Question

Consider the following statements: (1) Rate of a process is directly proportional to its free energy change. (2) The order of an elementary reaction step can be determined by examining the stoichiometry. (3) The first order reaction describe exponential time coarse. Of the statements a. 1 and 2 are correct b. 1 and 3 are correct c. 2 and 3 are correct d. 1,2 and 3 are correct

Short answer

The correct answer is c. Statements 2 and 3 are correct.

Step-by-step solution

Analyze Statement 1

Statement 1 claims that the rate of a process is directly proportional to its free energy change. This statement is false because the rate of a reaction is determined by the activation energy and the reaction mechanism, not the free energy change alone.

Analyze Statement 2

Statement 2 suggests that the order of an elementary reaction step can be determined by its stoichiometry. This is true, as elementary reactions have reaction orders that match their stoichiometric coefficients.

Analyze Statement 3

Statement 3 states that a first-order reaction describes an exponential time course. This statement is true because the concentration of reactants in a first-order reaction decreases exponentially over time, defined by the formula \([A] = [A_0]e^{-kt}\).

Determine Correct Statements

Since statement 1 is false and statements 2 and 3 are true, the correct choice is c. Statements 2 and 3 are correct.

Key concepts

Reaction Rate

Understanding the reaction rate is vital in the study of chemical kinetics. Reaction rate refers to the speed at which reactants are converted into products.
This can be influenced by several factors, including temperature, concentrations of reactants, and catalyst presence.
The reaction rate is also directly linked to how often reactants collide with the proper orientation and enough energy to overcome the activation energy. Factors such as temperature and catalysts play crucial roles in enhancing the frequency and energy of these collisions. It's critical to note that the reaction rate is not determined solely by the free energy change, as commonly misunderstood. Instead, it's dictated by the activation energy, which is the minimal amount of energy necessary to initiate a reaction. For instance: - Increasing the temperature raises the kinetic energy of particles, leading to more frequent and more energetic collisions. - Catalysts lower the activation energy, thereby accelerating the reaction without being consumed.

Elementary Reactions

Elementary reactions are the simplest types of reactions that occur in a single step. In these reactions, the rate law can be written directly based on the balanced chemical equation.
Each elementary step provides a unique insight into the reaction mechanism and allows us to understand the progression of the reactants to products. The order of these reactions corresponds directly to the stoichiometric coefficients of the reactants in the balanced equation.
For example, for a reaction \( aA + bB \rightarrow cC + dD \)- The rate law would simply be \( ext{Rate} = k[A]^a[B]^b \)This means that if a reaction step involves two molecules of A (\(a=2\)), then the reaction is second-order with respect to A. Elementary reactions are fundamental in determining the overall rate law and molecularity of a reaction, which explains the statement that the order of an elementary reaction step can be determined by its stoichiometry.

First-Order Reaction

First-order reactions have a distinct characteristic where the rate depends linearly on the concentration of a single reactant. This linear relationship creates a unique time-dependent behavior in the concentration of the reactants.
The concentration of reactants in a first-order reaction is described by the exponential relationship:\[ [A] = [A_0]e^{-kt} \]This formula shows that the concentration of a reactant decreases exponentially with time. Here, - \([A]\) is the concentration at time \(t\),- \([A_0]\) is the initial concentration, - \(k\) is the rate constant, and - \(t\) is time.Key characteristics of first-order reactions include:

• Half-life is independent of the initial concentration.
• Rate constant \(k\) can be determined graphically by plotting the natural logarithm of reactant concentration against time, producing a straight line with a slope of \(-k\).

First-order reactions are prevalent in processes such as radioactive decay, where the rate is governed exclusively by one reactant.

Stoichiometry

Stoichiometry involves using the balanced chemical equation to calculate the relative quantities of reactants and products involved in a reaction. It plays a crucial role in understanding and predicting the outcomes of chemical reactions.
With stoichiometry, you can:

• Determine the proportions in which chemicals react, which is essential for yield predictions.
• Understand the theoretical amount of products formed from given reactant amounts.
• Quantify the limiting reactant, which controls the amount of product formed.

When applied to reaction orders, particularly in elementary reactions, stoichiometry is vital. The stoichiometric coefficients of the reactants indicate their order in the rate equation, allowing scientists to draw connections between the macroscopic observations and the molecular-level kinetic processes occurring in the reactions. This interconnectedness is fundamental for solving problems involving complex reaction systems.