Problem 61 - Chemistry: Principles and Reactions

Question

Consider the following hypothetical reaction: $$\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D} \quad \Delta H=-125 \mathrm{~kJ}$$ Draw a reaction-energy diagram for the reaction if its activation energy is \(37 \mathrm{~kJ} .\)

Step-by-Step Solution

Answer

Question: Draw a reaction-energy diagram for a hypothetical reaction with an activation energy of 37 kJ and an enthalpy change of -125 kJ/mol. Answer: The reaction-energy diagram is drawn with the energy-axis on the left, reactants (A+B) at an arbitrary 0 kJ, and products (C+D) at -125 kJ (due to the exothermic reaction). The curve connects the energy levels of the reactants and products, reaching a maximum point 37 kJ above the reactants (activation energy). The diagram should include labels for everything and indicators for activation energy (Ea) and enthalpy change (ΔH).

Step 1: Identify the reactants and products

In the given reaction, A and B are the reactants, and C and D are the products. We will represent the reactants' energy level arbitrarily because we are only concerned with the change in energy levels throughout the reaction.

Step 2: Determine the activation energy and enthalpy change

We are given the activation energy (\(E_a\)) as \(37 \mathrm{~kJ}\), and the enthalpy change (\(\Delta H\)) as \(-125 \mathrm{~kJ}\). Since \(\Delta H\) is negative, it means the reaction is exothermic and the final energy level of the products will be lower than that of the reactants.

Step 3: Draw the reaction-energy diagram

To draw the reaction-energy diagram, follow these steps: 1. Draw the vertical energy axis, with energy increasing upwards. 2. Mark an arbitrary energy level for the reactants (A + B), say at 0 kJ. 3. Mark the energy level for the products (C + D) 125 kJ lower than the reactants, as the enthalpy change is -125 kJ. 4. Draw a curve that starts from the reactants' energy level, rises to the maximum energy level (the activation energy, 37 kJ above reactants), and then goes down to the products' energy level. 5. Label the axis and the energy levels, and indicate the activation energy and enthalpy change on the diagram. Your reaction-energy diagram should look like this: - The energy-axis on the left. - A horizontal line representing reactants (A+B) at 0 kJ (arbitrary choice). - A horizontal line representing products (C+D) at -125 kJ (due to the exothermic reaction). - A curve connecting the reactants and products energy levels and reaching a maximum point 37 kJ above the reactants (activation energy). - Indicators for the activation energy \(E_a\) and the enthalpy change \(\Delta H\). Remember to label everything correctly. You have now successfully drawn a reaction-energy diagram for the given reaction.

Key Concepts

Activation Energy

Activation energy is essentially the 'spark' needed to start a chemical reaction. Imagine you're at the bottom of a hill with a bike; to get to the other side, you first need to pedal hard and reach the top before you can enjoy the effortless ride down. Similarly, for reactants to transform into products, they must overcome an initial energy barrier—this is the activation energy, symbolized as E_a in chemical equations.

In the context of the hypothetical reaction provided, A + B → C + D, we have an activation energy of 37 kJ. This number tells us how much energy is required to initiate the reaction. Without this amount of energy, the reactants would remain stable, and no reaction would occur. Chemical catalysts can lower the activation energy, much like having a boost halfway up the hill, making the reaction easier to start.

Enthalpy Change

Enthalpy change (ΔH) is a term that refers to the heat absorbed or released during a reaction. Like your bank balance after you've paid all your bills, it's the difference between the energy stored in the reactants and the energy stored in the products. A negative ΔH indicates that the reaction releases energy, whereas a positive ΔH means it absorbs energy.

In our exercise, the enthalpy change is -125 kJ. This negative sign is critical; it informs us that the reaction is like a battery powering a device, releasing energy as it proceeds. The products, C and D, have less energy than the reactants A and B, which means that the surroundings absorb the difference as heat—the fundamental cause of temperature increase in exothermic reactions such as this one.

Understanding ΔH is crucial because it helps us determine whether a reaction is energy-efficient and predict how it will affect its environment.

Exothermic Reaction

An exothermic reaction is like a warm campfire on a cold night; it gives off heat, making the surroundings cozier. Simply put, exothermic reactions release more energy than they consume. The products of these reactions are typically at a lower energy level than the reactants because they've given that energy away to the environment in the form of heat, light, sound, or another energy form.

Our hypothetical reaction, where A + B turns into C + D and releases 125 kJ of energy, is a textbook example of an exothermic reaction. Such reactions often occur spontaneously once initiated because the release of energy drives the reaction forward. In daily life, burning wood, metabolic processes in the body, and even rusting iron are all exothermic reactions. They are key to numerous applications, from powering engines to keeping us alive through cellular respiration.

Remembering that exothermic reactions result in a temperature rise can help us apply these concepts in practical situations, like choosing materials that won't react dangerously to heat during storage or manufacturing processes.