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Chapter 5: Problem 62

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.

Short Answer

Expert verified
(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 by step solution

01

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.
02

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
03

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
04

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.
05

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.

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