Problem 10 - Chemistry An Atoms First Approach

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.

Step-by-Step Solution

Answer

Statement a: The activation energy of a reaction and the overall energy change \((\Delta E)\) are not directly related. Activation energy is related to the pathway of a chemical reaction, whereas the overall energy change \((\Delta E)\) is related to the initial and final states of the system. Statement b: The rate law cannot be determined directly from the balanced chemical equation, as it depends on the elementary steps and the mechanism of the reaction. The rate law is experimentally determined by measuring the reaction rate with different initial concentrations of reactants. Statement c: Most reactions actually proceed through a series of elementary steps or multiple-step mechanisms, as one-step mechanisms are rare and require simultaneous collisions among all reactants with correct orientation and energy. In reality, many reactions occur through a sequence of simpler steps leading to the formation of products.

Step 1: Statement a: The activation energy of a reaction depends on the overall energy change \((\Delta E)\) for the reaction.

This statement is false because activation energy and overall energy change \((\Delta E)\) are not directly related. The activation energy is the minimum energy that the reactants need to have in order to form the activated complex or the transition state. It determines the energy barrier that needs to be overcome for the reaction to proceed. On the other hand, the overall energy change \((\Delta E)\) is the difference between the energies of the products and the reactants. In other words, it is the net gain or loss of energy during the reaction. Activation energy is related to the pathway of a chemical reaction, whereas the overall energy change \((\Delta E)\) is related to the initial and final states of the system.

Step 2: Statement b: The rate law for a reaction can be deduced from examination of the overall balanced equation for the reaction.

This statement is false because the rate law cannot be determined directly from the balanced chemical equation. The rate law represents the mathematical relationship between the rate of the reaction and the concentrations of the reactants. It depends on the elementary steps and the mechanism of the reaction, which are not always apparent from the balanced chemical equation. To determine the rate law for a reaction, we need to experimentally measure the reaction rate with different initial concentrations of the reactants and then use that data to find the order of reaction with respect to each reactant. We cannot deduce the rate law solely based on the stoichiometry of the balanced equation.

Step 3: Statement c: Most reactions occur by one-step mechanisms.

This statement is false because most reactions actually proceed through a series of elementary steps or multiple-step mechanisms. One-step mechanisms, also known as elementary reactions, are rare since they require all reactants involved to collide simultaneously with the correct orientation and required energy for the reaction to proceed. In reality, many reactions occur through a sequence of simpler steps, each involving fewer reactants in individual collisions. These sequences ultimately lead to the formation of products. The collection of these elementary steps forms the reaction mechanism, providing a more detailed and accurate description of how the reaction proceeds.