Question

(a) What factors determine whether a collision between two molecules will lead to a chemical reaction? (b) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature? (c) Which factor is most sensitive to changes in temperature-the frequency of collisions, the orientation factor, or the fraction of molecules with energy greater than the activation energy?

Short answer

(a) The factors determining if a collision between two molecules leads to a chemical reaction are: 1. Energy – the molecules must have enough kinetic energy to overcome the activation energy. 2. Orientation – the molecules must collide in the correct geometry. 3. Steric factors – the molecular structure and size can affect the availability of reactive sites during collision. (b) The rate constant for a reaction, denoted by \(k\), generally increases with an increase in reaction temperature, as described by the Arrhenius equation: \(k = Ae^{(-E_a/RT)}\). (c) Among the three factors, the fraction of molecules with energy greater than the activation energy is the most sensitive to changes in temperature, as higher temperatures significantly increase the number of molecules with sufficient energy to overcome the activation energy barrier.

Step-by-step solution

a) Factors determining collision outcome

There are three main factors that determine if a collision between two molecules will lead to a chemical reaction: 1. Energy: The colliding molecules must have enough kinetic energy to overcome the energy barrier, also known as the activation energy. 2. Orientation: The molecules must collide in the correct geometry or orientation to allow bond formation and breaking. 3. Steric factors: The molecular structure and size can affect the availability of reactive sites during collision, affecting the probability of reaction.

b) Rate constant and reaction temperature relation

The rate constant for a reaction, usually denoted by \(k\), generally increases with an increase in reaction temperature. This is because as the temperature increases, the kinetic energy of molecules increases, resulting in a higher probability of having enough energy to overcome the activation energy barrier. This relationship is described by the Arrhenius equation: \[k = Ae^{(-E_a/RT)}\] where \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. As \(T\) increases, the exponent becomes less negative, which results in an increase in \(k\).

c) Temperature-sensitive factor

Among the three factors – frequency of collisions, orientation factor, and the fraction of molecules with energy greater than the activation energy – the most sensitive to changes in temperature would be the fraction of molecules with energy greater than the activation energy. The reason behind this is that as the temperature increases, the distribution of molecular energies becomes broader and shifts toward higher energy values. This change significantly increases the number of molecules with sufficient energy to overcome the activation energy barrier. The frequency of collisions and orientation factors are also influenced by temperature, but their effects are comparatively smaller and more predictable, thus making the energy factor more crucial to consider when evaluating temperature sensitivity.

Key concepts

Kinetic Energy

Kinetic energy is a fundamental concept in understanding how molecules react during collisions.

It is the energy that molecules possess due to their motion. In the context of chemical reactions, kinetic energy is crucial as it determines whether colliding molecules have enough energy to overcome the activation energy barrier.

Here’s what to remember about kinetic energy in reactions:

• Molecules must have enough kinetic energy to initiate a reaction, this means they should move fast enough to collide effectively.
• Temperature directly affects kinetic energy. As the temperature increases, molecules move faster, increasing their kinetic energy.

A faster movement increases the likelihood that they will collide with sufficient force to undergo a chemical transformation. So, greater kinetic energy in molecules usually means a higher chance of successful reactions.

Activation Energy

Activation energy is the minimum energy that reacting molecules must have to form the activated complex during a chemical reaction.

It acts as an energy barrier that junctions must overcome for a reaction to proceed, influencing how quickly or slowly reactions occur. Important aspects of activation energy include:

• It is unique to each chemical reaction, meaning different reactions have different energy requirements to get started.
• Even if molecules collide, they won't necessarily react unless they possess energy equal to or greater than the activation energy.

The importance of activation energy is highlighted in the Arrhenius equation, which shows how the rate constant of a reaction depends on temperature and activation energy. Lower activation energies mean that molecules with lower kinetic energy can still react, while higher temperatures also help more molecules reach this energy threshold effectively.

Reaction Rate

The reaction rate measures how fast a chemical reaction occurs and is profoundly affected by a few key factors.

A key component influencing reaction rate is temperature, which contributes to reactions in several ways:

• At higher temperatures, molecules have increased kinetic energy, leading to more frequent and energetic collisions.
• The number of molecules with kinetic energy above the activation energy increases, which is the primary reason why reaction rates speed up with temperature.

The relationship between reaction rate and temperature also introduces the idea of the rate constant, a factor that explains how the reaction speed can change under different conditions, often expressed using the Arrhenius equation. Enhancements in reaction rate due to increased temperature reveal the critical role that both kinetic energy and activation energy play in determining how swiftly reactions proceed.