Problem 12 - Chemistry The Central Science In Si Units

Question

Consider the conversion of compound A into compound B: \(\mathrm{A} \longrightarrow \mathrm{B}\). For both compounds \(\mathrm{A}\) and \(\mathrm{B}\), \(\Delta H_{f}{\underline{\phantom{xx}}}^{\circ}>0 .\) (a) Sketch an enthalpy diagram for the reaction that is analogous to Figure 5.23 . (b) Suppose the overall reaction is exothermic. What can you conclude? [Section 5.7]

Step-by-Step Solution

Answer

The enthalpy diagram shows B lower than A, indicating energy release. Since the reaction is exothermic, \(H_f^\circ(B) < H_f^\circ(A)\).

Step 1: Understand the Problem

The reaction involves converting compound A to compound B, and both have positive standard enthalpies of formation \(\Delta H_f^\circ > 0\). We need to sketch an enthalpy diagram and determine the implications of the reaction being exothermic.

Step 2: Draw the Enthalpy Diagram

Since both \(\Delta H_{f}{\underline{\phantom{xx}}}^{\circ}\) values are greater than zero, start by placing compound A at a higher enthalpy level than compound B in the diagram. The difference in height between A and B represents the enthalpy change of the reaction \(\Delta H_{reaction}\). If the reaction is exothermic, \(\Delta H_{reaction}\) should be negative.

Step 3: Interpret the Diagram

In an exothermic reaction, the system releases heat, meaning the final enthalpy of product B is lower than the initial enthalpy of reactant A. Therefore, draw B at a lower enthalpy level than A to indicate that energy is released in the reaction.

Step 4: Conclude from the Diagram

If the reaction from A to B is exothermic, even though both compounds have positive enthalpies of formation, \(\Delta H = H_f^\circ(B) - H_f^\circ(A)\) must be negative. This implies \(H_f^\circ(B) < H_f^\circ(A)\).

Key Concepts

Enthalpy Diagram

An enthalpy diagram visually represents the energy changes during a chemical reaction. It helps to understand how the energy of the system transforms when reactants convert into products. In an enthalpy diagram:

• The vertical axis represents enthalpy, denoted by the symbol **H**.
• Reactants begin at a certain energy level, while products end at another.
• Arrows or lines connect these levels, clearly showing the enthalpy change (**ΔH**).

In the case of the reaction \(\mathrm{A} \longrightarrow \mathrm{B}\), when both compounds A and B have positive standard enthalpies of formation (\(\Delta H_{f}^\circ > 0\)), you start by placing A at a higher energy level. If the reaction is exothermic, compound B will be at a lower enthalpy level than A. The marking of this difference highlights that energy is released as the system transitions from A to B. This drop signifies the exothermic nature of the transformation.

Enthalpy of Formation

The enthalpy of formation, denoted by \(\Delta H_{f}^{\circ}\), is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a fundamental thermodynamic quantity and:

• Expressed in units of energy per mole, such as kilojoules per mole (kJ/mol).
• Represents the energy changes for forming a compound from elemental substances.

For the conversion \(\mathrm{A} \longrightarrow \mathrm{B}\), both A and B have positive enthalpies of formation. This means energy is required to form both A and B from their elements. The overall reaction from A to B can still be exothermic if \(\Delta H_{f}^{\circ}(B)\) is less than \(\Delta H_{f}^{\circ}(A)\). This indicates that while energy is needed to form each, the transition from A to B releases more energy than is required to maintain either. Thus, the decrease in enthalpy for B from A's perspective leads to the net release of energy.

Exothermic Reaction

An exothermic reaction is characterized by the release of energy, usually in the form of heat. It occurs when the total energy required to break bonds in the reactants is less than the energy released as new bonds form in the products. Here’s what happens in an exothermic reaction:

• The reactants lose energy, resulting in lower enthalpy products.
• Energy released into the surroundings often increases temperature, felt as heat.
• Exothermic reactions have a negative enthalpy change (\(\Delta H < 0\)).

In the scenario of \(\mathrm{A} \longrightarrow \mathrm{B}\):

• Although both A and B have positive enthalpies of formation, the transition is exothermic if \(\Delta H_{reaction}\) is negative.
• This confirms that \(H_{f}^{\circ}(B)\) is smaller than \(H_{f}^{\circ}(A)\), ensuring that energy release outweighs any initial input required to create the compounds.

Thus, the reaction not only transforms A into B but also liberates heat, underlining the exothermic nature.