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

Question

Rate of a reaction can be expressed by Arrhenius 2 equation as, \(k=\mathrm{Ae}^{\mathrm{E} / \mathrm{RT}}\) In this equation, E represents (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) the energy below which colliding molecules will not react

Step 1: Introduction to Arrhenius Equation

The Arrhenius equation is given as \( k = A \cdot e^{-E/RT} \). Here, \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E \) is the activation energy, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin. The equation describes how the rate constant \( k \) changes with temperature.

Step 2: Understanding Activation Energy (E)

The activation energy, \( E \), is a critical component of the Arrhenius Equation. It is the minimum energy required for the reactants to undergo a reaction. Colliding molecules must have energy equal to or greater than this to overcome the energy barrier and form the products.

Step 3: Analyzing Answer Choices

(a) and (b) both refer to energy conditions for reacting molecules - (a) implies energy above which reaction is possible, while (b) implies energy below which reaction isn’t possible, both indicating activation energy. (c) refers to total energy at a given temperature, unrelated to activation barrier. (d) talks about the fraction of molecules with energy greater than activation energy, which is a result but not a definition of \( E \).

Step 4: Choosing the Correct Option

Based on the understanding of activation energy in the Arrhenius Equation, the correct choice is (b): \( E \) represents the energy below which the colliding molecules will not react. This defines the threshold energy that molecules need in order to successfully react.

Key Concepts

Activation Energy

Activation energy is the key threshold that molecules must overcome for a chemical reaction to occur. In the Arrhenius Equation, it is denoted as \( E \). Here's why activation energy is so crucial:

• It represents the minimum energy required for reactants to be converted into products.
• Molecules with energy below this threshold are unable to react, as they do not possess sufficient power to break bonds and form new ones.
• This concept explains why some reactions are slow or don't occur at all under certain conditions.

To think of it simply, if you're trying to roll a ball over a hill, the activation energy is the amount of push needed to get it to the top of the hill. Once at the peak (overcoming the activation barrier), the reaction can proceed to form products.

Reaction Rate

A key result of overcoming the activation energy is the increase in the reaction rate. Reaction rate, denoted by the rate constant \( k \) in the Arrhenius Equation, tells us how fast a reaction occurs once it gets started.

• The rate at which a reaction proceeds is directly related to both the activation energy and the temperature.
• Lower activation energy typically means a higher reaction rate because more molecules have the necessary energy to react.
• A higher \( k \) value indicates a faster reaction.

The balance between activation energy and temperature plays a pivotal role in determining how quickly reactants are transformed into products. Think of it as a race track where the activation energy sets the obstacles and \( k \) records the speed at which racers (molecules) finish the race.

Temperature Dependence

Temperature is a major factor influencing how a chemical reaction unfolds, particularly in the context of the Arrhenius Equation. Here’s how temperature comes into play:

• As temperature increases, the kinetic energy of molecules also rises.
• This results in more frequent and more energetic collisions, meaning more molecules can surpass the activation energy barrier.
• Thus, higher temperatures typically lead to quicker reactions by increasing the rate constant \( k \).

This dependence is key for understanding various natural processes and industrial applications, where controlling temperature helps manage reaction rates effectively. Consider this: just like making water boil faster by turning up the heat, raising the temperature speeds up the reaction.