Question

How does an increase in temperature result in an increase in the number of successful collisions between reactant molecules? What does an increase in temperature mean on a molecular basis?

Short answer

An increase in temperature results in an increase in the number of successful collisions between reactant molecules due to the increased kinetic energy of the molecules, leading to a higher frequency of collisions and a greater likelihood of collisions having sufficient energy to overcome the activation energy barrier. On a molecular basis, this is directly related to the increased average kinetic energy of the molecules in the system as temperature increases.

Step-by-step solution

Understanding Collision Theory

According to the collision theory, a chemical reaction occurs when reactant molecules collide with each other with sufficient energy and proper orientation. In order for a reaction to occur, molecules must have energy greater than or equal to the activation energy threshold and proper alignment of reacting species.

Relationship between Temperature and Kinetic Energy

To understand the effect of temperature on molecular collisions, we should first understand the relationship between temperature and kinetic energy. In general, temperature is a measure of the average kinetic energy of the molecules in a system. As the temperature increases, the kinetic energy of the molecules also increases. The kinetic energy of a molecule can be represented as: \( KE = \frac{1}{2}mv^2 \), where m is the mass of the molecule, and v is its velocity.

Factors Affecting the Rate of Successful Collisions

According to the collision theory, there are two main factors that affect the rate of successful collisions: the frequency of collisions and the fraction of collisions with energy greater than or equal to the activation energy. An increase in temperature affects both these factors. 1. Frequency of collisions: As the temperature increases, the molecules move faster due to the increased kinetic energy. This results in a higher frequency of collisions, increasing the probability of successful collisions. 2. Fraction of collisions with sufficient energy: The fraction of collisions with energy greater than or equal to the activation energy increases with an increase in temperature. This is because the molecules have more energy when the temperature is high, making it more likely for them to overcome the activation energy barrier and successfully collide.

Molecular Basis of Increased Temperature

On a molecular basis, an increase in temperature means an increase in the average kinetic energy of the molecules in a system. This results in faster-moving molecules and a higher frequency of collisions, as well as a greater likelihood of collisions with sufficient energy to result in a reaction. This overall increase in the probability of successful collisions leads to an increased rate of chemical reactions when the temperature is increased. In conclusion, an increase in temperature results in an increase in the number of successful collisions between reactant molecules due to the increased frequency of collisions and the greater likelihood of collisions having sufficient energy to overcome the activation energy barrier. This is directly related to the molecular basis behind increased temperature, which involves an increase in the average kinetic energy of the molecules in the system.