Problem 205 - A Complete Resource Book in Chemistry for JEE Main

Question

In the respect of the equation \(k=\mathrm{Ae}^{-\mathrm{Ea} \mathrm{KT}}\) in chemical kinetics, which one of the following statements is correct? (a) \(k\) is equilibrium constant (b) A is adsorption factor (c) \(\mathrm{E}_{\mathrm{o}}\) is energy of activation (d) \(\mathrm{R}\) is Rydberg constant

Step-by-Step Solution

Answer

Option (c) is correct: \( E_a \) is the activation energy.

Step 1: Understanding the Equation

The given equation is the Arrhenius equation used in chemical kinetics: \( k = A e^{-\frac{E_a}{RT}} \). It relates the rate constant \( k \) of a reaction with the temperature \( T \), the activation energy \( E_a \), and an exponential factor involving \( R \), the gas constant.

Step 2: Identifying Parameters in the Equation

In the equation, \( k \) is the rate constant, not an equilibrium constant. \( A \) is the pre-exponential factor, often related to the frequency of collisions. \( E_a \) is the activation energy. The equation involves \( R \), the universal gas constant, not the Rydberg constant.

Step 3: Eliminating Incorrect Options

Option (a) is incorrect because \( k \) is the rate constant, not an equilibrium constant. Option (b) is incorrect because \( A \) is not an adsorption factor but a pre-exponential factor. Option (d) is incorrect as \( R \) is the gas constant, not the Rydberg constant.

Step 4: Selecting the Correct Statement

The only correct statement is option (c): \( E_o \) (which should be \( E_a \) or simply \( E \)) is indeed the activation energy in the equation.

Key Concepts

Rate Constant

The rate constant, symbolized as \( k \), is a crucial concept in chemical kinetics. It provides a quantitative measure of how quickly a reaction proceeds. The rate constant is unique to each reaction and is influenced by factors such as temperature and the nature of the reactants.

In the Arrhenius equation, \( k = A e^{-\frac{E_a}{RT}} \), the rate constant \( k \) is determined by the product of a pre-exponential factor \( A \) and an exponential term. This exponential term significantly influences \( k \) by incorporating the activation energy \( E_a \), universal gas constant \( R \), and temperature \( T \).

• The higher the rate constant, the faster the reaction occurs.
• It helps in comparing the rates of different reactions or the same reaction under various conditions.

Understanding \( k \) is crucial for predicting how different conditions affect the speed of chemical reactions.

It is important to remember that \( k \) is not an equilibrium constant, which is a different parameter used to describe the state of balance in reversible reactions.

Activation Energy

Activation energy, denoted as \( E_a \), is a fundamental concept in the study of chemical reactions. It refers to the minimum energy necessary for reactants to transform into products. Essentially, it's the energy barrier that must be overcome for a reaction to proceed.

In the Arrhenius equation, \( E_a \) is part of the exponential factor \( e^{-\frac{E_a}{RT}} \), which shows its significance in impacting the rate constant and thus the reaction rate.

• High activation energy means that fewer molecules have sufficient energy to react at a given temperature, often resulting in a slower reaction rate.
• Conversely, low activation energy suggests that more molecules can overcome the energy barrier, generally leading to a faster reaction.

Understanding \( E_a \) helps chemists manipulate reaction conditions and design catalysts that lower this energy barrier to accelerate reactions. It's not the same as other energy measurements such as internal energy or bond energy, but is specifically the required energy to initiate the reaction.

Universal Gas Constant

The universal gas constant, symbolized as \( R \), plays a vital role in thermodynamics and chemical equations. It provides the link between various properties of gases, such as pressure, volume, and temperature, helping to predict how gases will behave under different conditions.

In the Arrhenius equation, \( R \) is part of the exponential term \( e^{-\frac{E_a}{RT}} \). It adjusts the activation energy to the scale of thermal motion, thus influencing the rate constant of a reaction.

• The value of \( R \) is approximately 8.314 J/mol K, a constant that appears in many fundamental equations.
• It unifies the energy scale for reactions, ensuring that calculations remain consistent.

This constant is essential for computations in physical chemistry and is distinct from the Rydberg constant, which is specific to atomic physics and unrelated to the Arrhenius equation.