Problem 70 - A Complete Resource Book in Chemistry for JEE Main

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 course. 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

Step-by-Step Solution

Answer

Statements 2 and 3 are correct; option (c) is the answer.

Step 1: Analyze Statement 1

Statement (1) suggests that the rate of a process is directly proportional to its free energy change. In general, the rate of a process is not determined by its free energy change but by the activation energy barrier according to the transition state theory. Therefore, statement (1) is generally considered incorrect.

Step 2: Analyze Statement 2

Statement (2) claims that the order of an elementary reaction step can be determined by examining the stoichiometry. For elementary reactions, this is true as the reaction order corresponds to the stoichiometric coefficients for each reactant in the rate law. Therefore, statement (2) is correct.

Step 3: Analyze Statement 3

Statement (3) suggests that a first-order reaction describes an exponential time course. This is true because the concentration of reactant decreasing over time in a first-order reaction follows the equation \([A] = [A]_0 e^{-kt}\), which is an exponential decay model. Hence, statement (3) is correct.

Step 4: Evaluate the Options

Based on the analysis: Statement 1 is incorrect. Statements 2 and 3 are correct. From the options provided: (c) "2 and 3 are correct" matches our findings.

Key Concepts

Rate of Reaction

In chemical kinetics, the **rate of reaction** refers to how quickly a reaction progresses. It's a measure of how fast reactants are converted into products. The rate is influenced by various factors such as:

• Concentration of reactants: Generally, higher concentrations lead to faster reactions because more reactant molecules are available to collide.
• Temperature: An increase in temperature typically increases the rate, as it provides more energy for collisions between reacting molecules.
• Catalysts: Catalysts can lower the activation energy required for a reaction, speeding up the process without being consumed themselves.
• Surface area: For reactions involving solids, a greater surface area allows for more collisions and a faster rate.

In line with the exercise, it's important to note that the rate of a chemical process is not directly proportional to its free energy change. Instead, the activation energy is a critical factor impacting the rate, as the reaction must surpass this energy barrier to proceed.

Elementary Reaction

An **elementary reaction** is a simple reaction that proceeds in a single step involving a direct transformation of reactants into products. In such reactions, no intermediates are formed. Each elementary reaction has its distinct characteristics and can be represented by a rate law. For these types of reactions, the order is determined directly from the balanced chemical equation.
When examining the stoichiometry of an elementary reaction:

• The order corresponds to the number of molecules involved in the step. For example, in the reaction \(A + B \rightarrow C\), if it's elementary, the reaction is first order in \(A\) and first order in \(B\).
• Understanding stoichiometry is crucial because it can directly inform us about the reaction kinetics without further experimentation.

This concept simplifies the study of reaction kinetics, allowing us to predict how changes in concentration can affect the rate.

First-order Reaction

A **first-order reaction** is characterized by its reaction rate being directly proportional to the concentration of a single reactant. This type of reaction is often represented by the equation:\[[A] = [A]_0 e^{-kt}\]where \([A]\) is the concentration of the reactant at time \(t\), \([A]_0\) is the initial concentration, \(k\) is the rate constant, and \(e\) is the base of the natural logarithm.

• **Exponential decay:** This equation describes an exponential decrease in concentration over time, which defines a first-order process.
• **Half-life:** The time it takes for the reactant concentration to fall to half its initial value is constant, regardless of the initial concentration, and is calculated as \(t_{1/2} = \frac{0.693}{k}\).

First-order reactions are prevalent in many natural and industrial processes, making them critical in understanding various chemical dynamics.