Problem 62 - Chemistry: The Central Science in SI Units, Global Edition

Question

Consider the following hypothetical reactions: $$ \begin{array}{l} \mathrm{A} \longrightarrow \mathrm{B} \quad \Delta H_{I}=+60 \mathrm{~kJ} \\ \mathrm{~B} \longrightarrow \mathrm{C} \quad \Delta H_{I I}=-90 \mathrm{~kJ} \end{array} $$ (a) Use Hess's law to calculate the enthalpy change for the reaction \(\mathrm{A} \longrightarrow \mathrm{C}\). (b) Construct an enthalpy diagram for substances A, B, and C, and show how Hess's law applies.

Step-by-Step Solution

Answer

(a) Using Hess's law, we calculate the enthalpy change for the reaction A -> C as follows: ΔH_total = ΔH_I + ΔH_II = (+60 kJ) + (-90 kJ) = -30 kJ. (b) To construct an enthalpy diagram, draw horizontal lines for substances A, B, and C. Show ΔH_I as an upward vertical line from A to B, and ΔH_II as a downward vertical line from B to C. The overall enthalpy change A -> C is represented as a diagonal line, demonstrating Hess's law, which states that enthalpy change depends only on the initial and final states, not on the specific pathway or intermediate steps.

Step 1: Understand Hess's law

Hess's law states that the total enthalpy change of a reaction is the same, whether it occurs in one step or several steps.

Step 2: Apply Hess's law to the given reactions

We want to find the enthalpy change for the overall reaction A → C. We can obtain this overall reaction by adding the given reactions together: A → B (ΔH_I = +60 kJ) B → C (ΔH_II = -90 kJ) ----------------------- A → C Now we'll add the enthalpy changes for each step: ΔH_total = ΔH_I + ΔH_II

Step 3: Calculate the enthalpy change

Using the given values for ΔH_I and ΔH_II, we can calculate the total enthalpy change: ΔH_total = (+60 kJ) + (-90 kJ) = -30 kJ So, the enthalpy change for the reaction A → C is -30 kJ. (b) Constructing an enthalpy diagram for substances A, B, and C and showing how Hess's law applies

Step 4: Draw the enthalpy diagram

In the enthalpy diagram, we'll represent the enthalpy changes as vertical lines, with positive ΔH values going upwards and negative ΔH values going downwards. 1. Start by drawing a horizontal line for substance A. 2. Draw an upward vertical line for ΔH_I = +60 kJ from A, and label the endpoint as substance B. 3. From B, draw a downward vertical line for ΔH_II = -90 kJ, and label the endpoint as substance C. 4. Now, draw a direct path from substance A to substance C using a diagonal line, representing the overall reaction and the calculated ΔH_total = -30 kJ.

Step 5: Explain Hess's law in the context of the diagram

The enthalpy diagram shows that the overall enthalpy change for the reaction A → C has the same value whether it goes through the intermediate B or directly from A to C. This demonstrates Hess's law, i.e., the overall enthalpy change of a reaction depends only on the initial and final states, not on the specific pathway or intermediate steps.

Key Concepts

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is a crucial concept in chemistry that helps describe the energy transferred in a chemical reaction. It is the difference between the enthalpy of products and the enthalpy of reactants. An enthalpy change can be either positive or negative.
If \( \Delta H \) is positive, the reaction is endothermic, meaning it absorbs energy from its surroundings. This occurs when the products have more enthalpy than the reactants.
On the other hand, a negative \( \Delta H \) indicates an exothermic reaction, in which energy is released into the surroundings, and products possess less enthalpy compared to reactants.
In the example given in the original exercise, the stepwise reactions \( \mathrm{A} \rightarrow \mathrm{B} \) and \( \mathrm{B} \rightarrow \mathrm{C} \) have enthalpy changes of +60 kJ and -90 kJ, respectively. Through Hess's Law, we combined these enthalpy changes to find the overall enthalpy change for the reaction \( \mathrm{A} \rightarrow \mathrm{C} \), which is -30 kJ, indicating an exothermic process.

Enthalpy Diagram

An enthalpy diagram is a visual representation that illustrates the changes in enthalpy during a chemical reaction. This diagram helps students and chemists to see how energy is absorbed or released as a reaction progresses from reactants to products.
The vertical axis of the diagram represents enthalpy levels, while the horizontal axis often indicates the progression of the reaction. In an enthalpy diagram:

• Upward vertical lines illustrate increases in enthalpy (endothermic changes).
• Downward vertical lines represent decreases in enthalpy (exothermic changes).

For the example provided, the enthalpy diagram begins with substance A at the baseline, followed by an upward vertical line of +60 kJ reaching substance B, then a downward line of -90 kJ reaching substance C.
This setup effectively demonstrates the enthalpy changes for each step, and the direct path connecting A to C (with enthalpy change -30 kJ) displays the result of Hess's Law. It shows that the total enthalpy change from A to C is the same, regardless of whether it proceeds through B or not.

Hypothetical Reactions

Hypothetical reactions, like those shown in the exercise, are conceptual scenarios that illustrate fundamental principles in chemistry. Although they do not occur in reality, these reactions help us understand complex concepts through simplified examples.
They allow us to apply abstract principles, such as Hess's Law, without the confusion of real-world variations. Hypothetical reactions often include imaginary substances or exaggerated enthalpy changes, chosen to highlight specific scientific ideas.
In the exercise, the hypothetical reactions \( \mathrm{A} \rightarrow \mathrm{B} \) and \( \mathrm{B} \rightarrow \mathrm{C} \), with specified \( \Delta H \) values, help visualize and calculate the overall enthalpy change when transforming from A to C.
This kind of analysis is critical for grasping core chemistry concepts and applying them to various situations in theoretical and practical scenarios.