# Structural Biochemistry/Enzyme/Activation energy

Arrhenius equation is a description of the relationship between the activation energy and the reaction rate.

k = Ae(-Ea/RT)

where: k = chemical reaction, T = temperature in Kelvin, Ea = activation energy, A = the pre-exponential factor, R = the gas constant

According to this equation, it is observed that at a higher temperature, the probability that the two molecules will collide is higher, resulting in a higher kinetic energy, which leads to the lower requirement on the activation energy.

The Arrhenius equation is particularly helpful when calculating the rate of production of products over time, which is characterized by the following:

d[products]/dt = rate = Ae(-Ea/RT)[AmBn]

where the [A] and [B] are the concentrations of the reactants and m and n are their respective reaction orders.

## Lowering the Activation Energy

A catalyst is something that lowers the activation energy; in biology it is an enzyme. The catalyst speeds up the rate of reaction without being consumed; it does not change the initial reactants or the end products.

The graph above shows how the activation energy is lowered in the presence of an enzyme (blue line) that is doing the catalysis, exempflified with the carbon anhydrase reaction. The transition state is usually the most unstable part of the reaction since it is the one with the highest free energy. The difference between the transition state and the reactants is the Gibbs free energy of activation, commonly known as activation energy ${\displaystyle (\Delta G^{\ddagger })}$.

Enzymes (blue line) change the formation of the transition state by lowering the energy and stabilizing the highly energetic unstable transition state. This allows the reaction rate to increase, but also the back reaction occurs more easily.

## Common Misconceptions

Some common misconceptions about activation energy barriers and catalysts to speed up the reaction. The catalyst does NOT lower activation energy of the same barrier, but rather chooses another chemical pathway with a lower activation energy.The catalysts lead to new pathways which don't require as high of an energy of activation in turn speeding up the reaction.

Another big misconception about activation energy is that reactions will not always give the most thermodynamically stable products. Sometimes, the product that forms is the one that is more kinetically stable, or forms faster. However, if a catalyst is available, the thermodynamically more stable product will be able to form, even if the energy barrier is high.