Problem 117 - A Complete Resource Book in Chemistry for JEE Main

Question

The basic theory of Arrhenius equation is that (1) activation energy and pre-exponential factors are always temperature independent (2) the number of effective collisions is proportional to the number of molecule above a certain thresh old energy. (3) as the temperature increases, the number of molecules with energies exceeding the threshold energy increases. (4) the rate constant in a function of temperature (a) 2,3 and 4 (b) 1,2 and 3 (c) 2 and 3 (d) 1 and 3

Step-by-Step Solution

Answer

(a) 2, 3, and 4

Step 1: Understanding the Arrhenius Equation

The Arrhenius Equation describes how the rate constant (\( k \) ) of a reaction is affected by temperature and activation energy, given by \( k = A e^{-\frac{E_a}{RT}} \) where \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. Understanding each element of this equation is crucial to answering the question.

Step 2: Analysis of Statements

We must analyze each given statement in the context of the Arrhenius equation:1. Activation energy and pre-exponential factors are assumed to be temperature-independent, aligning with part of theoretical assumptions.2. This implies that effective molecular collisions relate to molecules above a certain energy, which agrees with kinetic molecular theory.3. Raising temperature increases the fraction of molecules exceeding activation energy, improving reaction rates.4. The rate constant \( k \) is indeed a function of temperature according to the Arrhenius equation.

Step 3: Evaluating Answer Options

Each option combines different statements:(a) mentions 2, 3, and 4, all of which accurately describe kinetic and thermal principles from the Arrhenius equation.(b) lists 1, 2, and 3 but omits the acknowledgment that \( k \) is temperature-dependent.(c) involves only 2 and 3, missing the factor where \( k \) depends on temperature.(d) includes 1 and 3 without discussing the impact of temperature on \( k \).

Step 4: Choosing the Correct Option

Option (a), containing statements 2, 3, and 4, collectively upholds the theory associated with the Arrhenius equation in describing kinetic behavior and the relationship between temperature and reaction rates.

Key Concepts

Activation Energy

Activation energy is a key concept in understanding chemical reactions. It represents the minimum energy required for a reaction to occur. Think of it as the energy hurdle that reactants must overcome to transform into products.

When molecules collide, they must have enough energy to break bonds and form new ones. This energy is the activation energy, often denoted as \( E_a \). If the molecules don't have this energy, the reaction won't proceed. This explains why some reactions happen rapidly while others are slow or don't happen at all.

Activation energy is measured in joules per mole and is often unchanged by temperature. However, changing factors like the addition of a catalyst can lower the activation energy, making it easier for the reaction to occur. Catalysts are substances that speed up a chemical reaction without being consumed in the process. They work by providing an alternative pathway for the reaction, one that requires less activation energy.

• High activation energy: slower reaction rate
• Low activation energy: faster reaction rate

In the Arrhenius equation, the activation energy appears in the exponential term \( e^{-\frac{E_a}{RT}} \), showing its inverse relationship with the rate constant \( k \).

Pre-Exponential Factor

The pre-exponential factor, often symbolized as \( A \), is part of the Arrhenius equation, \( k = A e^{-\frac{E_a}{RT}} \). It represents the frequency of collisions between reactant molecules that result in a reaction when they have enough energy to overcome the activation energy.

You can think of \( A \) as the number of successful collision opportunities per unit time. It incorporates both the frequency of molecular collisions and the probability that these collisions have the correct orientation to lead to a reaction.

• \( A \) is specific to each reaction
• Depends on factors like molecular orientation and collision frequency
• Is typically constant over a range of temperatures

This factor is crucial because even if the molecules achieve the necessary activation energy, they still require the right conditions to react. The pre-exponential factor helps create an understanding of how often these conditions are met without factoring in the energy barrier.

Temperature Dependence of Reaction Rates

The rate of a chemical reaction is highly dependent on temperature, and this relationship is described by the Arrhenius equation. According to the equation, as the temperature increases, the rate constant \( k \) also increases, leading to a faster reaction rate.

This happens because a higher temperature means more molecules have the kinetic energy to overcome the activation energy barrier. Think of molecules at higher temperatures as being more energetic and moving faster. This quick movement increases their chances of colliding with enough energy and correct orientation to initiate a reaction.

Mathematically, this temperature dependency is shown in the exponential term \( e^{-\frac{E_a}{RT}} \).** As \( T \) (temperature) rises, the value of \( e^{-\frac{E_a}{RT}} \) increases, resulting in a higher \( k \).** This fundamentally alters reaction speed.

• Higher temperature: More energy in the system, faster reaction rate
• Lower temperature: Less energy, slower reaction rate

Understanding this concept is crucial, especially in industrial processes where controlling reaction rates is necessary for efficiency and safety.