Problem 213 - A Complete Resource Book in Chemistry for JEE Main

Question

Rate of a reaction can be expressed by Arrhenius 2 equation as, \(k=\mathrm{Ae}^{-\mathrm{E} \mathrm{kT}}\) In this equation, E represents [2006] (a) the energy above which all the colliding molecules will react (b) the energy below which colliding molecules will not react (c) the total energy of the reacting molecules at a tem perature, T (d) the fraction of molecules with energy greater than the activation energy of the reaction

Step-by-Step Solution

Answer

(b) Activation energy represents the energy below which colliding molecules will not react.

Step 1: Understanding the Arrhenius Equation

The Arrhenius equation is \( k = Ae^{-\frac{E}{kT}} \), where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E \) is the activation energy, \( k \) is the Boltzmann constant, and \( T \) is the temperature in Kelvin. The activation energy \( E \) indicates the minimum energy required for the reaction to occur.

Step 2: Analyzing the Role of Activation Energy

Activation energy \( E \) refers to the threshold energy that molecules must attain during collisions to form products. It determines the energy barrier for a chemical reaction.

Step 3: Identifying What \( E \) Represents

Given the context of the equation, \( E \) represents the minimum energy below which colliding molecules will not react because they cannot surmount the energy barrier.

Key Concepts

Understanding Activation Energy

In the realm of chemical reactions, the term activation energy plays a pivotal role. Activation energy, often denoted as \( E \), is the minimum amount of energy that reacting molecules must possess in order for a reaction to occur. Imagine it as the hurdle in a hurdle race. Molecules need to achieve a certain level of energy to 'jump over' the hurdle and transform into product molecules.
- This concept explains why some reactions only occur at high temperatures or why a catalyst can increase the reaction rate by lowering the activation energy.
- The higher the activation energy, the slower the reaction rate will be at a given temperature.
- Conversely, a lower activation energy results in a higher reaction rate, allowing the reaction to proceed more easily at lower temperatures.

Overall, activation energy defines the sensitivity of a reaction to temperature changes, making it a fundamental aspect of understanding chemical kinetics.

Exploring the Rate of Reaction

The rate of reaction is a critical component in chemical kinetics and provides insight into how quickly products form from reactants. It is represented by the rate constant \( k \) in the Arrhenius equation and can be influenced by several factors:

• Temperature: Generally, increasing the temperature will increase the reaction rate. This happens because higher temperatures provide more energy to molecules, increasing the fraction of molecules able to surpass the activation energy.
• Concentration: A higher concentration of reactants leads to more frequent collisions, thereby increasing the rate of reaction.
• Catalysts: These substances speed up reactions by providing an alternative pathway with a lower activation energy.
• Surface area: In heterogeneous reactions, increasing the surface area of a solid reactant increases the rate of reaction by providing more opportunities for particles to collide.

The understanding of reaction rates is essential for designing chemical processes, from industrial production to biochemical reactions occurring in the body.

The Role of the Boltzmann Constant

The Boltzmann constant, represented by \( k \), is a fundamental constant in the field of thermodynamics and statistical mechanics. In the Arrhenius equation, it is used to relate the activation energy to the temperature at which a reaction occurs.
- Its value is approximately \( 1.38 \times 10^{-23} \text{ J/K} \), which provides a link between the microscopic energy levels of individual particles and the macroscopic temperature of a system.
- The Boltzmann constant allows us to express energy in terms of temperature, harmonizing atomic-scale phenomena with macroscopic observations.
- In the context of chemical reactions, the Boltzmann constant helps determine what proportion of molecules have enough kinetic energy to exceed the activation energy barrier at a specific temperature.
Understanding this constant is crucial for bridging the gap between microscopic and macroscopic worlds, establishing a fundamental connection between energy, temperature, and the rate at which reactions occur.