Question

Each of the statements given below is false. Explain why. a. The activation energy of a reaction depends on the overall energy change \((\Delta E)\) for the reaction. b. The rate law for a reaction can be deduced from examination of the overall balanced equation for the reaction. c. Most reactions occur by one-step mechanisms.

Short answer

The activation energy is independent of the overall energy change \((\Delta E)\) for the reaction and is determined by the energy barrier that must be overcome. The rate law cannot be deduced solely from the overall balanced equation as it involves the reaction mechanism and requires experimental data. Most reactions occur through multi-step mechanisms, involving the formation and consumption of intermediates, rather than one-step mechanisms.

Step-by-step solution

Statement (a) Explanation

The activation energy of a reaction is the minimum energy required for reactants to successfully collide and form products. It deals with the energy barrier that must be overcome for a reaction to occur. On the other hand, the overall energy change \((\Delta E)\) for the reaction refers to the difference in energy between the reactants and the products. The statement is false because the activation energy of a reaction is independent of the overall energy change \((\Delta E)\) for the reaction. Two reactions may have the same overall energy change, but different activation energies depending on the reaction mechanism and the energy barrier that must be overcome.

Statement (b) Explanation

The rate law for a reaction describes the relationship between the rate of a reaction and the concentrations of the reactants. It cannot be deduced solely from the overall balanced equation for the reaction because the rate law involves the reaction mechanism, which is not evident from the balanced equation. The statement is false because the rate law is determined by the slowest step in the reaction mechanism, known as the rate-determining step, which is not visible just by looking at the balanced equation. Experimental data is required to determine the order of reaction with respect to each reactant, and thus deduce the rate law.

Statement (c) Explanation

Reactions occur through a series of steps called the reaction mechanism. One-step mechanisms occur when the reactants directly collide to form products in a single step, without the involvement of intermediates. The statement is false because most reactions, in reality, occur through multi-step mechanisms, involving the formation and consumption of intermediates. One-step mechanisms are relatively rare and mostly observed in simple reactions. Multi-step mechanisms better explain the complexities of chemical reactions and the dependence of reaction rates on the concentrations of the reactants.

Key concepts

Activation Energy

Activation energy is a fundamental concept in understanding how chemical reactions occur. It represents the minimum threshold of energy that colliding reactant molecules must have to start a reaction. Picture a hill, where reactants need enough energy to reach the top, called the transition state, before rolling down to become products.

As noted in the solution, activation energy does not depend on the overall energy change (\( \text{Delta} E \)) of the reaction. This energy change is simply the difference between the energy of products and reactants. Rather, activation energy is a property of the specific pathway taken from reactants to products. In essence, it's about the journey, not the destination. Each reaction may have a unique barrier to overcome, regardless of how much energy is released or consumed in the process.

Rate Law

Diving into the kinetics of chemistry, rate law is our way of quantifying how fast a reaction proceeds. It's an equation that relates the rate of a reaction to the concentration of its reactants raised to some power, which indicates the order with respect to each reactant.

The misconception in the textbook exercise comes from thinking that the stoichiometry of the reaction, as shown in the balanced chemical equation, dictates the rate law directly. However, the rate law is inherently tied to the sequence of steps in the reaction mechanism. Often, experiments are necessary to determine the specific form of the rate law. It's the detective work of chemistry, where we cannot simply assume but must investigate how concentrations affect reaction speed.

Reaction Mechanism

A reaction mechanism serves as the 'playbook' for a chemical reaction. It details the step-by-step sequence by which reactants transform into products, including all the intermediate species and transition states along the way. Just like a complex dance routine, it breaks down the choreography into individual moves.

The textbook solution clarifies a common misstep: assuming reactions proceed in one swift move. In fact, they often involve several stages, with intermediates appearing and disappearing throughout. Understanding the mechanism is crucial because it illuminates how the molecules interact, rearrange, and ultimately reach the final product formation.

Energy Change in Reactions

When we talk about energy change in reactions, we refer to the difference in energy between the final products and the initial reactants, denoted as \( \text{Delta} E \). This change can manifest as heat released in exothermic reactions, or heat absorbed in endothermic ones.

While this overall energy change is important for determining whether a reaction is energetically favorable, it is not the same as the activation energy discussed earlier. The energy change gives us a sense of a reaction's 'energy budget' but doesn't reveal anything about the process's speed or the route it takes to reach completion.

Rate-Determining Step

Consider the rate-determining step as the bottleneck of a reaction. No matter how fast the other steps are, the overall reaction rate can't exceed the pace of this slowest step. It's akin to the slowest runner in a relay race; their speed dictates the team's overall performance.

As we learned from the exercise, the rate law is intimately connected to this concept. The rate-determining step controls the reaction kinetics because its high activation energy or low concentration of intermediates slows down the entire process. Understanding this step is key to manipulating reaction rates in industrial and laboratory settings.