Problem 53 - Chemistry and Chemical Reactivity

Question

The standard enthalpy of formation of solid barium oxide, \(\mathrm{BaO},\) is \(-553.5 \mathrm{kJ} / \mathrm{mol},\) and the standard enthalpy of formation of barium peroxide, \(\mathrm{BaO}_{2},\) is \(-634.3 \mathrm{kJ} / \mathrm{mol}\) (a) Calculate the standard enthalpy change for the following reaction. Is the reaction exothermic or endothermic? \(2 \mathrm{BaO}_{2}(\mathrm{s}) \rightarrow 2 \mathrm{BaO}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g})\) (b) Draw an energy level diagram that shows the relationship between the enthalpy change of the decomposition of \(\mathrm{BaO}_{2}\) to \(\mathrm{BaO}\) and \(\mathrm{O}_{2}\) and the enthalpies of formation of \(\mathrm{BaO}(\mathrm{s})\) and \(\mathrm{BaO}_{2}(\mathrm{s})\)

Step-by-Step Solution

Answer

The reaction is endothermic with \(161.6 \, \mathrm{kJ}\) absorbed.

Step 1: Enthalpy Change for Reaction

To calculate the standard enthalpy change for the reaction, we need to apply Hess's Law. The reaction is \(2 \mathrm{BaO}_{2} (\mathrm{s}) \rightarrow 2 \mathrm{BaO} (\mathrm{s}) + \mathrm{O}_{2} (\mathrm{g})\). First, write down the standard enthalpy of formation for each compound: - \( \Delta H_f^\circ (\mathrm{BaO}_{2}) = -634.3 \, \mathrm{kJ/mol} \)- \( \Delta H_f^\circ (\mathrm{BaO}) = -553.5 \, \mathrm{kJ/mol} \)The standard enthalpy change for the reaction \( \Delta H_{\text{reaction}}^\circ \) is calculated by considering the difference in the formation enthalpies:\[ \Delta H_{\text{reaction}}^\circ = (2 \times \Delta H_f^\circ (\mathrm{BaO})) - (2 \times \Delta H_f^\circ (\mathrm{BaO}_{2})) \]\[ \Delta H_{\text{reaction}}^\circ = (2 \times -553.5) - (2 \times -634.3) \]\[ \Delta H_{\text{reaction}}^\circ = (-1107) - (-1268.6) \]\[ \Delta H_{\text{reaction}}^\circ = 161.6 \, \mathrm{kJ} \]

Step 2: Determine Reaction Type

Given that the enthalpy change \( \Delta H_{\text{reaction}}^\circ = 161.6 \, \mathrm{kJ} \), the reaction is endothermic because the enthalpy change is positive. An endothermic reaction absorbs energy from the surroundings.

Step 3: Draw Energy Level Diagram

An energy level diagram visually represents the energy changes in a reaction:- The axis labels should be 'Energy' (vertical) and 'Reaction Progress' (horizontal).- Start with \( \mathrm{BaO}_{2} \) higher on the energy scale since it is being decomposed, represented at an energy of \(-1268.6 \, \mathrm{kJ} \) for 2 moles.- Show \( \mathrm{BaO} \) at a lower energy level of \(-1107 \, \mathrm{kJ} \) for 2 moles.- Draw a line connecting these points indicating the energy change.- Show \( \mathrm{O}_{2} \) as an additional product.The energy absorbed is shown as the difference of \(161.6 \, \mathrm{kJ} \) between the starting energy of \( \mathrm{BaO}_{2} \) and the energy of the products, \( \mathrm{BaO} \) and \( \mathrm{O}_{2} \).

Key Concepts

Hess's Law

Hess's Law is a foundational principle in chemistry that helps us understand how energy changes occur in chemical reactions. It's based on the idea that the total enthalpy change for a chemical reaction is the same, no matter how many intermediate steps are taken. This principle implies that enthalpy, a measure of the total energy change in a system, is a state function.

This means the change in enthalpy only depends on the initial and final states of the system, not the path taken to get there.

• Hess's Law allows us to calculate difficult enthalpy changes indirectly by using known reactions and their enthalpy changes.
• We can add or subtract these enthalpy changes, much like algebraic equations, to find the enthalpy of the desired reaction.

In the exercise, Hess's Law helps calculate the enthalpy change for the decomposition of barium peroxide (\( \mathrm{BaO}_2 \)) into barium oxide (\( \mathrm{BaO} \)) and oxygen (\( \mathrm{O}_2 \)). By using the given formation enthalpies of the compounds, we apply Hess's Law to find the enthalpy change for the whole reaction. This ensures calculations are accurate and consistent, considering that we might not be able to measure it directly in a lab due to reaction conditions.

Endothermic Reaction

Endothermic reactions are fascinating because they absorb energy from their surroundings. This intake of energy usually appears as heat, and it can lead to a cooling effect in the surrounding environment. In an endothermic reaction, the products have more energy than the reactants because energy is taken in.

An easy way to identify an endothermic reaction is by the positive sign of the enthalpy change (\( \Delta H \)).

• Since the overall energy level of the system increases, the enthalpy change is positive.
• Think of melting ice. It takes in heat from the surroundings, turning solid into liquid, which is a classic endothermic process.

In our exercise, the reaction of converting barium peroxide to barium oxide and oxygen is endothermic.
This is because the calculated enthalpy change is \( 161.6 \, \mathrm{kJ} \), signifying that this amount of energy is absorbed by the reactants to form the products.
This is important because it helps us predict the conditions under which a reaction will occur naturally or will require external energy.

Energy Level Diagram

An energy level diagram is a useful tool in visualizing the energy changes that occur during a chemical reaction. It shows how the energy of reactants and products compares, and it also shows the overall energy change, \( \Delta H \), of the reaction.

Energy is represented on the vertical axis, and the reaction progress is shown on the horizontal axis. Understanding these diagrams helps students grasp abstract energy concepts more concretely.

• In the diagram, reactants are labeled on one side and products on the other, with lines indicating their relative energy levels.
• The change in energy is shown as an arrow between these lines.

For the exercise, we depict the \( \mathrm{BaO}_2 \) energy level higher than \( \mathrm{BaO} \) and \( \mathrm{O}_2 \), since it requires additional energy to decompose.
This layout represents the endothermic nature of the reaction.
The difference of \( 161.6 \, \mathrm{kJ} \) is shown in the diagram as the energy absorbed by the system.Such diagrams are not only informative but also visually engaging, aiding in a better understanding of enthalpy changes and the energetic nature of reactions.