Problem 21 - Chemistry in 30 days

Question

Rate of a reaction can be expressed by Arrhenius equation as, \(k=A e^{-K / R T}\), In this reaction \(E\) represents (a) The energy above which all the colliding molecules will react (b) The energy below which colliding molecules will not react

Step-by-Step Solution

Answer

The correct answer is (b). Activation energy is the energy threshold below which molecules will not react.

Step 1: Understanding the Arrhenius Equation

The Arrhenius equation is given by \( k = A e^{-E / (R T)} \), where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. The equation shows how the rate constant \( k \) depends on temperature and activation energy.

Step 2: Identifying the Role of Activation Energy

In the context of the Arrhenius equation, \( E \), the activation energy, is the minimum energy required for a chemical reaction to occur. It implies that molecules must collide with energy equal to or greater than this activation energy \( E \) to react.

Step 3: Interpreting the Options

(a) The energy above which all the colliding molecules will react means that the molecules need to have at least this much energy for a reaction to proceed. (b) The energy below which colliding molecules will not react indicates the same energy threshold, as molecules must collide with sufficient energy to exceed \( E \).

Step 4: Comparing the Options to the Definition

Based on the explanation of activation energy from the Arrhenius equation, the energy \( E \) represents the threshold that molecules must overcome for a reaction to occur, which corresponds to option (b).

Key Concepts

Activation Energy

Activation energy ( E ) is a critical concept in understanding chemical reactions. It refers to the minimum amount of energy that reacting molecules need to successfully collide and cause a reaction. This means that for a chemical transformation to occur, the colliding molecules must have E or more energy. If they have less, the reaction will not occur:

• This energy is like a barrier that reactants must overcome.
• The value of activation energy is specific to each reaction.
• Higher activation energy means slower reaction rate because fewer molecules have the required energy.

Understanding activation energy is crucial for predicting and controlling chemical processes. It helps chemists determine how changing conditions might affect a reaction.

Reaction Rate

The reaction rate is a measure of how fast a chemical reaction occurs. The Arrhenius equation directly links the reaction rate to the rate constant (k) , which gives us insight into the speed of a reaction:

• High reaction rates mean that reactions happen quickly, often desirable in industrial settings.
• Low reaction rates indicate slow reactions, which might be preferable for controlled releases.

By altering factors such as the concentration of reactants, the presence of catalysts, or the temperature, we can influence a reaction’s rate. Understanding the reaction rate allows us to optimize and control reactions effectively.

Temperature Dependence

Temperature plays a vital role in chemical reactions, dramatically affecting the rate at which they proceed. According to the Arrhenius equation, the reaction rate constant (k) increases with temperature:

• As temperature rises, molecules move faster, increasing their collisions.
• This higher kinetic energy means more molecules can surpass the activation energy barrier.
• A small change in temperature can lead to significant changes in reaction rate.

This temperature dependence is why cooking, for example, speeds up food reactions, changing textures and flavors.

Pre-exponential Factor

The pre-exponential factor ( A ) in the Arrhenius equation represents the frequency of collisions between reacting particles. It provides a glimpse into the inherent orientation and energy efficiency of the molecules:

• A is a constant for each reaction, not changing with temperature.
• It indicates the number of collisions resulting in a reaction when activation energy isn't a barrier.
• Higher pre-exponential factors reflect more favorable orientations, leading to more successful reactions.

Understanding A helps in assessing the potential success rate of particles colliding with enough energy to drive reactions.