Question

The rate of a chemical reaction generally increases rapidly, even for small increases in temperature, because of a rapid increase in (a) collision frequency; (b) fraction of reactant molecules with very high kinetic energies; (c) activation energy; (d) average kinetic energy of the reactant molecules.

Short answer

The rate of a chemical reaction increases rapidly, even for small increases in temperature, primarily because of (b) a rapid increase in the fraction of reactant molecules with very high kinetic energies.

Step-by-step solution

Understanding Collision Theory

Collision theory suggests that for a reaction to occur, it is not enough for molecules to simply collide with each other. These collisions must have sufficient energy (known as the activation energy) and a proper orientation.

Effect of Temperature on Collision Frequency and Energy

According to the kinetic theory of gases, an increase in temperature increases the average kinetic energy of the molecules, thus increasing the number of collisions. While temperature does increase the collision frequency, this does not have a significant effect on increasing the rate of a chemical reaction. It also does not have any effect on the activation energy, which is a property of the reaction itself.

Effect of Temperature on Fraction of Reactant Molecules with High Kinetic Energies

A key factor that temperature affects is the fraction of molecules that have very high kinetic energies. Recall that the kinetic energy of the molecules is distributed amongst the population according to the Maxwell-Boltzmann distribution. An increased temperature increases the fraction of molecules with kinetic energies high enough to overcome the activation energy barrier, hence increasing the rate of successful collisions and the speed of the reaction.

Key concepts

Collision Theory

Collision theory is a fundamental concept that helps to explain how and why chemical reactions occur. At its heart, this theory states that for a chemical reaction to take place, reactant molecules must collide with enough force and in the correct orientation. It's not enough for molecules to just bump into each other; they must also possess the minimum amount of energy necessary to break existing bonds and form new ones. This minimum energy is referred to as the activation energy.

For students grappling with the significance of collision frequency versus energy, it's crucial to recognize that increasing the number of collisions doesn't guarantee a faster reaction. The speed of the reaction is mainly determined by how many of those collisions are effective. An effective collision is one where molecules collide with the right orientation and with enough energy to surpass the activation energy barrier. Therefore, for a reaction's rate to be enhanced, the number of effective collisions must increase.

Activation Energy

Activation energy is a key term when discussing chemical reactions. It is the threshold energy that the reactant molecules need to achieve for a reaction to occur. Think of it as the energy required to push a ball over a hill; once the ball has reached the top (the activation energy), it can easily roll down the other side, resulting in a reaction.

In chemistry, this concept is central to understanding why certain reactions occur spontaneously while others require additional energy, like heat, to proceed. The link between temperature and activation energy is often misunderstood. It is important to clarify that temperature itself does not change the activation energy; rather, it influences the number of molecules that can reach or surpass this energy level. As the temperature increases, more molecules are endowed with the kinetic energy needed to overcome the activation energy barrier, leading to a higher reaction rate.

Kinetic Theory of Gases

The kinetic theory of gases gives us insight into the behavior of particles within a gas. According to this theory, gas particles are in constant, random motion, and they collide with each other and the walls of their container. As temperature rises, so does the average kinetic energy of these particles.

Higher temperature means that gas particles move faster, resulting in more frequent and energetic collisions. From an educational standpoint, comprehending the link between temperature and kinetic energy is crucial: with increased kinetic energy, particles collide more often and with greater force, which in turn can lead to an increase in the reaction rate because more particles will have sufficient energy to undergo effective collisions, as described by the collision theory.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution is a statistical representation of the distribution of energies among particles in a system. In the context of gases, it shows us how the kinetic energy of molecules is spread across different speeds at a given temperature.

When delving into this distribution, it's helpful to visualize a graph where the y-axis represents the number of molecules and the x-axis represents their kinetic energy. At lower temperatures, the peak of the curve is higher and sharper, indicating that most molecules have a moderate amount of energy. As the temperature increases, the peak flattens out and extends towards higher energies, reflecting that more molecules are achieving higher kinetic energies. For students, the takeaway is that with a rise in temperature, not only do more molecules have the energy needed to overcome the activation energy barrier, but there is also a broader range of energies present. This increases the likelihood of having enough reactive molecules with sufficient energy at any given moment to contribute to the reaction rate.