Problem 123 - Introductory Chemistry Atoms First

Question

Which reaction occurs fastest, one with \(E_{\mathrm{a}}=20 \mathrm{~kJ}\), one with \(E_{\mathrm{a}}=50 \mathrm{~kJ}\), or one with \(E_{\mathrm{a}}=75 \mathrm{~kJ}\) ?

Step-by-Step Solution

Answer

The reaction with the lowest activation energy occurs fastest. Comparing the given activation energies, \(E_{a} = 20\) kJ is the lowest. Thus, the reaction with \(E_{a} = 20\) kJ has the fastest rate.

Step 1: Comparing Activation Energies

The given activation energies for the three reactions are: 1. E_a = 20 kJ 2. E_a = 50 kJ 3. E_a = 75 kJ To identify the reaction with the fastest rate, we need to find the one with the lowest activation energy, as it requires less energy to overcome the energy barrier for the reaction to occur.

Step 2: Identifying the Fastest Reaction

Comparing the activation energies, we see: - The reaction with E_a = 20 kJ requires less energy than the one with E_a = 50 kJ and E_a = 75 kJ. - The reaction with E_a = 50 kJ requires less energy than the one with E_a = 75 kJ but more than E_a = 20 kJ. Thus, the reaction with the lowest activation energy is the one with E_a = 20 kJ. Therefore, the reaction with the fastest rate is the one with E_a = 20 kJ.

Key Concepts

Chemical Kinetics

Chemical kinetics is the branch of physical chemistry that concerns itself with understanding the rates of chemical reactions. It's essential for predicting how a reaction progresses over time and plays a crucial role in various fields, including engineering, environmental science, and medicine.

The study of kinetics involves examining factors that affect the speed of a chemical reaction. These factors include the concentration of reactants, temperature, presence of a catalyst, and the activation energy of the reaction. By understanding each of these elements, scientists can manipulate conditions to increase or decrease the rate of a chemical reaction as needed.

For example, a higher concentration of reactants typically leads to more frequent collisions among the particles, which can result in an increased reaction rate. Similarly, raising the temperature often causes particles to move more quickly and collide with greater energy, also enhancing the rate of the reaction.

Reaction Rate

The reaction rate is a measure of the speed at which reactants are turned into products in a chemical reaction. It can be represented as the change in concentration of reactants or products over time. Determining the reaction rate is crucial for understanding how quickly a reaction occurs, which has practical implications in industries like pharmaceuticals, where the speed of synthesis can impact production processes.

A faster reaction rate means that the reactants are being converted to products more quickly. Various factors influence the reaction rate, including those mentioned under chemical kinetics. Additionally, the nature of the reactants themselves (their molecular structure, for example) can also affect the reaction rate by determining how likely they are to interact effectively during collisions.

Energy Barrier

The energy barrier, or activation energy (Ea), is the minimum amount of energy that reacting particles must have for a chemical reaction to occur. It can be visualized as a hill that reactants need to climb over to become products; the higher the hill, the more energy required. The concept of an energy barrier is integral to the transition state theory of chemical reactions, which posits that reactants must first form a high-energy transition state before converting into products.

Importance in Reaction Rate

Activation energy is directly related to the reaction rate. A lower activation energy means that more particles have enough energy to overcome the energy barrier at a given temperature, leading to a faster reaction as observed in the initial textbook exercise. Conversely, a higher activation energy means that fewer particles can overcome the barrier, slowing down the rate of reaction.

Understanding the relationship between activation energy and reaction rates is a cornerstone of reaction kinetics. It also informs the design of catalysts, substances that lower the activation energy, thereby increasing the reaction rate without being consumed in the reaction itself.