Question

Draw a rough sketch of the energy profile for each of the following cases: a. \(\Delta E=+10 \mathrm{~kJ} / \mathrm{mol}, E_{\mathrm{a}}=25 \mathrm{~kJ} / \mathrm{mol}\) b. \(\Delta E=-10 \mathrm{~kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{~kJ} / \mathrm{mol}\) c. \(\Delta E=-50 \mathrm{~kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

In each case, draw horizontal lines representing the energy levels of reactants and products. For case a, the products have higher energy than reactants; for cases b and c, the products have lower energy than reactants. Mark the activation energy (\(E_a\)) and draw a curve that starts at reactants, reaches the maximum energy point, then goes down to the products.

Step-by-step solution

Sketch for Case a

For the first case, we have \(\Delta E=+10 \mathrm{~kJ/mol}\) and \(E_{\mathrm{a}}=25 \mathrm{~kJ/mol}\). To draw the energy profile, we can follow these steps: 1. Draw horizontal lines to represent the energy levels of reactants and products. Since the change in energy is positive, the energy of the products will be higher than the reactants. 2. Mark the activation energy on the profile. The difference in energy between the reactants and the highest point on the curve is the activation energy. 3. Draw a curve that starts at the reactants, goes up to the maximum energy point (activation energy), and then goes down to the products.

Sketch for Case b

For the second case, we have \(\Delta E=-10 \mathrm{~kJ/mol}\) and \(E_{\mathrm{a}}=50 \mathrm{~kJ/mol}\). To draw the energy profile, we can follow these steps: 1. Draw horizontal lines to represent the energy levels of reactants and products. Since the change in energy is negative, the energy of the products will be lower than the reactants. 2. Mark the activation energy on the profile. The difference in energy between the reactants and the highest point on the curve is the activation energy. 3. Draw a curve that starts at the reactants, goes up to the maximum energy point (activation energy), and then goes down to the products.

Sketch for Case c

For the third case, we have \(\Delta E=-50 \mathrm{~kJ/mol}\) and \(E_{\mathrm{a}}=50 \mathrm{~kJ/mol}\). To draw the energy profile, we can follow these steps: 1. Draw horizontal lines to represent the energy levels of reactants and products. Since the change in energy is negative, the energy of the products will be lower than the reactants. 2. Mark the activation energy on the profile. The difference in energy between the reactants and the highest point on the curve is the activation energy. 3. Draw a curve that starts at the reactants, goes up to the maximum energy point (activation energy), and then goes down to the products. By following these steps for each case, we can create a rough sketch of the energy profile for each given set of values for \(\Delta E\) and \(E_a\). Remember that these sketches are rough and not to scale; they are meant to show the general trend in energy during the reaction.

Key concepts

Activation Energy

In chemistry, activation energy (\(E_a\)) is a crucial concept that defines the minimum amount of energy required for a reaction to occur. Think of it as the 'energy barrier' that reactants must overcome to transform into products. The magnitude of the activation energy has a direct influence on the reaction rate; the higher the activation energy, the slower the reaction will be because fewer molecules will have enough energy to react at any given time.

For instance, in the step-by-step solution provided for Case a, where \(E_{a}=25 \mathrm{~kJ/mol}\) is greater than the enthalpy change (\(\Delta E=+10 \mathrm{~kJ/mol}\)), we notice that despite the endothermic nature of the reaction (absorbing energy), the activation energy provides a barrier that must be surpassed. This concept is integral because it helps us understand why some reactions require the addition of heat or use of a catalyst to proceed at a reasonable rate.

A catalyst, by the way, is a substance that can lower the activation energy without being consumed in the reaction, thereby increasing the reaction rate. This also explains why we get rapid reactions when we use catalysts, as they 'smooth out' the hill that reactants need to climb over.

Enthalpy Change

Enthalpy change (\(\Delta E\) or \(\Delta H\)), another key term in thermodynamics, refers to the total heat content change of a system during a chemical reaction under constant pressure. It's a measure of the amount of energy released (exothermic reaction) or absorbed (endothermic reaction) by the reaction. The sign of \(\Delta E\)\ tells us whether the reaction emits (+) or absorbs (-) energy.

In our exercise solutions for Cases b and c, the negative \(\Delta E\)\ indicates that the energy of the system decreases as the reaction occurs, illustrating exothermic reactions where energy is released. However, even though both are exothermic, the extent of enthalpy change is different. A larger negative value, as seen in Case c (\(\Delta E = -50 \text{kJ/mol}\)), indicates more energy is released compared to Case b (\(\Delta E = -10 \text{kJ/mol}\)).

Understanding \(\Delta E\)\ is essential for predicting the heat flow and system behaviour. It allows chemists to estimate the warmth or coolness we feel during a reaction---warmth in exothermic reactions like when wood burns, or coolness in endothermic reactions like when an ice pack is activated.

Reaction Coordinate Diagram

A reaction coordinate diagram visualizes the energy changes that occur during a chemical reaction. It's a graphical representation mapping the progress of the reaction from reactants to products against the total potential energy of the system. The x-axis of the diagram typically represents the progress of the reaction, while the y-axis represents the potential energy.

For visual learners, this diagram effectively communicates the dynamics of a reaction. You'll typically see a curve that starts with the reactants' energy level, gains to the peak (the activation energy) and finally descends to the products' energy level. In cases with a positive enthalpy change, the curve ends higher than it starts; for a negative enthalpy change, it ends lower.

For example, in the step-by-step solutions for Cases a, b, and c, a reaction coordinate diagram helps us to visually compare the initial and final energy states and the different activation energies. This type of diagram is not just a way to visualize reactions, but it's a powerful tool that gives insights into kinetic and thermodynamic aspects of a chemical process, like the feasibility and the speed of the reaction.