Problem 144 - Introductory Chemistry Atoms First

Question

Why is it unlikely that the reaction \(\mathrm{A}+2 \mathrm{~B}+\mathrm{C} \rightarrow \mathrm{P}\) occurs in one step?

Step-by-Step Solution

Answer

It is unlikely that the reaction \(A + 2B + C \rightarrow P\) occurs in one step due to the low probability of a three-particle collision and the requirement for precise coordination among the reactants. Reactions with more than two reactants typically proceed through a sequence of simpler elementary steps involving fewer reactant particles, making a one-step reaction for this scenario less likely.

Step 1: Understand the Reaction Collisions and Molecularity

For a reaction to occur in a single step, all the reactants involved in the reaction must collide simultaneously and with the correct orientation to form bonds. Molecularity refers to the number of reactant particles involved in an elementary step of the overall reaction. In this reaction, three reactant particles A, B, and C are involved in forming the product P. Since there are three reactant particles, the molecularity of the reaction is 3. It's essential to consider if it's highly probable for all three reactants to collide and bond simultaneously.

Step 2: Evaluate the Probability of a Three-Particle Collision

The probability of a three-particle collision is generally considered low. This is because, for this reaction to occur in a single step, the three reactant particles must come together and collide simultaneously with the correct orientation to form the product. Such a simultaneous collision requires a high level of precise coordination among the reactants and is, therefore, considered improbable in chemical kinetics.

Step 3: Analyze Reaction Mechanism and Relevant Elementary Steps

In reactions where the molecularity is greater than 2 (i.e., more than two particles are involved), it is often found that they typically occur via a sequence of simpler elementary steps. These steps occur sequentially, involving fewer reactants (usually one or two) in each step. Considering the improbability of a three-particle collision, it is more likely that the given reaction proceeds through a series of elementary steps involving two or fewer reactants. This results in an overall reaction mechanism that is more feasible in terms of collision theory and chemical kinetics. In conclusion, it is unlikely that the reaction A + 2B + C → P occurs in one step due to the low probability of a three-particle collision and the requirement for precise coordination. Reactions with more than two reactants typically proceed through a sequence of simpler elementary steps involving fewer reactant particles.

Key Concepts

Molecularity

Molecularity is a term used to describe the number of reactant particles involved in an elementary step of a reaction. It is important to note that molecularity is always an integer and directly relates to a single step within a multi-step process.
For example:

• A unimolecular reaction involves a single reactant molecule transitioning into products.
• A bimolecular reaction involves the collision of two Reactant molecules.
• A termolecular reaction, which involves three reactant molecules coming together simultaneously.

Molecularity is associated only with elementary steps because it speaks to the one-time collision of particles. Thus, in complex reactions which occur in more than one stage, each stage could have different molecularity.

Elementary Steps

An elementary step is a simple reaction that describes a single event in a reaction mechanism. Every elementary step has its own distinct molecularity and involves the direct interaction of the reactant particles to form an intermediate or final product.
When discussing elementary steps, it's crucial to understand:

• Each step involves only a few particles due to the improbability of multi-particle collisions.
• They are the building blocks of complex reactions, allowing the reaction to occur in phases.
• Elementary steps must sum to give the overall stoichiometry of the reaction.

Analyzing these steps helps outline a feasible pathway for the reaction to proceed, which ties into the overall reaction mechanism.

Collision Theory

Collision theory is essential in understanding chemical reactions, as it focuses on the requirement for reactant molecules to collide in order to form products. However, not all collisions lead to a reaction. For a successful collision:

• The particles must collide with sufficient energy to overcome the activation barrier.
• The particles must also be aligned in a specific orientation.

In the context of reactions, as discussed in the exercise, it becomes clear why three-particle collisions are rare. The simultaneous collision of three molecules meeting the criteria is highly improbable due to the precise alignment and energy required. The theory forms the backbone of understanding why many reactions proceed through multiple simpler steps.

Reaction Mechanism

A reaction mechanism is a step-by-step description of how a reaction occurs at a molecular level. It outlines each elementary step and intermediate that leads to the formation of the final product. Understanding the reaction mechanism provides insight into the pathway the reaction takes:

• It allows chemists to predict the kinetics and possible intermediates crucial for a deeper understanding.
• Mechanisms clarify the role of each reactant and intermediate in the overall process.
• Helps in identifying the rate-determining step, the slowest step that controls the reaction rate.

Considering the analysis in the exercise, mechanisms show why multi-reactant reactions with high molecularity rarely occur in a single step. Instead, they involve sequences of simpler, more probable elementary steps, explaining why multi-stage paths are more preferred in nature.