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

Statement a is false because the activation energy (\(E_a\)) is related to the energy barrier that must be overcome for the reaction to occur, not the overall energy change (\(\Delta E\)) between reactants and products. Statement b is false because the rate law is determined experimentally and cannot be deduced solely from the overall balanced equation for the reaction. Statement c is false because most reactions involve multi-step reaction mechanisms, not one-step mechanisms.

Step-by-step solution

Statement a: False Explanation

The activation energy of a reaction, often represented as \(E_a\), is the minimum energy required for a reaction to proceed. The overall energy change of a reaction, denoted as \(\Delta E\), is the difference between the energy of the reactants and the energy of the products. The activation energy is related to the energy barrier that must be overcome for the reaction to occur, whereas \(\Delta E\) refers to the difference in energy between the reactants and products once the reaction is complete. Thus, the activation energy of a reaction does not depend on the overall energy change (\(\Delta E\)) for the reaction, making statement a false.

Statement b: False Explanation

The rate law for a reaction describes the relationship between the rate of a reaction and the concentrations of the reactants. The rate law is determined experimentally and cannot be deduced solely from examination of the overall balanced equation for the reaction. The balanced equation provides the stoichiometric relationships between the reactants and products but does not provide information on the reaction's mechanism or the molecular steps involved in the process. Therefore, statement b is false because the rate law cannot be deduced from the examination of the overall balanced equation for the reaction.

Statement c: False Explanation

Most chemical reactions occur through a series of steps known as the reaction mechanism, which describes the sequence of molecular events that lead to the formation of the overall reaction's products. While some reactions indeed occur by one-step mechanisms (elementary reactions), most reactions involve multiple steps. These multi-step mechanisms can involve the formation and subsequent consumption of reaction intermediates, which do not appear in the overall balanced equation for the reaction. Therefore, statement c is false because most reactions do not occur by one-step mechanisms; instead, they typically involve multi-step reaction mechanisms.

Key concepts

Activation Energy

Just like a runner needs a boost of energy to jump over a hurdle, molecules require a certain amount of energy to start a reaction. This essential energy is known as activation energy (\( E_a \)), and it's vital in ensuring that molecules collide with enough power to break bonds and form new ones. Contrary to what some may think, this energy threshold is unaffected by the overall energy change (\( \text{Delta} E \)) of the reaction, which is the total energy difference from reactants to products.

Imagine two runners—one jumping over a high hurdle and one over a low one. If they both finish at the same level, the height of their hurdles (analogous to activation energy) did not depend on their starting or finishing points but on the hurdle itself. This analogy helps clarify why statement a from the exercise is false and reinforces that while activation energy is crucial for a reaction's initiation, it is independent of the reaction's end energy state.

Rate Law

Figuring out the pace at which a chemical reaction proceeds is like solving a mystery—it requires careful observation and data collection. This is where the rate law steps in, acting as a detective's tool to establish the 'speed formula' for a chemical reaction. It expresses how the rate of the reaction is affected by the concentration of reactants. One might think the balanced chemical equation lays it all out, but it's not that straightforward. The rate law cannot be deduced solely by inspecting the balanced equation, as it does not reveal the secret pathway—the reaction mechanism. This is why statement b is false.

Consider a chef's recipe as an illustration; the ingredients list (like a balanced equation) won't tell you how quickly the chef can cook the dish. For that, you'd need to observe the chef in action, just like scientists must measure reaction rates to determine the rate law empirically. This emphasizes the fact that the rate law encompasses dynamics of reactant interaction, which can't be anticipated from the overall reaction equation.

Overall Energy Change

In the grand scheme of a chemical reaction, the overall energy change is the energetic net result—it's the final score after all the action has taken place. Symbolized as (\( \text{Delta} E \)), this value measures whether energy was released to or absorbed from the environment. Was the reaction like a downhill slide, releasing energy, or an uphill climb, absorbing it?

The misconception lies in linking this overall energy score to the initial activation energy — but they're not directly related. The total energy shift is dependent on the individual properties and quantities of reactants and products, like a final tally that accounts for all energetic exchanges during reaction steps. Illustratively, it's as if at the end of a sports game, where win or loss doesn't depend on the initial energy or motivation of the team but on the sum of all plays and their outcomes throughout the game.

Reaction Intermediates

The journey from reactants to products can be complex, and along the way, molecules often form temporary structures called reaction intermediates. These intermediates are like pit stops in a race, existing momentarily before transforming into the final product. They're crucial players in the reaction mechanism but often remain behind the scenes, not appearing in the overall chemical equation.

Because most chemical reactions involve multiple steps, the presence of intermediates shows why statement c is false. To grasp the concept, imagine a production line—raw materials are turned into intermediate products before emerging as the final item. These intermediate goods are necessary transition points, just like reaction intermediates in chemistry, which help us understand the sequential narrative of how substances are transformed on a molecular level.