to gases composed of unrealistically helpful particles, but the results are qualitatively applicable to beakers of peroxide.

The y-axis shows how probable it is that a molecule is travelling at some given speed, and is therefore a measure of how likely it is that a collision in the beaker will have some particular energy. From the graph, you can see that the majority of the molecules are travelling somewhere between 250 and 1000  m s⁻¹. The peak is centred on 500 m s⁻¹ (in old money, this is about 1000 mph!)

For the uncatalysed reaction, the activation energy is large (75 kJ mol⁻¹), so the number of molecules moving fast enough to react when they collide is small. This is represented by the purple shaded area on the graph, which is related to the proportion of molecules in the beaker that could collide fast enough to react.

In the presence of the catalase enzyme, we saw that the apparent activation energy is much smaller (25 kJ mol⁻¹). The speed of collision doesn’t need to be so high to get the molecules to react, and the proportion of molecules that can react is therefore larger. This is represented by the sum of the shaded purple area plus the extra red area.

So, it does appear that in the presence of a catalyst, the reaction really does have a lower activation energy. The catalysed reaction runs faster and the reaction reaches equilibrium more quickly.

But…

Why would the addition of a catalyst lower the activation energy of the reaction?

The short answer is that it doesn’t, because when you add the enzyme, the peroxide is no longer reacting on its own to make oxygen and water, it is reacting with the enzyme. The enzyme becomes a fundamental part of the reaction, and the enzyme-catalysed reaction is completely different from the uncatalysed reaction. The reaction is no longer:

Peroxide → unstable ‘transition state’ → oxygen + water

but (at least):

Peroxide + enzyme → enzyme/peroxide complex →

unstable ‘transition state’ →

enzyme/product complex → oxygen + water

An enzyme doesn’t lower the activation energy for a reaction, because the reactions with and without the enzyme are very different things.

A better way of thinking about how enzymes catalyse reactions is that…

An enzyme provides an alternative route to products that has a lower activation energy

Quite why an enzyme-catalysed reaction will have a lower activation energy than an equivalent one that does not involve an enzyme is a matter of some interesting debate, and I’ll leave that to some other time.