Problem 164 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following statements (a) The rate of a process is always proportional to its free energy change. (b) The molecularity of an elementary chemical reaction step can be determined by examining its stoichiometry. (c) The first order reactions follow an exponential time course. (d) Energy of activation is inversely proportional to temperature. The correct statement (s) is/are (a) \(1,2,3\) (b) \(1,2,3,4\) (c) 2 and 3 (d) 1 and 3

Step-by-Step Solution

Answer

The correct statements are 2 and 3 (option c).

Step 1: Analyze Statement 1

Statement 1 claims that the rate of a process is always proportional to its free energy change. This is incorrect because the rate of reaction is determined by the activation energy, not directly by the free energy change. The free energy change determines the spontaneity of a reaction, not its rate.

Step 2: Analyze Statement 2

Statement 2 asserts that the molecularity of an elementary reaction can be determined by its stoichiometry. This is true, as the molecularity refers to the number of reactant molecules involved in an elementary reaction, which is given by its stoichiometry.

Step 3: Analyze Statement 3

Statement 3 mentions that first-order reactions follow an exponential time course. This statement is true because first-order reactions have the rate law \( Rate = k[A] \) and the concentration of reactant decreases exponentially over time according to the equation \( [A] = [A]_0 e^{-kt} \).

Step 4: Analyze Statement 4

Statement 4 says that the energy of activation is inversely proportional to temperature. This is incorrect. According to the Arrhenius equation \( k = A e^{-E_a/RT} \), the rate constant \( k \) is related to the activation energy \( E_a \) and the temperature \( T \). The effect of temperature is calculated through \( RT \), but energy of activation itself is not inversely proportional to temperature.

Step 5: Determine the Correct Statements

From the analysis: Statement 2 and Statement 3 are correct. Statement 1 and Statement 4 are incorrect.

Key Concepts

Rate of Reaction

In chemical kinetics, the rate of reaction refers to how fast a chemical reaction proceeds. It is a measure of the change in concentration of reactants or products per unit time. Understanding the rate of a reaction is crucial for controlling and predicting the outcome of chemical processes.
The factors that can influence the rate of reaction include:

• Concentration of reactants: Higher concentration usually increases the reaction rate.
• Temperature: Increasing temperature generally increases the reaction rate by providing more energy to the reactants.
• Presence of catalysts: Catalysts lower the activation energy, increasing the rate of reaction without being consumed.
• Surface area: A larger surface area can lead to a faster reaction in heterogeneous reactions.

It’s important to note that the rate of reaction is not directly proportional to the free energy change (Gibbs free energy) of the process. Instead, the activation energy, a separate factor, is a more direct determinant of the rate.

Molecularity

Molecularity in chemical reactions refers to the number of molecules that participate in an elementary reaction step. It is tied to the stoichiometry of the reaction in an elementary process.
There are three common types of molecularity:

• Unimolecular: A single molecule undergoes a reaction, changing its form or breaking apart.
• Bimolecular: Two molecules collide and react with each other.
• Termolecular: Three molecules are involved in the reaction. This type is rare due to the low probability of three molecules colliding at the same time.

Molecularity should not be confused with order of reaction, which is determined experimentally and not necessarily a simple whole number. While molecularity relates directly to a single step of a mechanism, order relates to the overall process as determined by kinetic studies.

First Order Reactions

First order reactions are characterized by a rate that is directly proportional to the concentration of one reactant. These reactions have a distinct rate law given by:\[ Rate = k[A] \]where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant.
The behavior of first order reactions includes the concentration of the reactant decreasing exponentially over time following the formula:\[ [A] = [A]_0 e^{-kt} \]This indicates that the rate decreases over time as the reactant is consumed, forming a characteristic exponential decay curve when plotted. An example of a first order reaction is radioactive decay, where the rate at which unstable nuclei decay is proportional to the number of those nuclei present.

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that must be overcome for reactants to transform into products.The effect of activation energy can be understood using the Arrhenius equation:\[ k = A e^{-E_a/RT} \]where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.
The equation shows that activation energy is related to the rate constant, influencing how temperature affects reaction rates. A lower activation energy means a faster reaction at a given temperature, as it requires less energy to surpass the barrier.Contrary to some misconceptions, activation energy itself is not inversely proportional to temperature. Instead, an increase in temperature provides more kinetic energy to the molecules, facilitating a faster reaction rate.