Question

Suppose we compared two reactions, one requiring the simultaneous collision of three molecules and the other requiring a collision between two molecules. From the standpoint of statistics, and all other factors being equal, which reaction should be faster? Explain your answer.

Short answer

The bimolecular reaction (collision between two molecules) should be faster because it is statistically more probable than a termolecular reaction (simultaneous collision of three molecules).

Step-by-step solution

Understanding Molecular Collisions

To begin with, we need to understand that the rate at which a reaction occurs depends on the frequency of effective collisions between reactant molecules. The more molecules that must collide simultaneously for a reaction to proceed, the less likely those collisions will occur frequently. Collisions involving three molecules (termed a termolecular reaction) are statistically less likely to happen than collisions between two molecules (a bimolecular reaction).

Considering the Probability of Effective Collisions

In a bimolecular reaction, only two molecules need to come together with the correct orientation and sufficient energy for a reaction to take place. However, in a termolecular reaction, three molecules must collide simultaneously with the correct orientation and sufficient energy, which is an event with lower probability.

Comparing Reaction Rates

With all other factors being equal (e.g., temperature, pressure, concentration, and energy), the bimolecular reaction should be faster because it is more statistically likely for two molecules to collide effectively than for three molecules to do so.

Key concepts

Molecular Collisions

Imagine a crowded room where people are constantly moving around, sometimes bumping into each other. This is somewhat similar to how molecules behave in a substance. Molecular collisions are the movements where molecules bump into one another, and these interactions can lead to chemical reactions if certain conditions are met. These conditions include the correct orientation at the moment of impact and enough energy to overcome the activation energy barrier.

The rate of a chemical reaction is fundamentally determined by how often effective collisions occur. An effective collision is one that results in a chemical reaction, meaning the molecules collide with adequate energy and in the right way to break bonds and form new ones. In a dense substance or under high pressure, collisions can become more frequent, potentially increasing reaction rates.

Bimolecular Reactions

In a bimolecular reaction, two reactant molecules collide and react with each other. Picture a dance floor where dancers move around, and when two specific dancers meet, they start dancing together. This is a good metaphor for bimolecular reactions. These reactions depend on the chance meeting of two reactive partners in the right orientation.

The mathematical representation of bimolecular reactions often involves second-order kinetics, expressed as rate = k[A][B], where k is the rate constant, [A] and [B] are the molar concentrations of the reactants. Because only two particles need to collide, these reactions tend to occur more frequently, hence they are generally faster than reactions requiring more than two molecules to collide.

Termolecular Reactions

Think of a termolecular reaction as a group hug involving three friends. For the hug to take place, all three friends must come together at the same time. Similarly, a termolecular reaction involves three reactant molecules colliding simultaneously. It's not just about bumping into each other; they must also have the correct orientation and sufficient energy.

Termolecular reactions are rare and much slower due to their complexity - the odds of three molecules meeting in the exact needed manner is relatively low. These reactions are typically associated with third-order kinetics, but they're so uncommon that some scientists suggest they may involve a sequence of bimolecular steps rather than a single termolecular step.

Probability of Effective Collisions

To better understand reaction rates, we need to delve into the probability of effective collisions. Effective collisions are like winning a mini-lottery; not every ticket (collision) wins (results in a reaction). For a successful reaction, molecules must collide with correct orientations and with sufficient energy. The probability is tied to factors including molecule size, concentration, temperature, and the presence of a catalyst.

With bimolecular reactions, where two molecules collide, the probability is higher compared to termolecular reactions, which require three molecules to collide effectively at the same time. So, in our original exercise, the bimolecular reaction is expected to be faster because statistically, it's much more likely to achieve successful collisions frequently.