Question

Consider the following hypothetical reactions: $$\begin{array}{ll}{\mathrm{A} \longrightarrow \mathrm{B}} & {\Delta H=+30 \mathrm{kJ}} \\ {\mathrm{B} \longrightarrow \mathrm{C}} & {\Delta H=+60 \mathrm{kJ}}\end{array}$$ (a) Use Hess's law to calculate the enthalpy change for the reaction \(A \longrightarrow C .\) (b) Construct an enthalpy diagram for substances \(A,\) and C, and show how Hess's law applies.

Short answer

(a) To calculate the enthalpy change for the reaction \(A \longrightarrow C\), use Hess's law: \(\Delta H_{Total} = \Delta H_1 + \Delta H_2 = (+30\, \text{kJ}) + (+60\, \text{kJ}) = +90\, \text{kJ}\). (b) In the enthalpy diagram, represent each reaction and its enthalpy change with arrows and label them accordingly: \(A \longrightarrow B\) with \(\Delta H_1=+30\, \text{kJ}\), \(B \longrightarrow C\) with \(\Delta H_2=+60\, \text{kJ}\), and \(A \longrightarrow C\) with \(\Delta H_{Total}=+90\, \text{kJ}\). The diagram shows Hess's law in action as the enthalpy change for the direct reaction \(A \longrightarrow C\) is equal to the sum of the enthalpy changes for the two hypothetical reactions.

Step-by-step solution

Analyze given reactions and enthalpy changes

The given reactions are: 1. \(A \longrightarrow B\), with enthalpy change \(\Delta H_1 = +30\, \text{kJ}\) 2. \(B \longrightarrow C\), with enthalpy change \(\Delta H_2 = +60\, \text{kJ}\) Our goal is to find the enthalpy change for the reaction \(A \longrightarrow C\).

Apply Hess's law

According to Hess's law, the enthalpy change of the desired reaction (\((A \longrightarrow C)\)) is equal to the sum of the enthalpy changes of the given reactions. So, \(\Delta H_{Total} = \Delta H_1 + \Delta H_2\) Substitute the given enthalpy changes: \(\Delta H_{Total} = (+30\, \text{kJ}) + (+60\, \text{kJ})\) \(\Delta H_{Total} = +90\, \text{kJ}\) Therefore, the enthalpy change for the reaction \(A \longrightarrow C\) is \(+90\, \text{kJ}\). #b) Construct an enthalpy diagram for substances A, and C#

Set up the enthalpy diagram

An enthalpy diagram is a graphical representation of the enthalpy changes in chemical reactions. It allows us to visualize how the enthalpy changes as the reactants transform into products. On the vertical axis, we will represent the enthalpy level (H). We start by showing substances \(A\), \(B\), and \(C\) on the horizontal axis.

Represent the reactions and their enthalpy changes on the diagram

Now, we will represent the given reactions and their enthalpy changes on the enthalpy diagram: 1. For the reaction \(A \longrightarrow B\), draw an arrow from \(A\) to \(B\) with a positive slope (since \(\Delta H_1 = +30\, \text{kJ}\) is an endothermic reaction). Label the arrow with \(\Delta H_1=+30\, \text{kJ}\). 2. For the reaction \(B \longrightarrow C\), draw an arrow from \(B\) to \(C\) with a positive slope (since \(\Delta H_2 = +60\, \text{kJ}\) is again an endothermic reaction). Label the arrow with \(\Delta H_2=+60\, \text{kJ}\). 3. To represent the overall reaction \(A \longrightarrow C\), draw an arrow directly from \(A\) to \(C\), skipping \(B\). According to Hess's law, the enthalpy change for this reaction will be equal to the sum of \(\Delta H_1\) and \(\Delta H_2\), calculated in part (a). Label the arrow with \(\Delta H_{Total}=+90\, \text{kJ}\). The enthalpy diagram shows the enthalpy changes for each given reaction and the overall reaction \(A \longrightarrow C\). It visually demonstrates how Hess's law applies: the enthalpy change for the direct reaction \(A \longrightarrow C\) is equal to the sum of the enthalpy changes for the two hypothetical reactions.

Key concepts

Enthalpy Change

In chemical reactions, the enthalpy change, denoted by \( \Delta H \), represents the heat absorbed or released. It is measured in kilojoules (kJ) per mole. When analyzing reactions, we often want to know how the energy shifts. For example, consider the reaction \( A \rightarrow B \). Here, the enthalpy change is \( +30 \text{kJ} \), meaning the system absorbs 30 kJ of heat. Similarly, \( B \rightarrow C \) has an enthalpy change of \( +60 \text{kJ} \).

By using Hess's Law, we can determine the overall enthalpy change for a series of reactions. Hess's Law states that the total enthalpy change for a reaction is the same regardless of the pathway taken. This means we can add up the enthalpy changes from steps to find the overall change from \( A \rightarrow C \). Hence, \( \Delta H_{Total} = +30 \text{kJ} + 60 \text{kJ} = +90 \text{kJ} \).

Understanding enthalpy changes is crucial, as it tells us whether heat is absorbed or released during a reaction. This helps predict feasibility and conditions needed for reactions to occur.

Endothermic Reaction

An endothermic reaction is a chemical process where the system absorbs energy from its surroundings, usually in the form of heat. This absorption results in a positive enthalpy change, which is why in our reactions \( A \rightarrow B \) and \( B \rightarrow C \), \( \Delta H = +30 \text{kJ} \) and \( +60 \text{kJ} \) respectively.

Why is it important to know if a reaction is endothermic? For one, it determines how we might need to supply energy for the reaction to proceed. During an endothermic process, energy is needed to break bonds in the reactants. This energy intake often makes the surrounding area feel colder. For instance:

• Endothermic reactions often require heat input, such as in reactions within a refrigerator where heat is absorbed.
• These reactions are typically less spontaneous at low temperatures and may need thermal input to continue.

Recognizing endothermic reactions helps us plan how to control and manage thermal conditions in practical and laboratory settings.

Enthalpy Diagram

An enthalpy diagram is a graphical tool used to visualize the enthalpy changes of reactions. It shows energy changes as the reactants transform into products. In our scenario, this diagram provides a clear illustration of how enthalpy changes from \( A \rightarrow B \rightarrow C \), then directly \( A \rightarrow C \).

On an enthalpy diagram:

• The vertical axis depicts enthalpy levels, indicating the relative energy of substances involved.
• Start with substance \( A \) at a lower energy level than \( B \), with an upward arrow showing \( \Delta H_1 = +30 \text{kJ} \), indicating the absorption of heat.
• Similarly, an upward arrow represents the transition from \( B \) to \( C \), reflecting \( \Delta H_2 = +60 \text{kJ} \).
• Finally, a direct arrow from \( A \) to \( C \) illustrates the total enthalpy change, \( +90 \text{kJ} \), showing how the system's energy increases.

The overall reaction path depicted by enthalpy diagrams clearly shows Hess's Law in action, reaffirming that the direct path energy change equals the sum of individual steps. This graphical representation makes it easier to identify and understand energy transformations in a chemical reaction.