Energy Diagrams: Videos & Practice Problems

An energy diagram is a graphical representation that illustrates the energies of reactants, products, and the transition state throughout a chemical reaction. In this diagram, the reactants, denoted as r, are positioned on the left side, while the products, represented by p, are found on the right side at the end of the curve. The transition state, abbreviated as ts, corresponds to the peak of the curve and signifies the maximum energy structure along the reaction coordinate, which is the pathway from reactants to products. This transition state is also known as the activated complex.

The reaction coordinate, depicted along the x-axis, indicates the progress of the reaction, while the y-axis represents the change in energy, ranging from 80 kilojoules to 200 kilojoules. The activation energy, or energy barrier, abbreviated as E_a, is the minimum energy required for the reaction to proceed. It is defined as the height difference between the reactants and the transition state. Understanding these components is crucial, as they form the foundation of any energy diagram encountered in the study of chemical reactions.

The speed of a chemical reaction is significantly influenced by the activation energy, denoted as \( E_a \). Activation energy is defined as the difference in energy between the transition state and the reactants. In an energy diagram, the transition state represents the peak of the curve, while the starting point of the curve indicates the energy level of the reactants. The relationship between activation energy and reaction speed is straightforward: a higher activation energy results in fewer reactive molecules possessing the necessary energy to convert into products, leading to a slower reaction rate. Conversely, a lower activation energy allows more molecules to overcome the energy barrier, resulting in a faster reaction.

To illustrate this concept, consider two reactions represented by energy diagrams. For the first reaction, if the transition state is at 90 kilojoules and the reactant line is at 20 kilojoules, the activation energy can be calculated as follows:

\[ E_a = \text{Transition State} - \text{Reactant Line} = 90 \, \text{kJ} - 20 \, \text{kJ} = 70 \, \text{kJ} \]

This indicates a higher activation energy, suggesting a slower reaction. In contrast, for the second reaction, if the transition state is at 60 kilojoules and the reactant line remains at 20 kilojoules, the activation energy is:

\[ E_a = 60 \, \text{kJ} - 20 \, \text{kJ} = 40 \, \text{kJ} \]

This lower activation energy correlates with a faster reaction rate. Thus, the key takeaway is that the activation energy, or energy barrier, is crucial in determining the speed of a chemical reaction: higher \( E_a \) values lead to slower reactions, while lower \( E_a \) values facilitate faster reactions.

The overall energy change in a chemical reaction, represented by the symbol \(\Delta E\), is crucial in determining the favorability of that reaction. This change is calculated as the difference between the energy of the products and the energy of the reactants, expressed as:

\[\Delta E = \text{Products} - \text{Reactants}\]

In this context, we can further explore two important concepts: enthalpy and Gibbs free energy. Enthalpy, denoted as \(\Delta H\), specifically refers to thermal energy, which is the energy associated with heat. In contrast, Gibbs free energy, represented as \(\Delta G\), relates to the favorability of product formation in a reaction. A reaction is considered favorable if it can produce products from reactants, indicating a successful transformation.

When analyzing energy diagrams, if the product line is lower than the reactant line, the reaction releases energy. For example, if the product line is at 15 kilojoules and the reactant line is at 40 kilojoules, the calculation would yield:

\[\Delta E = 15 \, \text{kJ} - 40 \, \text{kJ} = -25 \, \text{kJ}\]

This negative value indicates that the reaction is exothermic, meaning it releases energy. Similarly, if \(\Delta G\) is negative, the reaction is termed exergonic, which is favorable for product formation since the products are at a lower energy state, thus more stable.

Conversely, if the product line is higher than the reactant line, such as a product line at 50 kilojoules and a reactant line at 30 kilojoules, the calculation would be:

\[\Delta E = 50 \, \text{kJ} - 30 \, \text{kJ} = +20 \, \text{kJ}\]

This positive value indicates an endothermic reaction, where energy is absorbed. If \(\Delta G\) is also positive, the reaction is classified as endergonic, which is unfavorable because it results in products that possess more energy than the reactants, leading to decreased stability.

In summary, understanding the distinctions between overall energy, enthalpy, and Gibbs free energy is essential for evaluating the favorability and stability of chemical reactions. Lower energy states correspond to greater stability, making the concepts of exothermic and exergonic reactions particularly significant in the study of thermodynamics in chemistry.