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 \(\mathrm{A} \longrightarrow\) C. (b) Construct an enthalpy diagram for substances \(A, B,\) and \(C,\) and show how Hess's law applies.

Short answer

(a) Using Hess's law, we find the enthalpy change for the reaction A → C is +90 kJ. (b) The enthalpy diagram shows the energy levels of A, B, and C, with B being 30 kJ above A and C being 60 kJ above B. The diagram visualizes how the sum of the individual enthalpy changes for A → B and B → C equals the total enthalpy change for A → C, which confirms our calculated value of +90 kJ.

Step-by-step solution

Identify the enthalpy changes for each step

The given enthalpy changes are: A → B: ΔH = +30 kJ B → C: ΔH = +60 kJ

Apply Hess's law

Hess's law states that the total enthalpy change for the reaction is the sum of the enthalpy changes for the individual steps. Therefore, we can calculate the enthalpy change for A → C by adding the enthalpy changes for A → B and B → C: ΔH(A → C) = ΔH(A → B) + ΔH(B → C) Substitute the given values: ΔH(A → C) = +30 kJ + 60 kJ

Calculate the enthalpy change for A → C

Add the values together: ΔH(A → C) = 90 kJ This means that the enthalpy change for the reaction A → C is +90 kJ. #b) Construct an enthalpy diagram for substances A, B, and C#

Draw the energy levels for A, B, and C

On the y-axis, represent the energy levels of A, B, and C. The energy level of B is 30 kJ above A (due to the enthalpy change of +30 kJ for A → B), and the energy level of C is 60 kJ above B (due to the enthalpy change of +60 kJ for B → C).

Draw the reaction pathways

Draw arrows to represent the reactions A → B and B → C, with the enthalpy changes written next to each arrow. The reaction A → C can be represented by a single arrow connecting A and C directly or by showing how the two separate steps add up to the overall reaction pathway.

Apply Hess's law to the enthalpy diagram

The enthalpy diagram visualizes Hess's law by showing the sum of the individual enthalpy changes for A → B and B → C equaling the total enthalpy change for A → C, which we calculated as +90 kJ. The completed enthalpy diagram should help visualize how Hess's law applies to this problem, confirming our calculated value.

Key concepts

Enthalpy Change

Enthalpy change, denoted as ΔH, is a measure of the heat energy absorbed or released during a chemical reaction at constant pressure. This concept is essential in thermodynamics and chemistry as it helps predict the energy changes involved in reactions.
Hess's Law is based on the principle that enthalpy is a state function. This means that the total change in enthalpy for a chemical process depends only on the initial and final states, not on the path taken to get there.
In the provided exercise example, two steps are given:

• A → B with ΔH = +30 kJ
• B → C with ΔH = +60 kJ

To find the enthalpy change for the overall process (A → C), we add these changes together. Thus, ΔH for A → C is +90 kJ. This shows that the process requires an input of 90 kJ of energy to proceed from A to C.

Hypothetical Reactions

Hypothetical reactions are idealized steps used to simplify complex processes for easier calculation and understanding. They allow us to break down reactions into simpler parts, which can then be analyzed more effectively using concepts like Hess's Law.
In the example provided, the reactions A → B and B → C are hypothetical reactions. They are tools for applying Hess's Law, which helps in understanding how enthalpy is conserved over these steps.
When dealing with hypothetical reactions, it's crucial to

• Clearly identify individual steps and their enthalpy changes
• Consider the overall reaction as a combination of these steps
• Apply proper calculations using the given data

Thus, in practice, even for parts of a system that we cannot observe directly, we can understand the total energy change by understanding each individual hypothetical reaction involved.

Enthalpy Diagram

An enthalpy diagram is a graphical representation used to visualize the enthalpy changes in chemical reactions. This helps in understanding how energy is transferred and transformed during a reaction.
In an enthalpy diagram, energy levels of different substances are plotted on the y-axis while the reaction pathways are illustrated with arrows.
For the reactions in the exercise:

• Start with substance A at a baseline
• Show B 30 kJ above A due to the enthalpy change
• Place C 60 kJ above B, indicating the further enthalpy change

These placements construct a stepped path that visually describes the process according to Hess's Law: the overall change from A to C (+90 kJ) can either be split into these steps or represented directly. This visualization confirms the calculated overall enthalpy change and demonstrates how individual reactions contribute to the total energy transformation.