The magnitude of the energy of activation determines the _____ -- how fast the reaction occurs.

The magnitude of the energy of activation determines the rate at which the reaction occurs. The energy of activation, or activation energy, is the minimum amount of energy required to initiate a chemical reaction. A high activation energy means that fewer molecules have the necessary energy to collide successfully and transition into products, resulting in a slower reaction rate. Conversely, a low activation energy signifies that more molecules can overcome the energy barrier, leading to a faster reaction rate.

In the context of chemical kinetics, the relationship between activation energy and reaction rate can be described using the Arrhenius equation:

$k = A e^{-\frac{E_a}{RT}}$

where:

• $k$ is the rate constant,
• $A$ is the pre-exponential factor (related to the frequency of the collisions),
• $E_a$ is the activation energy,
• $R$ is the universal gas constant,
• $T$ is the absolute temperature in Kelvin.

Due to this equation, it is clear that as the activation energy $E_a$ increases, the rate constant $k$ decreases, thus providing a clear link between the energy of activation and the speed of the reaction.